Gaussian 16 Users Reference

09 November 2017. [G16 Rev. B.01]

Compiled by Zork on July 20, 2018

Copyright ⃝
c 2017 Roger Young for the LATEX book template.

Derived from the material at http://gaussian.com/man/ which is copyright ⃝

c Gaussian, Inc.

Documented in LATEX& compiled using XELATEX & Biber integrated in TEXLive 2018.
 Contents

I Part One

1 Gaussian 16 Citation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Additional Citation Recommendations 4

2 Gaussian 16 Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Model Chemistries 5
2.2 Job Types 6
2.2.1 Molecular Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Program Limits 8

2.4 Links 8

3 About Gaussian 16 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1 Syntax 11
3.1.1 Syntax Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Molecule Specifications 13

3.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2.2 Nuclei Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2.3 Fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.4 MM Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.5 PDB Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.6 Ghost Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.7 Periodic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Basis Sets 17
3.3.1 Issues Arising from Pure vs. Cartesian Basis Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3.2 Density Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.4 Constructing Z-Matrices 23

3.4.1 Dummy Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.2 Model Builder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.5 Multistep Jobs 28

3.6 Section Ordering 29

4 Running Gaussian 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1 Preliminaries 31
4.1.1 System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.2 Configuring the Gaussian Execution Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.3 Initialization Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.4 Environment Variables Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Running under UNIX 32

4.2.1 Scripts and Gaussian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2.2 Batch Execution with NQS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.3 Scratch Files 34

4.3.1 Splitting Scratch Files Across Disks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3.2 Saving and Deleting Scratch Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.4 Memory Use 36

4.5 Parallel Jobs 37
4.5.1 Shared-Memory Multiprocessor Parallel Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.5.2 Cluster/Network Parallel Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.5.3 Combining Shared-Memory and Network/Cluster Parallelism . . . . . . . . . . . . . . . . . . . . . . . 38
4.5.4 Starting and Monitoring Parallel Gaussian 16 Jobs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.6 Using GPUs 39

4.6.1 Allocating Memory for Jobs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.6.2 About Control CPUs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.6.3 Specifying GPUs & Control CPUs for a Gaussian Job . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.6.4 GPUs and Overall Job Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.6.5 GPUs in a Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.7 g16 Command Line Options 41

4.8 Setting Defaults 42
4.9 The Default.Route File 43
4.9.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.9.2 Parallel Job Directives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.9.3 formchk Directives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.9.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.9.5 Directive List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.10 Running Gaussian Test Jobs 47

II Part Two

5 List of Gaussian Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.1 Link 0 Commands 52
5.1.1 Parallel Job Directives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.2 # 55
5.2.1 Alternate Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.3 ADMP 55
5.3.1 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3.2 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.3 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.4 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.3.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.4 BD 59
5.4.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.4.2 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.4.3 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.4.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.5 BOMD 61
5.5.1 Required Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.5.2 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.5.3 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.5.4 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.5.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.6 CacheSize 67
5.6.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.7 CASSCF 68
5.7.1 Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.7.2 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.7.3 Availability and Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.7.4 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.7.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.8 CBS Methods 76

5.8.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.8.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.8.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.9 CBSExtrapolate 78
5.9.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.9.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.9.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.10 CCD and CCSD 79

5.10.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.10.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.10.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.10.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.11 Charge 81
5.11.1 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.11.2 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.11.3 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.11.4 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.11.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.12 ChkBasis 82
5.12.1 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.12.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.13 CID and CISD 82

5.13.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.13.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.13.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.13.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.14 CIS 83
5.14.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.14.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.14.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.14.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.15 CNDO 87
5.15.1 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.15.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.16 Complex 87
5.16.1 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.16.2 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.17 Constants 88
5.17.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.17.2 Current Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.18 Counterpoise 89
5.18.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.18.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.18.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.19 CPHF 90
5.19.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.19.2 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.20 Density 92
5.20.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.20.2 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.20.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.21 DensityFit and NoDensityFit 94

5.21.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.21.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.21.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.22 DFT (Density Functional Theory) Methods 95

5.22.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.22.2 Keywords: Hybrid Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.22.3 Keyword: Pure Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.22.4 Empirical Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.22.5 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.22.6 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.22.7 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.23 DFTB and DFTBA 103

5.23.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.23.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.23.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.23.4 Modifying Slater-Koster Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.24 EET 105

5.24.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.24.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.25 EOMCCSD 107

5.25.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.25.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.25.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.25.4 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.26 EPT 110

5.26.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.26.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.26.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.27 External 112

5.27.1 Script Invocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.27.2 File Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.27.3 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.27.4 Related Info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.27.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

5.28 ExtraBasis & ExtraDensityBasis 115

5.28.1 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.28.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

5.29 Field 117

5.29.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.29.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.29.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.29.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.30 FMM 119

5.30.1 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

5.31 Force 119

5.31.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.31.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.31.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

5.32 Freq 121

5.32.1 Calculation Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.32.2 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.32.3 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.32.4 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.32.5 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.32.6 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.32.7 ReadAnharm Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.32.8 ReadFCHT Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

5.33 G09Defaults 153

5.33.1 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

5.34 Gen and GenECP 153

5.34.1 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.34.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.34.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
5.34.4 Basis Function Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

5.35 GenChk 159

5.35.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

5.36 Geom 160

5.36.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
5.36.2 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
5.36.3 GIC Info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

5.37 GFInput 173

5.37.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
5.37.2 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
5.38 GFPrint 174
5.38.1 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

5.39 Gn Methods 174

5.39.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
5.39.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

5.40 Guess 177

5.40.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5.40.2 Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
5.40.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
5.40.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

5.41 GVB 187

5.41.1 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
5.41.2 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
5.41.3 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
5.41.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

5.42 HF 189
5.42.1 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
5.42.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

5.43 Huckel 190

5.43.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
5.43.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
5.43.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
5.43.4 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

5.44 INDO 191

5.44.1 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
5.44.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

5.45 Integral 191

5.45.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
5.45.2 Relativistic Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
5.45.3 Related Keyword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

5.46 IOp 194

5.47 IRC 194
5.47.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
5.47.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
5.47.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
5.47.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

5.48 IRCMax 199

5.48.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
5.48.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
5.48.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
5.48.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

5.49 LSDA 201

5.50 MaxDisk 202
5.51 MINDO3 202
5.51.1 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
5.51.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

5.52 MNDO 202

5.52.1 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
5.52.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

5.53 MM (Molecular Mechanics) Methods 203

5.53.1 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
5.53.2 Atom Types & Charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
5.53.3 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
5.53.4 MM Potential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
5.53.5 Specifying Force Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
5.53.6 Force Field Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

5.54 MP Methods 226

5.54.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
5.54.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
5.54.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
5.54.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

5.55 Name 228

5.55.1 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

5.56 NMR 228

5.56.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
5.56.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
5.56.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

5.57 ONIOM 231

5.57.1 Required Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
5.57.2 Per-layer Charge and Spin Multiplicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
5.57.3 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
5.57.4 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
5.57.5 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
5.57.6 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

5.58 Optimization 237

5.58.1 Set Opt. Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
5.58.2 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
5.58.3 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
5.58.4 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
5.58.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
5.58.6 GIC Info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
5.59 Output 263
5.59.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
5.59.2 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

5.60 PBC 264

5.60.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
5.60.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
5.60.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

5.61 Polar 266

5.61.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
5.61.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
5.61.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
5.61.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

5.62 Population 270

5.62.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
5.62.2 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
5.62.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

5.63 Pressure 277

5.63.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

5.64 Prop 277

5.64.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
5.64.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
5.64.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

5.65 Pseudo 279

5.65.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
5.65.2 Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
5.65.3 Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
5.65.4 SD ECP Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
5.65.5 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
5.65.6 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

5.66 Punch 285

5.66.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
5.66.2 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

5.67 QCI 285

5.67.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
5.67.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
5.67.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
5.67.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

5.68 Restart 287

5.68.1 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
5.68.2 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
5.68.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
5.69 SAC-CI 288
5.69.1 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
5.69.2 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
5.69.3 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
5.69.4 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
5.69.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

5.70 Scale 294

5.70.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

5.71 Scan 294

5.71.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
5.71.2 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
5.71.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

5.72 SCF 295

5.72.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

5.73 SCRF 299

5.73.1 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
5.73.2 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
5.73.3 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
5.73.4 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
5.73.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
5.73.6 Additional Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
5.73.7 Solvents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314

5.74 Semi-Empirical Methods 315

5.74.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
5.74.2 Specifying Semi-Empirical Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
5.74.3 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
5.74.4 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
5.74.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

5.75 SP 321
5.75.1 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
5.75.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

5.76 Sparse 322

5.76.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322

5.77 Stable 322

5.77.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
5.77.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
5.77.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

5.78 Symmetry 324

5.78.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
5.78.2 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
5.79 TD 325
5.79.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
5.79.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
5.79.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
5.79.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

5.80 Temperature 328

5.80.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

5.81 Test 328

5.82 TestMO 328
5.83 TrackIO 328
5.83.1 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

5.84 Transformation 328

5.84.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

5.85 Units 329

5.85.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
5.85.2 Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

5.86 Volume 330

5.86.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
5.86.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
5.86.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330

5.87 W1 Methods 330

5.87.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
5.87.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

5.88 Window Keyword and Frozen Core Options 332

5.88.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

5.89 ZIndo 334

5.89.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
5.89.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
5.89.3 Related Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

6 Utility Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

6.1 c8616 336
6.2 chkchk 336
6.3 cubegen 338
6.3.1 Output File Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
6.3.2 Reading Cube Files with Fortran Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

6.4 cubman 340

6.5 Example 341
6.6 formchk 342
6.6.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

6.7 freqchk 344

6.7.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
6.7.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

6.8 freqmem 347

6.8.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

6.9 gauopt 348

6.9.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348

6.10 ghelp 349

6.11 mm 349
6.11.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350

6.12 newzmat 350

6.12.1 Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
6.12.2 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
6.12.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

6.13 testrt 356

6.13.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

6.14 unfchk 357

6.14.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

III Part Three: Appendix

A Program Development Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

A.1 Keywords 361
A.1.1 General Job Restart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
A.1.2 IOp Setting Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

A.2 Options 362

A.2.1 Changing Link Invocation and Ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

A.3 The Standard Orientation 365

A.3.1 Selection Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
A.3.2 General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
A.3.3 Rules for Positioning an Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
A.3.4 Rules for Positioning Principal Axes of Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
A.3.5 Special Rules for Symmetric Top Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
A.3.6 Special Rules for Spherical Top Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367

A.4 Non-Standard Routes 367

A.5 RWF Numbers 371
B Obsolete Keywords and Deprecated Features . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
B.1 Obsolete 379
B.2 Deprecated 380

C Gaussian 16 Release Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

C.1 New Features 385
C.1.1 New Modeling Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
C.1.2 Performance Enhancements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
C.1.3 Usage Enhancements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

C.2 Functional Changes 387

C.2.1 Changes from Gaussian 16 Rev. A.03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
C.2.2 Changes from Gaussian 09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

C.3 Using GPUs 387

C.4 Parallel Usage and Performance Notes 387
C.4.1 Shared-memory parallelism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
C.4.2 Cluster (Linda) parallelism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

C.5 CCSD Performance 389

C.5.1 Memory requirements for CCSD, CCSD(T) and EOM-CCSD calculations . . . . . . . . . . . . . . 389

C.6 Equivalencies 389

C.7 Bugs Fixed 391

D Gaussian 16W Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

E Interfacing to Gaussian 16 (v2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

E.1 Introduction 395
E.2 Description 396
E.2.1 Goals for a General Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396
E.2.2 Structure of the General Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
E.2.3 About the Interface Libraries and Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
E.2.4 Generating Interface Data Files in Gaussian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
E.2.5 Using Data Files as Input to Gaussian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
E.2.6 Running Gaussian from within other programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

E.3 Matrix Element File 399

E.3.1 Labeled Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
E.3.2 Gaussian Scalars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

E.4 FChk File 406

E.4.1 Formatted Checkpoint File FAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410

E.5 Example FChk File 410

E.6 License 411
E.7 Download 411
E.8 Release History 411

F Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
F.1 Gaussian 16 Documentation 413
F.2 GaussView 6 Help Documentation 413
F.3 Installation Instructions 413
F.4 Linda Documentation 414
F.5 White Papers and Technical Notes 414
F.6 Historical Documents 414

G Gaussian 16 FAQs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
I
Part One

1 Gaussian 16 Citation . . . . . . . . . . . . . . . . . . 3

2 Gaussian 16 Capabilities . . . . . . . . . . . . . . 5

3 About Gaussian 16 Input . . . . . . . . . . . . . 11

4 Running Gaussian 16 . . . . . . . . . . . . . . . . 31
 1. Gaussian 16 Citation

Gaussian 16 represents further development of the Gaussian 70, Gaussian 76, Gaussian 80, Gaussian 82,
Gaussian 86, Gaussian 88, Gaussian 90, Gaussian 92, Gaussian 92/DFT, Gaussian 94, Gaussian 98, Gaussian
03 and Gaussian 09 systems previously published [1–13]. The current required citation for this work is given
below; note that you should replace Revision B.01 with the identifier for the revision of the program that you
actually use.

Normal Name Order :

Gaussian 16, Revision B.01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R.
Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. V. Marenich,
J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J.
L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T.
Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara,
K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven,
K. Throssell, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. J. Bearpark, J. J. Heyd, E. N. Brothers,
K. N. Kudin, V. N. Staroverov, T. A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. P. Rendell,
J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J.
W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman, and D. J. Fox, Gaussian, Inc.,
Wallingford CT, 2016.
Last Name First :
Gaussian 16, Revision B.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M.
A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; Li, X.; Caricato, M.;
Marenich, A. V.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V.;
Izmaylov, A. F.; Sonnenberg, J. L.; Williams-Young, D.; Ding, F.; Lipparini, F.; Egidi, F.; Goings, J.;
Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.;
Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda,
Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.;
 4 Chapter 1. Gaussian 16 Citation

Bearpark, M. J.; Heyd, J. J.; Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Keith, T. A.; Kobayashi,
R.; Normand, J.; Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.;
Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.;
Farkas, O.; Foresman, J. B.; Fox, D. J. Gaussian, Inc., Wallingford CT, 2016.
BibTex Starting Point :
@misc{g16,
author={M. J. Frisch and G. W. Trucks and H. B. Schlegel and G. E. Scuseria
and M. A. Robb and J. R. Cheeseman and G. Scalmani and V. Barone and G.
A. Petersson and H. Nakatsuji and X. Li and M. Caricato and A. V.
Marenich and J. Bloino and B. G. Janesko and R. Gomperts and B. Mennucci
and H. P. Hratchian and J. V. Ortiz and A. F. Izmaylov and J. L.
Sonnenberg and D. Williams-Young and F. Ding and F. Lipparini and F.
Egidi and J. Goings and B. Peng and A. Petrone and T. Henderson and D.
Ranasinghe and V. G. Zakrzewski and J. Gao and N. Rega and G. Zheng and
W. Liang and M. Hada and M. Ehara and K. Toyota and R. Fukuda and J.
Hasegawa and M. Ishida and T. Nakajima and Y. Honda and O. Kitao and H.
Nakai and T. Vreven and K. Throssell and Montgomery, {Jr.}, J. A. and J.
E. Peralta and F. Ogliaro and M. J. Bearpark and J. J. Heyd and E. N.
Brothers and K. N. Kudin and V. N. Staroverov and T. A. Keith and R.
Kobayashi and J. Normand and K. Raghavachari and A. P. Rendell and J. C.
Burant and S. S. Iyengar and J. Tomasi and M. Cossi and J. M. Millam
and M. Klene and C. Adamo and R. Cammi and J. W. Ochterski and R. L.
Martin and K. Morokuma and O. Farkas and J. B. Foresman and D. J. Fox},
title={Gaussian~16 {R}evision {B}.01},
year={2016},
note={Gaussian Inc. Wallingford CT}
}

EndNote/Papers Import File :

Clicking on the following link will have variable results, depending on your browser and system config-
uration. Right click to download the file (save with extension .enw): http://gaussian.com/dl/
g16_b01.enw

1.1 Additional Citation Recommendations

In general, we recommend citing the original references describing the theoretical methods used when
reporting results obtained from Gaussian calculations, as well as giving the citation for the program itself.
These references are given in the discussions of the relevant keywords. The only exceptions occur with long
established methods such as Hartree-Fock theory which have advanced to the state of common practice and are
essentially self-citing at this point.
In some cases, Gaussian output will display the references relevant to the current calculation type.
Gaussian also includes the NBO program as link 607. If this program is used, it should be cited separately
as:
NBO Version 3.1, E. D. Glendening, A. E. Reed, J. E. Carpenter, and F. Weinhold.
The original literature references for NBO can also be cited [14–21].
 2. Gaussian 16 Capabilities

2.1 Model Chemistries

The combination of method and basis set specifies a model chemistry to Gaussian, specifying the level of
theory. Every Gaussian job must specify both a method and basis set. This is usually accomplished via two
separate keywords within the route section of the input file, although a few method keywords imply a choice of
basis set. Some jobs using a density functional method may also include a density fitting set (see Basis Sets for
more information).
The following table lists methods which are available in Gaussian, along with the job types for which each
one may be used. An asterisk indicates analytic calculations, while numerical-only calculations are indicated
by num (see the discussion of the specific keyword in question for details).
 6 Chapter 2. Gaussian 16 Capabilities

If no method keyword is specified, HF is assumed. Most method keywords may be prefaced by R for
closed-shell restricted wavefunctions, U for unrestricted open-shell wavefunctions, or RO for restricted open-
shell wavefunctions: for example, ROHF, UMP2, or RQCISD. RO is available only for Hartree-Fock and
Density Functional methods, and AM1, PM3, PM3MM, PM6, and PDDG energies and gradients, and MP2,
MP3, MP4, and CCSD energies.
In general, only a single method keyword should be specified, and including more than one of them will
produce bizarre results. However, there are exceptions:
♢ CASSCF may be specified along with MP2 to request a CASSCF calculation including dynamic electron
correlation.
♢ ONIOM and IRCMax jobs require multiple method specifications. However, they are given as options to
the corresponding keyword.
♢ The form model2 // model1 described in Job Type may be used to generate an automatic optimization
followed by a single point calculation at the optimized geometry.

2.2 Job Types

The following table lists the job types available in Gaussian 16:
♢ SP: Single point energy.
♢ Opt: Geometry optimization.
♢ Freq: Frequency and thermochemical analysis.
♢ IRC: Reaction path following.
♢ IRCMax: Find the maximum energy along a specific reaction path.
♢ Scan: Potential energy surface scan.
♢ Polar: Polarizabilities and hyperpolarizabilities.
♢ ADMP and BOMD: Direct dynamics trajectory calculation.
♢ EET: Excitation energy transfer calculation.
♢ Force: Compute forces on the nuclei.
♢ Stable: Test wavefunction stability.
♢ Volume: Compute molecular volume.
♢ Density=Checkpoint Guess=Only: Recompute population analysis only.
♢ Guess=Only: Print initial guess only; generate fragment-based initial guess.

In general, only one job type keyword should be specified. The exceptions to this rule are:
♢ Polar and Opt may be combined with Freq. In the latter case, the geometry optimization is automatically
followed by a frequency calculation at the optimized structure.
♢ Opt may be combined with the compound method keywords in order to specify options for the optimiza-
tion portion of the calculation: e.g., Opt=(TS,ReadFC) CBS-QB3.

When no job type keyword is specified within the route section, the default calculation type is usually a
single point energy calculation (SP). However, a route section of the form: method2/basis2 // method1/basis1
may be used to request an optimization calculation (at method1/basis1) followed by a single point energy
calculation (at method2/basis2) at the optimized geometry. For example, the following route section requests
 2.2 Job Types 7

a B3LYP/6-31G(d) geometry optimization followed by a single point energy calculation using the CCSD/6-
31G(d) model chemistry:
# CCSD/6-31G(d)//B3LYP/6-31G(d)
In this case, the Opt keyword is optional and is the default. Note that Opt Freq calculations may not use this
syntax.

2.2.1 Molecular Properties

The following table provides a mapping between commonly-desired predicted quantities and the Gaussian
16 keywords that will produce them:
♢ Anharmonic IR/Raman/VCD/ROA spectra: Freq=Anharmonic
♢ Antiferromagnetic coupling: Guess=Fragment, Stable
♢ Atomic charges: Pop
♢ ∆G of solvation: SCRF=SMD
♢ Dipole moment: Pop
♢ Electron affinities: CBS-QB3, CCSD, EPT
♢ Electron density: cubegen
♢ Electronic circular dichroism: CIS, TD, EOM, SAC-CI
♢ Electrostatic potential: cubegen, Prop
♢ Electrostatic potential-derived charges: Pop=Chelp, ChelpG or MK
♢ Electronic transition band shape: Freq=FranckCondon, Freq=HerzbergTeller
♢ Polarizabilities/hyperpolarizabilities: Freq, Polar, CPHF=RdFreq, Polar=DCSHG
♢ High accuracy energies: CBS-QB3, G2, G3, G4, W1U, W1BD
♢ Hyperfine coupling constants (anisotropic): Prop
♢ Hyperfine spectra tensors (including g tensors): Freq=(VCD, VibRot, Anharmonic)
♢ Ionization potentials: CBS-QB3, CCSD, EPT
♢ IR and Raman spectra: Freq
♢ Pre-resonance Raman spectra: Freq CPHF=RdFreq
♢ Resonance Raman spectra: Freq=ReadFCHT
♢ Molecular orbitals: Pop=Regular
♢ Multipole moments: Pop
♢ NMR shielding and chemical shifts: NMR
♢ NMR spin-spin coupling constants: NMR=Mixed
♢ Optical rotations: Polar=OptRot
♢ Raman optical activity: Freq=ROA
♢ Thermochemical analysis: Freq
♢ UV/Visible spectra: CIS, ZIndo, TD, EOM, SAC-CI
♢ Vibration-rotation coupling: Freq=VibRot
♢ Vibrational circular dichroism: Freq=VCD
♢ Vibronic spectra: Freq=ReadFCHT
 8 Chapter 2. Gaussian 16 Capabilities

2.3 Program Limits

This section lists the various size limitations that exist within Gaussian 16.
♢ The integral program has the following limitations:
• The maximum number of atoms is 250,000.
• The maximum total number of primitive shells is 750,000.
• The maximum number of primitive d-shells and higher is 250,000.
• The maximum number of contracted shells is 250,000.
• The maximum degree-of-contraction allowed is 100.
♢ Opt=(EF,EnOnly) optimizations–useful only for methods without analytic gradients–are limited to 50
variables.
♢ The GVB program is limited to 100 paired orbitals (which is not a restriction in practice).
♢ The internal version of NBO 3 is dimensioned for 250,000 atoms and 10,000 basis functions.

2.4 Links
The following are the component programs of Gaussian 16–known as links–along with their primary
functions:
♢ L0: Initializes program and controls overlaying
♢ L1: Processes route section, builds list of links to execute, and initializes scratch files
♢ L101: Reads title and molecule specification
♢ L102: Fletcher-Powell optimizations
♢ L103: Berny optimizations to minima and TS, STQN transition state searches
♢ L105: Murtaugh-Sargent optimizations
♢ L106: Numerical differentiation of forces/dipoles to obtain polarizability/ hyperpolarizability
♢ L107: Linear-synchronous-transit (LST) transition state search
♢ L108: Unrelaxed potential energy surface scan
♢ L109: Newton-Raphson optimization
♢ L110: Double numerical differentiation of energies to produce frequencies
♢ L111: Double numerical differentiation of energies to compute polarizabilities and hyperpolarizabilities
♢ L112: Performs the Self-Consistent Virial Scaling method (SCVS), T. A. Keith’s extension of [22–24]
♢ L113: EF optimization using analytic gradients
♢ L114: EF numerical optimization (using only energies)
♢ L115: Follows reaction path using GS3 algorithm
♢ L116: Numerical self-consistent reaction field (SCRF)
♢ L117: Performs IPCM solvation calculations.
♢ L118: BOMD calculations
♢ L120: Controls ONIOM calculations
♢ L121: ADMP calculations
♢ L122: Counterpoise calculations
♢ L123: Follows reaction path using the HPC algorithm (and others)
♢ L124: Performs ONIOM with PCM and external-iteration PCM
♢ L202: Reorients coordinates, calculates symmetry, and checks variables
2.4 Links 9

♢ L301: Generates basis set information

♢ L302: Calculates overlap, kinetic, and potential integrals
♢ L303: Calculates multipole integrals
♢ L308: Computes dipole velocity and Rx∇ integrals
♢ L310: Computes spdf 2-electron integrals in a primitive fashion
♢ L311: Computes sp 2-electron integrals
♢ L314: Computes spdf 2-electron integrals
♢ L316: Prints 2-electron integrals
♢ L319: Computes 1-electron integrals for approximate spin orbital coupling
♢ L401: Forms the initial MO guess
♢ L402: Performs semi-empirical and molecular mechanics calculations
♢ L405: Initializes an MCSCF calculation
♢ L502: Iteratively solves the SCF equations (conven. UHF & ROHF, all direct methods, SCRF)
♢ L503: Iteratively solves the SCF equations using direct minimization
♢ L506: Performs an ROHF or GVB-PP calculation
♢ L508: Quadratically convergent SCF program
♢ L510: MC-SCF
♢ L601: Population and related analyses (including multipole moments)
♢ L602: 1-electron properties (potential, field, and field gradient)
♢ L604: Evaluates MOs or density over a grid of points
♢ L607: Performs NBO analyses
♢ L608: Non-iterative DFT energies
♢ L609: Atoms in Molecules properties
♢ L610: Numerical integration (for testing integral codes)
♢ L701: 1-electron integral first or second derivatives
♢ L702: 2-electron integral first or second derivatives (sp)
♢ L703: 2-electron integral first or second derivatives (spdf)
♢ L716: Processes information for optimizations and frequencies
♢ L801: Initializes transformation of 2-electron integrals
♢ L802: Performs integral transformation (N3 in-core)
♢ L804: Integral transformation
♢ L811: Transforms integral derivatives & computes their contributions to MP2 2nd derivatives
♢ L901: Anti-symmetrizes 2-electron integrals
♢ L902: Determines the stability of the Hartree-Fock wavefunction
♢ L903: Old in-core MP2
♢ L904: Complete basis set (CBS) extrapolation method of Petersson, et. al.
♢ L905: Complex MP2
♢ L906: Semi-direct MP2
♢ L908: Electron Propagator Program
♢ L909: ADC(3) and related electron propagator models
♢ L913: Calculates post-SCF energies and gradient terms
10 Chapter 2. Gaussian 16 Capabilities

♢ L914: CI-Singles, RPA and ZIndo excited states; SCF stability

♢ L915: Computes fifth order quantities (for MP5, QCISD(TQ) and BD(TQ))
♢ L916: Old MP4 and CCSD
♢ L918: Reoptimizes the wavefunction
♢ L923: SAC-CI program
♢ L925: Implements the Excited State Electron Transfer (EET) model
♢ L1002: Iteratively solves the CPHF equations; computes various properties (including NMR)
♢ L1003: Iteratively solves the CP-MCSCF equations
♢ L1014: Computes analytic CI-Singles second derivatives
♢ L1101: Computes 1-electron integral derivatives
♢ L1102: Computes dipole derivative integrals
♢ L1110: 2-electron integral derivative contribution to F(x)
♢ L1111: 2 particle density matrix and post-SCF derivatives
♢ L1112: MP2 second derivatives
♢ L9999: Finalizes calculation and output
 3. About Gaussian 16 Input

3.1 Syntax
Gaussian 16 input consists of a series of lines in an ASCII text file. The basic structure of a Gaussian input
file includes several different sections:
♢ Link 0 Commands: Locate and name scratch files (not blank line terminated).
♢ Route section (# lines): Specify desired calculation type, model chemistry, and other options (blank line
terminated). See Model Chemistries and Job Types for information about Gaussian 16 capabilities.
♢ Title section: Brief description of the calculation (blank line-terminated). This section is required in
the input, but is not interpreted in any way by the Gaussian 16 program. It appears in the output for
purposes of identification and description. Typically, this section might contain the compound name, its
symmetry, the electronic state, and any other relevant information. The title section cannot exceed five
lines and must be followed by a terminating blank line. The following characters should be avoided in
the title section: @ # ! – _ \ control characters (especially Ctrl-G)
♢ Molecule specification: Specify molecular system to be studied (blank line-terminated). Full information
is available in Molecule Specifications.
♢ Optional additional sections: Additional input needed for specific job types (usually blank line-terminated).

Many Gaussian 16 jobs will include only the second, third, and fourth sections. Here is an example of
such a file, which requests a single point energy calculation on water:

# HF/6-31G(d) Route section

water energy Title section

0 1 Molecule specification
O -0.464 0.177 0.0
H -0.464 1.137 0.0
 12 Chapter 3. About Gaussian 16 Input

H 0.441 -0.143 0.0

In this job, the route and title sections each consist of a single line. The molecule specification section
begins with a line giving the charge and spin multiplicity for the molecule: 0 charge (neutral molecule) and spin
multiplicity 1 (singlet) in this case. The charge and spin multiplicity line is followed by lines describing the
location of each atom in the molecule; this example uses Cartesian coordinates to do so. Molecule specifications
are discussed in more detail later in this chapter.
The following input file illustrates the use of Link 0 commands and an additional input section:

%Chk=heavy Link 0 section

# HF/6-31G(d) Opt=ModRedun Route section

Opt job Title section

0 1 Molecule Specification section

atomic coordinates· · ·

3 8 Add a bond and an angle to the internal

2 1 3 coordinates used during the geom. opt.

This job requests a geometry optimization. The input section following the molecule specification is
used by the Opt=ModRedundant keyword, and it serves to add an additional bond and angle in the internal
coordinates used in the geometry optimization. The job also specifies a name for the checkpoint file.
For convenience, the table in the Section Ordering section details all possible sections that might appear
within a Gaussian 16 input file along with the keywords associated with each one.

3.1.1 Syntax Rules

In general, Gaussian input is subject to the following syntax rules:
♢ Input is free-format and case-insensitive.
♢ Spaces, tabs, commas, or forward slashes can be used in any combination to separate items within a line.
Multiple spaces are treated as a single delimiter.
♢ Options to keywords may be specified in any of the following forms:
• keyword = option
• keyword(option)
• keyword=(option1, option2, · · · )
• keyword(option1, option2, · · · )
♢ Multiple options are enclosed in parentheses and separated by any valid delimiter (commas are conven-
tional and are shown above). The equals sign before the opening parenthesis may be omitted, or spaces
may optionally be included before and/or after it. Note that some options also take values; in this case,
the option name is followed by an equals sign: for example, CBSExtrap(NMin=6).
♢ All keywords and options may be shortened to their shortest unique abbreviation within the entire Gaus-
sian 16 system. Thus, the Conventional option to the SCF keyword may be abbreviated to Conven,
but not to Conv (due to the presence of the Convergence option). This holds true whether or not both
Conventional and Convergence happen to be valid options for any given keyword.
 3.2 Molecule Specifications 13

♢ The contents of an external file may be included within a Gaussian 16 input file using the following
syntax: @filename. This causes the entire file to be placed at the current location in the input stream.
Appending /N to such commands will prevent the included file’s contents from being echoed at the start
of the output file.
♢ Comments begin with an exclamation point (!), which may appear anywhere on a line. Separate comment
lines may appear anywhere within the input file.

3.2 Molecule Specifications

3.2.1 Overview
This input section specifies the nuclear positions and the number of electrons of α - and β -spin. There are
several ways in which the nuclear configuration can be specified: as a Z-matrix, as Cartesian coordinates, or as
a mixture of the two (note that Cartesian coordinates are just a special case of the Z-matrix).
The first line of the molecule specification section specifies the net electric charge (a signed integer) and
the spin multiplicity (usually a positive integer). Thus, for a neutral molecule in a singlet state, the entry 0 1
is appropriate. For a radical anion, -1 2 would be used. Multiple charge/spin pairs may/must be included for
some calculation types.
The charge and spin line is the only molecule specification input required if Geom=Checkpoint is used.
The entire molecule specification (and title section) may be omitted by including Geom=AllCheck in the route
section.
The remainder of the molecule specification gives the element type and nuclear position for each atom in
the molecular system. The most general format for the line within it is the following:
Element-label[-Atom-type[-Charge]][(param=value[, · · · ])] Atom-position-parameters
Each line contains the element type, and possibly an optional molecular mechanics atom type and partial
charge. Nuclear parameters for this atom are specified in the parenthesized list. The remainder of the line
contains information about the atom’s location, either as Cartesian coordinates or as a Z-matrix definition.
We’ll begin by considering the initial and final items, and then go on to discuss the remaining items.
Here is the basic format for specifying atoms within the molecule specification (omitting all of the optional
items):
Element-label [freeze-code] x y z
Although these examples use spaces to separate items within a line, any valid separator may be used.
The position of the atom is specified in Cartesian coordinates. freeze-code is an optional parameter related to
freezing atoms during optimizations.
Element-label is a character string consisting of either the chemical symbol for the atom or its atomic num-
ber. If the elemental symbol is used, it may be optionally followed by other alphanumeric characters to create
an identifying label for that atom. A common practice is to follow the element name with a secondary identi-
fying integer: C1, C2, C3, and so on; this technique is useful in following conventional chemical numbering.
The maximum length of the element label is 4 characters.
The remaining items on each line are Cartesian coordinates specifying the position of that nucleus.
Here is a simple molecule specification section for ethane which uses element labels for the carbon atoms
and element types for the hydrogen atoms:

0,1
 14 Chapter 3. About Gaussian 16 Input

C1 0.00 0.00 0.00

C2 0.00 0.00 1.52
H 1.02 0.00 -0.39
H -0.51 -0.88 -0.39
H -0.51 0.88 -0.39
H -1.02 0.00 1.92
H 0.51 -0.88 1.92
H 0.51 0.88 1.92

Additional information can be specified for each atom with a parenthecized keyword list following the
element specification/label. For example:
C(Iso=13,Fragment=2) 0.00 0.00 0.00
The available items are documented in the other tabs.

Z-matrix Input

Z-matrix molecule specifications are also accepted. In this case, the atom-position-parameters are the
labels or line numbers for previously-specified atoms which will be used to define the current atom’s position;
we will designate them here as atom1, atom2 and atom3. The position of the current atom is specified by
giving the length of the bond joining it to atom1, the angle formed by this bond and the bond joining atom1 and
atom2, and the dihedral (torsion) angle formed by the bond joining atom2 and atom3 with the plane containing
the current atom, atom1 and atom2.
See Constructing Z Matrices for details.

3.2.2 Nuclei Properties

Isotopes and other nuclear parameters can be specified within the atom type field using parenthesized
keywords and values, as in the following example:
C(Iso=13,Spin=3) 0.0 0.0 0.0
The line specifies a 13 C atom with a nuclear spin of 3/2 (3 * 1/2), located at the origin. The following
items may be included in the list of parameters:
♢ Iso=n: Isotope selection. If integers are used to specify the atomic masses, the program will automatically
use the corresponding actual exact isotopic mass (e.g., 18 specifies 18 O, and Gaussian uses the value
17.99916).
♢ Spin=n: Nuclear spin, in units of 1/2.
♢ ZEff=n: Effective charge. This parameter is used in spin orbit coupling (see CASSCF=SpinOrbit), and
the ESR g tensor and the electronic spin-molecular rotation hyperfine tensor (NMR, Output=Pickett).
♢ QMom=n: Nuclear quadrupole moment.
♢ NMagM=n: Nuclear magnetic moment in nuclear magnetons.
♢ ZNuc=n: Modifies nuclear charge.
♢ RadNuclear=radius: Specifies the radius to use when finite (non-point) nuclei are used. radius is a
floating point value in atomic units.
 3.2 Molecule Specifications 15

3.2.3 Fragments
Fragments within a molecular system may be defined using the Fragment parameter, which appears in
parentheses following the atom label along with any isotope and/or nuclear parameter values. The value to
Fragment is an integer; all atoms with the same fragment number are defined as a fragment. Fragments are
useful for fragment guess calculation, counterpoise calculations, and so on.
For example, the following biphenyl structure is divided into two fragments by benzene ring:
0,1 0,1 0,1 Total spin & charge, followed by fragment-specific ones.
C(Fragment=1) -3.05015529 -0.24077322 0.00000698
C(Fragment=1) -1.64875545 -0.24070572 0.00067327
C(Fragment=1) -0.94811361 0.97297577 0.00020266
C(Fragment=1) -1.64887160 2.18658975 -0.00093259
C(Fragment=1) -3.05027145 2.18652225 -0.00159819
C(Fragment=1) -3.75091329 0.97284076 -0.00112735
H(Fragment=1) -3.58511088 -1.16744597 0.00036555
H(Fragment=1) -1.11371117 -1.16732692 0.00154256
H(Fragment=1) -1.11391601 3.11326250 -0.00129286
H(Fragment=1) -3.58531573 3.11314346 -0.00246648
H(Fragment=1) -4.82091317 0.97278922 -0.00163655
C(Fragment=2) 0.59188622 0.97304995 0.00093742
C(Fragment=2) 1.29252806 2.18673144 0.00046795
C(Fragment=2) 1.29264421 -0.24056403 0.00207466
C(Fragment=2) 2.69392790 2.18679894 0.00113535
C(Fragment=2) 2.69404405 -0.24049653 0.00274263
C(Fragment=2) 3.39468590 0.97318496 0.00227326
H(Fragment=2) 0.75768862 -1.16723678 0.00243403
H(Fragment=2) 0.75748378 3.11335264 -0.00040118
H(Fragment=2) 3.22888349 3.11347169 0.00077519
H(Fragment=2) 3.22908834 -1.16711773 0.00360969
H(Fragment=2) 4.46468577 0.97323650 0.00278063

This example also illustrates the use of fragment-specific charge and spin multiplicity specifications. The
format of the corresponding input line in this case is:
total charge, total spin, fragment1 charge, fragment1 spin, fragment2 charge, fragment2 spin
Negative spin multiplicity values have a special meaning for Guess=Fragment calculations, indicating that
the unpaired orbitals for the corresponding fragment are to become β spin orbitals in the combined set specified.
Negative spin multiplicities will generate an error in any other job type.
For Guess=Fragment and Counterpoise calculations, fragment numbers must begin at 1 and run consecu-
tively. For other calculation types, this restriction is not enforced, but violating it may result in some extraneous,
empty data sections in the output (e.g., all zero fragment population analyses).
GaussView provides a graphical tool for defining fragments.

3.2.4 MM Types
Molecule specifications for molecular mechanics calculations may also include atom typing and partial
charge information. Here are some examples:

C-CT Specifies an SP3 aliphatic carbon atom.

C-CT-0.32 Specifies an SP3 aliphatic carbon atom with a partial charge of 0.32.
 16 Chapter 3. About Gaussian 16 Input

O-O-0.5 Specifies a carbonyl group oxygen atom with a partial charge of -0.5.

Atom types and optional partial charges can be specified for each atom. Nuclear parameters can also be
defined, as in these examples:
C-CT(Iso=13)
C-CT--0.1(Spin=3)

3.2.5 PDB Parameters

Several additional items may be defined along with the nuclear parameters and/or fragment definitions.
These items are designed for use with PDB files to retain residue and other structural information they contain
and as such will not be defined by the user. However, you may see them in Gaussian 16 input files created by
GaussView using structures originating in PDB files.
♢ RESNum specifies the residue in which the atom is located. The value takes the form of n[X[Y]], where
n is an integer (which need not be positive), X is the optional one-character insertion code, and Y is the
optional chain letter. If the chain is specified but there is no insertion code, then X can be an underscore:
ResNum=-17_C for the residue with number -17 in chain C.
♢ RESName specifies the three character residue name.
♢ PDBName specifies the name assigned to the atom if it is not just the element name.

3.2.6 Ghost Atoms

An atom with mechanics type Bq (e.g., O-Bq) is set up as a ghost [25] of the corresponding atom, with its
normal basis functions and numerical integration grid points but no nuclear charge or electrons. This requests
a counterpoise calculation. Such calculations differ slightly from ones requested with Massage in previous
versions of Gaussian in that they include the grid points from the ghost atoms in DFT XC quadrature. The new
way is a more consistent superposition correction and also easier to use. Note that counterpoise calculations
can also be requested with the Counterpoise keyword.

3.2.7 Periodic Systems

Periodic systems are specified with a normal molecule specification for the unit cell. The only addi-
tional required input are one, two or three translation vectors appended to the molecule specification (with no
intervening blank line), indicating the replication direction(s). For example, the following input specifies a
one-dimensional PBC single point energy calculation for neoprene:

# PBEPBE/6-31g(d,p)/Auto SCF=Tight

neoprene, -CH2-CH=C(Cl)-CH2- optimized geometry

0 1
C,-1.9267226529,0.4060180273,0.0316702826
H,-2.3523143977,0.9206168644,0.9131400756
H,-1.8372739404,1.1548899113,-0.770750797
C,-0.5737182157,-0.1434584477,0.3762843235
H,-0.5015912465,-0.7653394047,1.2791284293
 3.3 Basis Sets 17

C,0.5790889876,0.0220081655,-0.3005160849
C,1.9237098673,-0.5258773194,0.0966261209
H,1.772234452,-1.2511397907,0.915962512
H,2.3627869487,-1.0792380182,-0.752511583
Cl,0.6209825739,0.9860944599,-1.7876398696
TV,4.8477468928,0.1714181332,0.5112729831

The final line specifies the translation vector. Note that it specifies TV as the atom symbol.
The following molecule specification could be used for a two-dimensional PBC calculation on a graphite
sheet:

0 1
C 0.000000 0.000000 0.000000
C 0.000000 1.429118 0.000000
TV 2.475315 0.000000 0.000000
TV -1.219952 2.133447 0.000000

Here is the molecule specification that could be used for a three-dimensional PBC calculation on gallium
arsenide:

0 1
Ga 0.000000 0.000000 0.000000
Ga 0.000000 2.825000 2.825000
Ga 2.825000 0.000000 2.825000
Ga 2.825000 2.825000 0.000000
As 1.412500 1.412500 1.412500
As 1.412500 4.237500 4.237500
As 4.237500 1.412500 4.237500
As 4.237500 4.237500 1.412500
TV 5.650000 0.000000 0.000000
TV 0.000000 5.650000 0.000000
TV 0.000000 0.000000 5.650000

3.3 Basis Sets

Most methods require a basis set be specified; if no basis set keyword is included in the route section, then
the STO-3G basis will be used. The exceptions consist of a few methods for which the basis set is defined as
an integral part of the method; they are listed below:
♢ All semi-empirical methods, including ZIndo for excited states.
♢ All molecular mechanics methods.
♢ Compound model chemistries: all Gn, CBS and W1 methods.

Basis sets other than those listed here may also be input to the program using the ExtraBasis and Gen
keywords. The ChkBasis keyword indicates that the basis set is to read from the checkpoint file (defined via
the %Chk command). See the individual descriptions of these keywords for details.
18 Chapter 3. About Gaussian 16 Input

The following basis sets are stored internally in the Gaussian 16 program (see references cited for full
descriptions), listed below by their corresponding Gaussian 16 keyword (with two exceptions):
♢ STO-3G [26, 27]
♢ 3-21G [28–33]
♢ 6-21G [28, 29]
♢ 4-31G [34–37]
♢ 6-31G [34–43]
♢ 6-31G† 1 : Gaussian 16 also includes the 6-31G† and 6-31G‡ basis sets of George Petersson and cowork-
ers, defined as part of various Complete Basis Set methods [44, 45]. These are accessed via the 6-31G(d’)
and 6-31G(d’,p’) keywords (respectively). Single or double diffuse functions may also be added, as can
f functions: e.g., 6-31+G(d’f).
♢ 6-311G: Specifies the 6-311G basis for first-row atoms and the McLean-Chandler (12s,9p) → (621111,
52111) basis sets for second-row atoms [46, 47] (note that the basis sets for P, S, and Cl are those called
negative ion basis sets by McLean and Chandler; these were deemed to give better results for neutral
molecules as well), the basis set of Blaudeau and coworkers for Ca and K [41], the Wachters-Hay [48,
49] all electron basis set for the first transition row, using the scaling factors of Raghavachari and Trucks
[50], and the 6-311G basis set of McGrath, Curtiss and coworkers for the other elements in the third
row [40, 51, 52]. Note that Raghavachari and Trucks recommend both scaling and including diffuse
functions when using the Wachters-Hay basis set for first transition row elements; the 6-311+G form
must be specified to include the diffuse functions. MC-311G is a synonym for 6-311G.
♢ D95V: Dunning/Huzinaga valence double-zeta [53].
♢ D95: Dunning/Huzinaga full double zeta [53].
♢ SHC: D95V on first row, Goddard/Smedley ECP on second row [53, 54]. Also known as SEC.
♢ CEP-4G: Stevens/Basch/Krauss ECP minimal basis [55–57].
♢ CEP-31G: Stevens/Basch/Krauss ECP split valance [55–57].
♢ CEP-121G: Stevens/Basch/Krauss ECP triple-split basis [55–57].
Note that there is only one CEP basis set defined beyond the second row, and all three keywords are
equivalent for these atoms.
♢ LanL2MB: STO-3G [26, 27] on first row, Los Alamos ECP plus MBS on Na-La, Hf-Bi [58–60].
♢ LanL2DZ: D95V on first row [53], Los Alamos ECP plus DZ on Na-La, Hf-Bi [58–60].
♢ SDD: D95 up to Ar [53] and Stuttgart/Dresden ECPs on the remainder of the periodic table [61–85]. The
SDD, SHF, SDF, MHF, MDF, MWB forms may be used to specify these basis sets/potentials within Gen
basis input. Note that the number of core electrons must be specified following the form (e.g., MDF28
for the MDF potential replacing 28 core electrons). OldSDD requests the previous default.
♢ SDDAll: Selects Stuttgart potentials for Z > 2.
♢ cc-pVDZ, cc-pVTZ, cc-pVQZ, cc-pV5Z, cc-pV6Z: Dunning’s correlation consistent basis sets [86–90]
(double, triple, quadruple, quintuple-zeta and sextuple-zeta, respectively). These basis sets have had re-
dundant functions removed and have been rotated [91] in order to increase computational efficiency.
These basis sets include polarization functions by definition. The following table lists the valence polar-
ization functions present for the various atoms included in these basis sets:

1 6-31G† is not a keyword of basis set in Gaussian. Don’t confuse it with 6-31+G. – Noted by the editor.
3.3 Basis Sets 19

Atoms cc-pVDZ cc-pVTZ cc-pVQZ cc-pV5Z cc-pV6Z

H 2s,1p 3s,2p,1d 4s,3p,2d,1f 5s,4p,3d,2f,1g 6s,5p,4d,3f,2g,1h
He 2s,1p 3s,2p,1d 4s,3p,2d,1f 5s,4p,3d,2f,1g not available
Li-Be 3s,2p,1d 4s,3p,2d,1f 5s,4p,3d,2f,1g 6s,5p,4d,3f,2g,1h not available
B-Ne 3s,2p,1d 4s,3p,2d,1f 5s,4p,3d,2f,1g 6s,5p,4d,3f,2g,1h 7s,6p,5d,4f,3g,2h,1i
Na-Ar 4s,3p,1d 5s,4p,2d,1f 6s,5p,3d,2f,1g 7s,6p,4d,3f,2g,1h not available
Ca 5s,4p,2d 6s,5p,3d,1f 7s,6p,4d,2f,1g 8s,7p,5d,3f,2g,1h not available
Sc-Zn 6s,5p,3d,1f 7s,6p,4d,2f,1g 8s,7p,5d,3f,2g,1h 9s,8p,6d,4f,3g,2h,1i not available
Ga-Kr 5s,4p,2d 6s,5p,3d,1f 7s,6p,4d,2f,1g 8s,7p,5d,3f,2g,1h not available

These basis sets may be augmented with diffuse functions by adding the AUG- prefix to the basis set
keyword (rather than using the + and ++ notation–see below).
♢ Basis sets of Ahlrichs and coworkers: the SV, SVP, TZV, TZVP keywords refer to the initial forma-
tions of the split valence and triple zeta basis sets from this group [92, 93]. The newer redefinitions of
these basis sets in [94, 95] are requested with the keywords Def2SV, Def2SVP, Def2SVPP, Def2TZV,
Def2TZVP, Def2TZVPP, Def2QZV, Def2QZVP, Def2QZVPP, and QZVP. Note that Def2SVPP corre-
sponds to the “def2-SV(P)” basis set in [94]; all other names follow those in the paper with the hyphen
removed.
♢ MIDI! of Truhlar and coworkers [96]. The MidiX keyword is used to request this basis set.
♢ EPR-II and EPR-III: The basis sets of Barone [97] which are optimized for the computation of hyperfine
coupling constants by DFT methods (particularly B3LYP). EPR-II is a double zeta basis set with a single
set of polarization functions and an enhanced s part: (6,1)/[4,1] for H and (10,5,1)/[6,2,1] for B to F.
EPR-III is a triple-zeta basis set including diffuse functions, double d-polarizations and a single set of
f-polarization functions. Also in this case the s-part is improved to better describe the nuclear region:
(6,2)/[4,2] for H and (11,7,2,1)/[7,4,2,1] for B to F.
♢ UGBS: The universal Gaussian basis set of de Castro, Jorge and coworkers [98–106]. Additional polar-
ization functions may be added by including a suffix to this keyword:
UGBSnP|V|O
where n is an integer indicating whether to add 1, 2 or 3 polarization functions for each function in the
normal UGBS basis set. The second item is a code letter indicating which function should be augmented
polarization functions: P adds them to all functions, V adds them to all valence functions, and O requests
the scheme used in Gaussian 03 (see below). For example, the UGBS1P keyword requests this basis set
with one additional polarization function to all orbitals, and UGBS2V adds two additional polarization
function to all valence orbitals.
The O suffix adds the same functions as the UGBSnP keywords in Gaussian 03. UGBS1O adds a p
function for each s, a d function for each p, and so on; UGBS2O adds a p and d function for each s, a d
and f function for each p, and UGBS3O adds a p, d and f for each s, etc.
Diffuse functions may be added as usual with + or ++; the first of these may be specified as 2+ to add
two diffuse functions for heavy atoms.
♢ MTSmall of Martin and de Oliveira, defined as part of their W1 method (see the W1U keyword) [107].
♢ The DGDZVP, DGDZVP2 and DGTZVP basis sets used in DGauss [108, 109].
♢ CBSB7: Selects the 6-311G(2d,d,p) basis set used by CBS-QB3 high accuracy energy method [110].
20 Chapter 3. About Gaussian 16 Input

The notation specifies two additional d polarization functions on second rows atoms, one d function on
first row atoms and a p function on hydrogens (note that this three-field polarization function syntax is
not supported by Gaussian 16).

Adding Polarization and Diffuse Functions

Single first polarization functions can also be requested using the usual * or ** notation. Note that (d,p)
and ** are synonymous – 6-31G** is equivalent to 6-31G(d,p), for example – and that the 3-21G* basis set has
polarization functions on second row atoms only. The + and ++ diffuse functions [111] are available with some
basis sets, as are multiple polarization functions [112]. The keyword syntax is best illustrated by example:
6-31+G(3df,2p) designates the 6-31G basis set supplemented by diffuse functions, 3 sets of d functions and one
set of f functions on heavy atoms, and supplemented by 2 sets of p functions on hydrogens.
When the AUG- prefix is used to add diffuse functions to the cc-pV*Z basis sets, one diffuse function of
each function type in use for a given atom is added [87, 88]. For example, the AUG-cc-pVTZ basis places one
s, one d, and one p diffuse functions on hydrogen atoms, and one d, one p, one d, and one f diffuse functions
on B through Ne and Al through Ar.
There are several options for augmenting the cc-pV*Z basis sets with diffuse functions:
♢ spAug-cc-pV*Z augments with s and p functions only, including s functions on H and He.
♢ dAug-cc-pV*Z augments with with 2 shells of each angular momentum instead of one.
♢ Truhlar’s “calendar” basis set variations [113] are available. The naming of this series of basis sets
comes from the fact that the cc-pV*Z basis sets with added polarization functions are known as the Aug-
cc-pV*Z. Truhlar noted that “Aug” is also an abbreviation for the month of August in English, so he pro-
posed new augmentation schemes for the cc-pV*Z basis sets, also named after months of the year. They
are constructed by removing diffuse functions from the Aug basis sets. For example, the Jul-cc-pV*Z
basis sets remove the diffuse function from H and He from Aug-cc-pV*Z. Jun-cc-pV*Z also removes
the highest angular momentum diffuse function from all other atoms, May-cc-pV*Z removes the two
highest angular momentum functions, and Apr-cc-pV*Z removes the three highest angular momentum
functions.
Nevertheless, by default, at least s and p diffuse functions are always included in these basis sets. This
serves to avoid some inherent inconsistencies, but it differs from Truhlar and coworkers’ original defi-
nitions. Use the forms TJul, TJun, and so on to specify the original versions where the limit is applied
unconditionally: e.g., TMay-cc-ppVDZ includes only a diffuse s function on Cl but both diffuse s and p
functions on Fe and Br, while May-cc-ppVDZ has diffuse s and p functions on all of these atoms.
Adding a single polarization function to 6-311G (i.e. 6-311G(d)) will result in one d function for first and
second row atoms and one f function for first transition row atoms, since d functions are already present for the
valence electrons in the latter. Similarly, adding a diffuse function to the 6-311G basis set will produce one s,
one p, and one d diffuse functions for third-row atoms.
When a frozen core calculation is done using the D95 basis, both the occupied core orbitals and the
corresponding virtual orbitals are frozen. Thus while a D95** calculation on water has 26 basis functions, and
a 6-31G** calculation on the same system has 25 functions, there will be 24 orbitals used in a frozen core
post-SCF calculation involving either basis set.
The following table lists polarization and diffuse function availability and the range of applicability for
each built-in basis set in Gaussian 16:
 3.3 Basis Sets 21

Basis Set Applies to Polarization Functions Diffuse Functions

3-21G H-Xe +
6-21G H-Cl * or **
4-31G H-Ne * or **
6-31G H-Kr through (3df,3pd) +,++
6-311G H-Kr through (3df,3pd) +,++
D95 H-Cl except Na and Mg through (3df,3pd) +,++
D95V H-Ne (d) or (d,p) +,++
SHC H-Cl *
CEP-4G H-Rn * (Li-Ar only)
CEP-31G H-Rn * (Li-Ar only)
CEP-121G H-Rn * (Li-Ar only)
LanL2MB H-La, Hf-Bi
LanL2DZ H, Li-La, Hf-Bi
SDD, SDDAll all but Fr and Ra
cc-pVDZ H-Ar, Ca-Kr included in definition added via AUG- prefix (H-Ar, Sc-Kr)
cc-pVTZ H-Ar, Ca-Kr included in definition added via AUG- prefix (H-Ar, Sc-Kr)
cc-pVQZ H-Ar, Ca-Kr included in definition added via AUG- prefix(H-Ar, Sc-Kr)
cc-pV5Z H-Ar, Ca-Kr included in definition added via AUG- prefix (H-Na, Al-Ar,
Sc-Kr)
cc-pV6Z H, B-Ne included in definition added via AUG- prefix (H, B-O)
SV H-Kr
SVP H-Kr included in definition
TZV and TZVP H-Kr included in definition
QZVP and Def2 H-La, Hf-Rn included in definition
MidiX H, C-F, S-Cl, I, Br included in definition
EPR-II, EPR-III H, B, C, N, O, F included in definition
UGBS H-Lr UGBS(1,2,3)P +,++,2+,2++
MTSmall H-Ar
DGDZVP H-Xe
DGDZVP2 H-F, Al-Ar, Sc-Zn
DGTZVP H, C-F, Al-Ar
CBSB7 H-Kr included in definition +,++

STO-3G and 3-21G accept a * suffix, but this does not actually add any polarization functions.

3.3.1 Issues Arising from Pure vs. Cartesian Basis Functions

The following additional keywords are useful in conjunction with these basis set keywords:
♢ 5D and 6D: Use 5 or 6 d functions (pure vs. Cartesian d functions), respectively.
♢ 7F and 10F: Use 7 or 10 f functions (pure vs. Cartesian f functions), respectively. These keywords also
apply to all higher functions (g and beyond).
 22 Chapter 3. About Gaussian 16 Input

Gaussian users should be aware of the following points concerning pure vs. Cartesian basis functions:
♢ All of the built-in basis sets use pure f functions. Most also use pure d functions; the exceptions are
3-21G, 6-21G, 4-31G, 6-31G, 6-31G†, 6-31G‡, CEP-31G, D95 and D95V. The preceding keywords may
be used to override the default pure/Cartesian setting. Note that basis functions are generally converted
to the other type automatically when necessary, for example, when a wavefunction is read from the
checkpoint file for use in a calculation using a basis consisting of the other type [114].
♢ Within a job, all d functions must be 5D or 6D, and all f and higher functions must be pure or Cartesian.
♢ When using the ExtraBasis, Gen and GenECP keywords, the basis set explicitly specified in the route
section always determines the default form of the basis functions (for Gen, these are 5D and 7F). For
example, if you use a general basis set taking some functions from the 3-21G and 6-31G basis sets, pure
functions will be used unless you explicitly specify 6D in the route section in addition to Gen. Similarly,
if you add basis functions for a transition metal from the 6-311G(d) basis set via ExtraBasis to a job that
specifies the 6-31G(d) basis set in the route section, Cartesian d functions will be used. Likewise, if you
want to add basis functions for Xe from the 3-21G basis set to the 6-311 basis set via the ExtraBasis
keyword, the Xe basis functions will be pure functions.

3.3.2 Density Fitting

Gaussian 16 provides the density fitting approximation for pure DFT calculations [115, 116]. This ap-
proach expands the density in a set of atom-centered functions when computing the Coulomb interaction in-
stead of computing all of the two-electron integrals. It provides significant performance gains for pure DFT
calculations on medium sized systems too small to take advantage of the linear scaling algorithms without a
significant degradation in the accuracy of predicted structures, relative energies and molecular properties. Gaus-
sian 16 can generate an appropriate fitting basis automatically from the AO basis, or you may select one of the
built-in fitting sets.
The desired fitting basis set is specified as a third component of the model chemistry, as in this example:
# BLYP/TZVP/TZVPFit
Note that slashes must be used as the separator characters between the method, basis set, and fitting set
when a density fitting basis set is specified.
The following fitting sets keywords are available in Gaussian 16:
♢ DGA1 and DGA2 [108, 109]. DGA1 is available for H through Xe, and DGA2 is available for H, He
and B through Ne.
♢ SVPFit [117, 118] and Def2SV [94], corresponding to the SVP basis set.
♢ TZVPFit [117, 118] and Def2TZV [94], corresponding to the TZVP basis set.
♢ The W06 fitting set of Ahlrichs and coworkers [94, 95], designed for use with the Def2SVP, Def2TZV,
and QZVP basis sets.
♢ Fit: Select the fitting set corresponding to the specified basis set. If there is no such fitting set, the result
will produce an error.
♢ NoFit: Turn off fitting set use for this calculation. This keyword is used to override the DensityFit
keyword present within the Default.Route file.
♢ Auto: Generate a fitting set automatically (see below).

Density fitting sets can be generated automatically from the AO primitives within the basis set. This is re-
 3.4 Constructing Z-Matrices 23

quested using the Auto fitting set keyword. The program automatically truncates the set at a reasonable angular
momentum: the default is Max(MaxTyp+1,2*MaxVal), where MaxTyp is the highest angular momentum in the
AO basis, and MaxVal is the highest valence angular momentum. You can request that all generated functions
be used with Auto=All, or request those up to a certain level with Auto=N, where N is the maximum angular
momentum retained in the fitting functions. Finally, the PAuto form generates all products of AO functions on
one center instead of just squares of the AO primitives, but this is typically more functions than are needed.
By default, no fitting set is used. Density fitting basis sets may be augmented with the ExtraDensityBasis
keyword, defined in full with the Gen keyword, and optionally retrieved from the checkpoint file (use ChkBasis
to do so). The options to the DensityFit keyword can be used to control some aspects of the fitting set used
within calculations.
Density fitting can be made the default for jobs using pure DFT functionals by adding the DensityFit
keyword to the route section (-#-) line in the Default.Route file. Fitting is faster than doing the Coulomb term
exactly for systems up to several hundred atoms (depending on basis set), but is slower than exact Coulomb
using linear scaling techniques (which are turned on automatically with exact Coulomb) for very large systems.

3.4 Constructing Z-Matrices

This section presents a brief overview of traditional Z-matrix descriptions of molecular systems. There are
restrictions on the size of a Z-matrix: the maximum number of variables and the maximum number of atoms
within a calculation. These are set consistently for a maximum of 250,000 real atoms (including ghost but not
dummy atoms), and a maximum of 250,000 Z-matrix centers (atoms, ghost atoms, and dummy atoms).
Each line of a Z-matrix gives the internal coordinates for one of the atoms within the molecule. The most-
used Z-matrix format uses the following syntax:
Element-label, atom 1, bond-length, atom 2, bond-angle, atom 3, dihedral-angle [format-code]
Although these examples use commas to separate items within a line, any valid separator may be used.
Element-label is a character string consisting of either the chemical symbol for the atom or its atomic number.
If the elemental symbol is used, it may be optionally followed by other alphanumeric characters to create an
identifying label for that atom. A common practice is to follow the element name with a secondary identifying
integer: C1, C2, etc.
Atom1, atom2, atom3 are the labels for previously-specified atoms and are used to define the current atoms’
position. Alternatively, the other atoms’ line numbers within the molecule specification section may be used
for the values of variables, where the charge and spin multiplicity line is line 0.
The position of the current atom is then specified by giving the length of the bond joining it to atom1, the
angle formed by this bond and the bond joining atom1 and atom2, and the dihedral angle formed by the plane
containing atom1, atom2 and atom3 with the plane containing the current atom, atom1 and atom2. Note that
bond angles must be in the range 0o < angle < 180o . Dihedral angles may take on any value.
The optional format-code parameter specifies the format of the Z-matrix input. For the syntax being
described here, this code is always 0. This code is needed only when additional parameters follow the normal
Z-matrix specification data, as in an ONIOM calculation.
As an initial example, consider hydrogen peroxide. A Z-matrix for this structure would be:

H
O 1 0.9
24 Chapter 3. About Gaussian 16 Input

O 2 1.4 1 105.0
H 3 0.9 2 105.0 1 120.0

The first line of the Z-matrix simply specifies a hydrogen. The next line lists an oxygen atom and specifies
the internuclear distance between it and the hydrogen as 0.9 Angstroms. The third line defines another oxygen
with an O-O distance of 1.4 Angstroms (i.e., from atom 2, the other oxygen) and having an O-O-H angle (with
atoms 2 and 1) of 105 degrees. The fourth and final line is the only one for which all three internal coordinates
need be given. It defines the other hydrogen as bonded to the second oxygen with an H-O distance of 0.9
Angstroms, an H-O-O angle of 105 degrees and a H-O-O-H dihedral angle of 120 degrees.
Variables may be used to specify some or all of the values within the Z-matrix. Here is another version of
the previous Z-matrix:

H
O 1 R1
O 2 R2 1 A
H 3 R1 2 A 1 D
Variables:
R1 0.9
R2 1.4
A 105.0
D 120.0

Symmetry constraints on the molecule are reflected in the internal coordinates. The two H-O distances are
specified by the same variable, as are the two H-O-O bond angles. When such a Z-matrix is used for a geometry
optimization in internal coordinates (Opt=Z-matrix), the values of the variables will be optimized to locate the
lowest energy structure. For a full optimization (FOpt), the variables are required to be linearly independent
and include all degrees of freedom in the molecule. For a partial optimization (POpt), variables in a second
section (often labeled Constants:) are held fixed in value while those in the first section are optimized:

Variables:
R1 0.9
R2 1.4
A 105.0
Constants:
D 120.0

See the examples in the discussion of the Opt keyword for more information about optimizations in internal
coordinates.

Mixing Internal and Cartesian Coordinates

Cartesian coordinates are actually a special case of the Z-matrix, as in this example:

C 0.00 0.00 0.00

C 0.00 0.00 1.52
H 1.02 0.00 -0.39
H -0.51 -0.88 -0.39
3.4 Constructing Z-Matrices 25

H -0.51 0.88 -0.39

H -1.02 0.00 1.92
H 0.51 -0.88 1.92
H 0.51 0.88 1.92

It is also possible to use both internal and Cartesian coordinates within the same Z-matrix, as in this
example:

O 0 xo 0. zo
C 0 0. yc 0.
C 0 0. -yc 0.
N 0 xn 0. 0.
H 2 r1 3 a1 1 b1
H 2 r2 3 a2 1 b2
H 3 r1 2 a1 1 -b1
H 3 r2 2 a2 1 -b2
H 4 r3 2 a3 3 d3
Variables:
xo -1.
zo 0.
yc 1.
xn 1.
r1 1.08
r2 1.08
r3 1.02
a1 125.
a2 125.
d3 160.
b1 90.
b2 -90.

This Z-matrix has several features worth noting:

♢ The variable names for the Cartesian coordinates are given symbolically in the same manner as for
internal coordinate variables.
♢ The integer 0 after the atomic symbol indicates symbolic Cartesian coordinates to follow.
♢ Cartesian coordinates can be related by a sign change just as dihedral angles can.

Alternate Z-matrix Format

An alternative Z-matrix format allows nuclear positions to be specified using two bond angles rather than
a bond angle and a dihedral angle. This is indicated by a 1 in an additional field following the second angle
(this field defaults to 0, which indicates a dihedral angle as the third component):

C4 O1 0.9 C2 120.3 O2 180.0 0

C5 O1 1.0 C2 110.4 C4 105.4 1
C6 O1 R C2 A1 C3 A2 1
 26 Chapter 3. About Gaussian 16 Input

The first line uses a dihedral angle while the latter two use a second bond angle.

3.4.1 Dummy Atoms

This section will illustrate the use of dummy atoms within Z-matrices, which are represented by the pseudo
atomic symbol X. The following example illustrates the use of a dummy atom to fix the three-fold axis in C3v
ammonia:

N
X 1 1.
H 1 nh 2 hnx
H 1 nh 2 hnx 3 120.0
H 1 nh 2 hnx 3 -120.0

nh 1.0
hnx 70.0

The position of the dummy on the axis is irrelevant, and the distance 1.0 used could have been replaced
by any other positive number. hnx is the angle between an N-H bond and the threefold axis.
Here is a Z-matrix for oxirane:

X
C1 X halfcc
O X ox C1 90.
C2 X halfcc O 90. C1 180.0
H1 C1 ch X hcc O hcco
H2 C1 ch X hcc O -hcco
H3 C2 ch X hcc O hcco
H4 C2 ch X hcc O -hcco

halfcc 0.75
ox 1.0
ch 1.08
hcc 130.0
hcco 130.0

This example illustrates two points. First, a dummy atom is placed at the center of the C-C bond to help
constrain the cco triangle to be isosceles. ox is then the perpendicular distance from O to the C-C bond, and the
angles oxc are held at 90 degrees. Second, some of the entries in the Z-matrix are represented by the negative
of the dihedral angle variable hcco.
The following examples illustrate the use of dummy atoms for specifying linear bonds. Geometry op-
timizations in internal coordinates are unable to handle bond angles of l80 degrees which occur in linear
molecular fragments, such as acetylene or the C4 chain in butatriene. Difficulties may also be encountered
in nearly linear situations such as ethynyl groups in asymmetrical molecules. These situations can be avoided
by introducing dummy atoms along the angle bisector and using the half-angle as the variable or constant:
 3.4 Constructing Z-Matrices 27

N
C 1 cn
X 2 1. 1 90.
H 2 ch 3 90. 1 180.

cn 1.20
ch 1.06

Similarly, in this Z-matrix intended for a geometry optimization, half represents half of the N-C-O angle
which is expected to be close to linear. Note that a value of half less than 90 degrees corresponds to a cis
arrangement:

N
C 1 cn
X 2 1. 1 half
O 2 co 3 half 1 180.0
H 4 oh 2 coh 3 0.0

cn 1.20
co 1.3
oh 1.0
half 80.0
coh 105.

3.4.2 Model Builder

The model builder is another facility within Gaussian for quickly specifying certain sorts of molecular
systems [119]. It is requested with the ModelA or ModelB options, and it requires additional input in a separate
section within the job file.
The basic input to the model builder is called a short formula matrix, a collection of lines, each of which
defines an atom (by atomic symbol) and its connectivity, by up to six more entries. Each of these can be either
an integer, which is the number of the line defining another explicitly specified atom to which the current atom
is bonded, or an atomic symbol (e.g. H, F) to which the current atom is connected by a terminal bond, or a
symbol for a terminal functional group which is bonded to the current atom. The functional groups currently
available are OH, NH2, Me, Et, NPr, IPr, NBu, IBu, and TBu.
The short formula matrix also implicitly defines the rotational geometry about each bond in the following
manner. Suppose atoms X and Y are explicitly specified. Then X will appear in row Y and Y will appear in row
X. Let I be the atom to the right of X in row Y and J be the atom to the right of Y in row X. Then atoms I and
J are put in the trans orientation about the X-Y bond. The short formula matrix may be followed by optional
lines modifying the generated structure. There are zero or more of each of the following lines, which must be
grouped together in the order given here:
AtomGeom,I,Geom:
Normally the local geometry about an atom is defined by the number and types of bond about the atom
(e.g., carbon in methane is tetrahedral, in ethylene is trigonal, etc.). All bond angles at one center must
 28 Chapter 3. About Gaussian 16 Input

be are equal. The AtomGeom line changes the value of the bonds at center I. Geom may be the angle as
a floating point number, or one of the strings Tetr, Pyra, Trig, Bent, or Line.
BondRot,I,J,K,L,Geom:
This changes the orientations of the I-J and K-L bonds about the J-K bond. Geom is either the dihedral
angle or one of the strings Cis (≥0), Trans (≥180), Gaup (≥+60), or Gaum (≥-60).
BondLen,I,J,NewLen:
This sets the length of the I-J bond to NewLen (a floating point value).

The model builder can only build structures with atoms in their normal valencies. If a radical is desired, its
extra valence can be effectively “tied down” using dummy atoms, which are specified by a minus sign before
the atomic symbol (e.g., -H). Only terminal atoms can be dummy atoms.
The two available models (A and B) differ in that model A takes into account the type (single, double,
triple, etc.) of a bond in assigning bond lengths, while model B bond lengths depend only on the types of the
atoms involved. Model B is available for all atoms from H to Cl except He and Ne. If Model A is requested
and an atom is used for which no Model A bond length is defined, the appropriate Model B bond length is used
instead.

3.5 Multistep Jobs

Multiple Gaussian jobs may be combined within a single input file. The input for each successive job is
separated from that of the preceding job step by a line of the form:
--Link1--
Here is an example input file containing two job steps:

%Chk=freq
# HF/6-31G(d) Freq

Frequencies at STP

Molecule specification

--Link1--
%Chk=freq
%NoSave
# HF/6-31G(d) Geom=Check Guess=Read Freq=(ReadFC,ReadIsotopes)

Frequencies at 300 K

charge and spin

300.0 2.0
Isotope specifications
 3.6 Section Ordering 29

This input file computes vibrational frequencies and performs thermochemical analysis at two different
temperatures and pressures: first at 298.15 K and 1 atmosphere, and then again at 300 K and 2 atmospheres.
Note that a blank line must precede the --Link1-- line.

3.6 Section Ordering

Section Keywords Final

blank line?
Link 0 commands % commands no
Route Section (# lines) all yes
Extra Overlays ExtraOverlays yes
Title section all except Geom=AllCheck yes
Molecule specification all except Geom=AllCheck yes
Connectivity specifications Geom=Connect or ModConnect yes
Alterations to frozen atoms Geom=ReadOpt yes
Modifications to coordinates Opt=ModRedundant yes
2nd title and molecule specification Opt=QST2 or QST3 yes for both
Connectivity specs. for 2nd set of coordinates Geom=Connect or ModConnect and Opt=QST2 or QST3 yes
2nd Alterations to frozen atoms Geom=ReadOpt yes
Modifications to 2nd set of coordinates Opt=QST2 or QST3 yes
3rd title and initial TS structure Opt=QST3 yes for both
Connectivity specs. for 3rd set of coords. Geom=Connect or ModConnect Opt=(ModRedun, QST3) yes
3rd Alterations to frozen atoms Geom=ReadOpt yes
Modifications to 3rd set of coordinates Opt=(ModRedun, QST3) yes
PDB secondary structure information automatic if residue info in molecule specification yes
Atomic masses ReadIsotopes option yes
External External=(· · · ,ReadInput) yes
Molecular Mechanics parameters HardFirst, SoftFirst, SoftOnly, Modify options yes
Frequency of interest CPHF=RdFreq or Freq=ROA yes
Background charge distribution Charge yes
BOMD/ADMP input (1 or more sections) ADMP and BOMD required input and ReadVelocity, yes
ReadMWVelocity options
PCM input SCRF=(ExternalIteration,Read) and yes
(SCRF=ONIOMPCM=A,Read)
Coordinates for IRC table IRC(Report=Read) yes
Harmonic constraints Geom=ReadHarmonic yes
Semi-empirical parameters (Gaussian format) Input option and Both options yes
Semi-empirical parameters (MOPAC format) MOPACExternal and Both options yes
Basis set specification Gen, GenECP, ExtraBasis yes
Basis set alterations Massage yes
Finite field coefficients Field=Read yes
ECP specification Pseudo=Cards, GenECP yes
Density fitting basis set specification ExtraDensityBasis yes
PCM solvation model input SCRF=Read yes
DFTB parameters DFTB yes
Source for initial guess Guess=Input yes
30 Chapter 3. About Gaussian 16 Input

Symmetry types to combine Guess=LowSymm no

Orbital specifications (separate α & β ) Guess=Cards yes
Orbital alterations (separate α & β ) Guess=Alter yes
Orbital reordering (separate α & β ) Guess=Permute yes
# Orbitals/GVB pair GVB no
Weights for CAS state averaging CAS=StateAverage yes
States of interest for spin orbit coupling CASSCF=SpinOrbit no
Orbital freezing information ReadWindow options yes
EPT orbitals to refine EPT=ReadOrbitals yes
Atoms list for spin-spin coupling constants NMR=ReadAtoms yes
Alternate atomic radii Pop=ReadRadii or ReadAtRadii yes
Antechamber output file Pop=MK IOp(6/50=1) yes
Data for electrostatic properties Prop=Read or Opt yes
NBO input Pop=NBORead or Pop=NBO6Read no
Harmonic Normal Mode selection Freq=SelectNormalModes yes
Hindered Rotor input Freq=ReadHindered yes
Anharmonic Normal Mode selection Freq=SelectAnharmonicModes yes
Input for Anharmonic Freq=ReadAnharmonic yes
Input for FCHT Freq=ReadFCHT yes
Atom list for Pickett file generation Output=Pickett no
ACID output filename NMR=CGST IOp(10/93=1) yes
PROAIMS output filename Output=WFN no
Matrix element filename Output=MatrixElement or Output=Raw yes
 4. Running Gaussian 16

4.1 Preliminaries
4.1.1 System Requirements
♢ The Gaussian directories will require about 2-3 GB of disk space for the executables, depending on the
computer system.
♢ The default memory allocation in Gaussian 16 is 800 MB. The large fixed dimensions in the program
necessitate a swap space size of 1 - 2 GB. Of course, additional swap space will be required if more
memory is requested in a job by using the %Mem Link 0 command, or via the -M- command in the
Default.Route file. These requirements are for each simultaneously executing job.
♢ Refer to the platform list which comes with the CD. The most recent version of this document can always
be found at www.gaussian.com/g16/g16_plat.pdf.

4.1.2 Configuring the Gaussian Execution Environment

Gaussian locates executables and creates scratch files in directories specified by several environment vari-
ables. The user is responsible for defining two of them:
♢ g16root: Indicates the directory where the g16 subdirectory resides (i.e., the directory above it).
♢ GAUSS_SCRDIR: Indicates the directory which should be used for scratch files.

4.1.3 Initialization Files

The Gaussian system includes initialization files to set up the user environment for running the program.
These files are:

$g16root/g16/bsd/g16.login C shell
$g16root/g16/bsd/g16.profile Bourne shell

It is customary to include lines like the following within the .login or .profile file for Gaussian users:

.login files:
 32 Chapter 4. Running Gaussian 16

setenv g16root /location

source $g16root/g16/bsd/g16.login
setenv GAUSS_SCRDIR /path

.profile files:
export g16root=/location
. $g16root/g16/bsd/g16.profile
export GAUSS_SCRDIR=/location

Once things are set up correctly, the g16 command is used to execute Gaussian 16.

4.1.4 Environment Variables Reference

The environment variables created by g16.login and g16.profile include:
♢ GAUSS_EXEDIR: Specifies the directories in which the Gaussian images are stored. By default it in-
cludes the main directory $g16root/g16 and several alternate directories.
♢ GAUSS_ARCHDIR: Specifies the directory in which the main site-wide archive file is kept, and into
which temporary archive files should be placed if the main archive is unavailable. It defaults to $g16root/g16/arch
if unset.
♢ G16BASIS: The directory which contains files specifying the standard Gaussian internally stored basis
sets, as well as some additional basis sets in the form of general basis set input. This environment variable
is provided for convenience and is designed for use with the @ include mechanism.
♢ Gaussian defaults may be set via environment variables of the form GAUSS_xDEF. See the documenta-
tion for the Default.Route file for details.
♢ Network/cluster parallel calculations using Linda may also use the GAUSS_LFLAGS environment vari-
able to pass options to the Linda process. See Parallel Jobs for details.

4.2 Running under UNIX

Once all input and resource specifications are prepared, you are ready to run the program. Gaussian 16
may be run interactively using one of two command styles:
g16 job-name
g16 <input-file >output-file
In the first form, the program reads input from job-name.gjf and writes its output to job-name.log. When
job-name is not specified, the program reads from standard input and writes to standard output, and these can
be redirected or piped in the usual UNIX fashion. Either form of command can be forced in the background in
the same manner as any shell command using the ampersand.

4.2.1 Scripts and Gaussian

Scripts designed to run Gaussian 16 may also be created in several ways. First, g16 commands like those
above may be included in a shell script. Secondly, actual Gaussian input may be included in the script using
the « construct:
#!/bin/sh
4.2 Running under UNIX 33

g16 <<END >water.log

%Chk=water
# RHF/6-31G(d)

water energy

0 1
O
H 1 1.0
H 1 1.0 2 120.0

END
echo "Job done."

All lines preceding the string following the « symbols are taken as input to the g16 command.
Finally, loops may be created to run several Gaussian jobs in succession. For example, the following
script runs all of the Gaussian input files specified as its command line arguments, and it maintains a log of its
activities in the file Status:
#!/bin/sh

echo "Current Job Status:" > Status

for file in $argv; do
nam=‘echo $file | sed ’s/\..*$//’‘
echo "Starting file $file at ‘date‘" >> Status
g16 < $file > $nam.log
echo "$file Done with status $status" >> Status
done
echo "All Done." >> Status

The following more complex script creates Gaussian input files on-the-fly from the partial input in the files
given as the script’s command line arguments. The latter are lacking full route sections; their route sections
consist of simply a # sign or a # line containing special keywords needed for that molecular system, but no
method, basis set, or calculation type.
The script creates a two-step job for each partial input file – a Hartree-Fock optimization followed by an
MP2 single point energy calculation – consisting of both the literal commands included in the script and the
contents of each file specified at script execution time. It includes the latter by exploiting the Gaussian 16
include file mechanism:
#!/bin/sh

echo "Current Job Status:" > Status

for file in $argv; do
echo "Starting file $file at ‘date‘" >> Status
nam=‘echo $file | sed ’s/\..*$//’‘
g16 <<END> $nam.log
%Chk=$nam
# HF/6-31G(d) FOpt
@$file/N

--Link1--
 34 Chapter 4. Running Gaussian 16

%Chk=$nam
%NoSave
# MP2/6-31+G(d,p) SP Guess=Read Geom=AllCheck
END
echo "$file Done with status $status" >> Status
done # end of for...do
echo "All Done." >> Status

4.2.2 Batch Execution with NQS

Gaussian may be run using the NQS batch facility on those UNIX systems that support it. The subg16
command, defined in the initialization files, submits an input file to a batch queue. It has the following syntax:
subg16 queue-name job-name [-scrdir dir1] [-exedir dir2] [-p n]
The two required parameters are the queue and job names. Input is taken from job-name.gjf and output
goes to job-name.log, just as for interactive runs. The NQS log file is sent to job-name.batch-log.
The optional parameters -scrdir and -exedir are used to override the default scratch and executable directo-
ries, respectively. Any other parameters are taken to be NQS options. In particular, -p n can be used to set the
priority within the queue to n. This is priority for initiation (1 being lowest), and does not affect the run-time
priority.
To submit an NQS job from an interactive session, a file like the following should be created (with filename
name.job):

# QSUB -r name -o name.out -eo

# QSUB -lt 2000 -lT 2100
# QSUB -lm 34mw -lM 34mw
g16 <name.gjf

where name should be replaced with a name that is appropriate to your calculation. The first line names the
running job, names the output file, and causes errors to be included in the output file. The time parameters are
different to allow addition of job control for cleanup, (for example, archiving the checkpoint file in the event
that the job exceeds its time limit). The memory parameters are used both for initial scheduling of your job for
execution and by the program to determine dynamic memory use.
This job would then be submitted by issuing the command,
$ qsub name.job
and the output would be placed in your current working directory.

4.3 Scratch Files

Gaussian uses several scratch files in the course of its computation. They include:
♢ The Checkpoint file: name.chk
♢ The Read-Write file: name.rwf
♢ The Two-Electron Integral file: name.int (empty by default)
♢ The Two-Electron Integral Derivative file: name.d2e (empty by default)
♢ The Scratch file: name.skr
 4.3 Scratch Files 35

By default, scratch files are deleted at the end of a successful run. However, you may wish to save the
checkpoint file for later use in another Gaussian job, for use by a visualization program, to restart a failed job,
and so on. This may be accomplished by naming the checkpoint file, providing an explicit name and/or location
for it, via a %Chk command within the Gaussian input file. Here is an example:
%Chk=water
This command, which is placed at the very beginning of the input file – before the route section – gives
the checkpoint file the name water.chk, overriding the usual generated name and causing the file to be saved at
job conclusion. In this case, the file will reside in the current directory. However, a command like this one will
specify an alternate directory location as well as filename:
%Chk=/chem/scratch2/water
While scratch files are deleted automatically for successful jobs, they are not deleted when a job is killed
externally or otherwise terminates abnormally. Consequently, leftover files may accumulate in the scratch
directory. An easy method for avoiding excessive clutter is to have all users share a common scratch directory
and to have that scratch directory cleared at system boot time by adding an rm command to the appropriate
system boot script (e.g., /etc/rc or one of the files under /etc/rc.d/rc3.d). If the NQS batch system is in use,
clearing the scratch directory should also be done before NQS is started, ensuring that no jobs are using the
directory when it is cleared.
If disk space in the scratch directory is limited, but space is available elsewhere on the system, you may
want to split the various scratch files among several disk locations. The following commands allow you to
specify the names and locations of the other scratch files:

%RWF=path Read-Write file

%Int=path Integral file
%D2E=path Integral Derivative file

In general, the read-write file is by far the largest, and so it is the one for which an alternate location is
most often specified.

4.3.1 Splitting Scratch Files Across Disks

An alternate syntax is provided for splitting the read-write file, the Integral file, and/or the Integral Deriva-
tive file among two or more disks (or file systems). Here is the syntax for the %RWF command:
%RWF=loc1,size1,loc2,size2, · · ·
where each loc is a directory location or a file pathname, and each size is the maximum size for the file segment
at that location. Gaussian will automatically generate unique filenames for any loc which specifies a directory
only. On UNIX systems, directory specifications (without filenames) must include a terminal slash.
By default, the sizes are in units of 8-byte words. This value may also be followed by KB, MB, GB, TB,
KW, MW, GW or TW (without intervening spaces) to specify units of kilo-, mega-, giga-, or tera-bytes or
words. Note that 1 MB = 10242 bytes = 1,048,576 bytes (not 1,000,000 bytes).
A value of -1 for any size parameter indicates that any and all available space may be used, and a value of
0 says to use the current size of an existing segment. -1 is useful only for the last file specified, for which it is
the default.
For example, the following directive splits the read-write file across three disks:
 36 Chapter 4. Running Gaussian 16

%RWF=/dalton/s0/,4GB,/scratch/,3GB,/temp/s0/my_job,-1
The maximum sizes for the file segments are 4 GB, 3 GB, and unlimited, respectively. Gaussian will
generate names for the first two segments, and the third will be given the name my_job. Note that the directory
specifications include terminal slashes.
Due to limitations in current UNIX implementations, -1 should be used with caution, as it will attempt
to extend a file segment beyond all remaining disk capacity on these systems; using it will also have the side
effect of keeping any additional file segments included in the list from ever being used.
Gaussian 16 can address single scratch files of up to 16 GB under 32-bit operating systems. There is no
need to split scratch files into 2 GB files. The 16 GB total scratch space limit is inherent in 32-bit integers,
however, and splitting the scratch file will not overcome it.

4.3.2 Saving and Deleting Scratch Files

By default, unnamed scratch files are deleted at the end of the Gaussian run, and named files are saved.
The %NoSave command may be used to change this default behavior. When this directive is included in an
input file, named scratch files whose directives appear in the input file before %NoSave will be deleted at the
end of a run (as well as all unnamed scratch files). However, if the % directive naming the file appears after the
%NoSave directive, the file will be retained. For example, these commands specify a name for the checkpoint
file, and an alternate name and directory location for the read-write file, and cause only the checkpoint file to
be saved at the conclusion of the Gaussian job:

%RWF=/chem/scratch2/water Files to be deleted go here.

%NoSave
%Chk=water Files to be saved go here.

Note that all files are saved when a job terminates abnormally.

4.4 Memory Use

The %Mem command controls the amount of dynamic memory to be used by Gaussian. By default, 800
MB (100MW) are used. This can be changed to a different value by specify a number followed by KB, MB,
GB, TB, KW, MW, GW or TW (without intervening spaces) to specify units of kilo-, mega-, giga-, or tera-bytes
or words. The default units are megawords.
For example, the following command also sets the amount of dynamic memory to 1 GB:
%Mem=1GB
Even larger allocations may be needed for very large direct SCF calculations, at least 3N 2 words, where
N is the number of basis functions.
Warning: Requesting more memory than the amount of physical memory actually available on a computer
system will lead to very poor performance.
If Gaussian is being used on a machine with limited physical memory, so that the default amount is not
available, the default algorithms as well as the default memory allocation will be set appropriately during
installation.
 4.5 Parallel Jobs 37

4.5 Parallel Jobs

4.5.1 Shared-Memory Multiprocessor Parallel Execution
Gaussian defaults to execution on only a single processor. If your computer system has multiple proces-
sors/cores, and parallel processing is supported in your version of Gaussian, you may the specific CPUs on
which to run with the %CPU link 0 command. For example, the following specifies that the program should
run on the first 5 cores of a hexacore system (reserving one core for other use):
%CPU=0,1,2,3,4
The node list can also be specified as a range (e.g., 0-5). Ranges can also be followed by a suffix of the
form /n, which says to use every nth processor in the range (e.g., /2 specifies every second processor/core).
The older %NProcShared link 0 command can be used to specify the total number of processors on which
to execute (leaving the selection of processors to the operating system). Clearly, the number of processors
requested should not exceed the number of processors available, or a substantial decrease in performance will
result.

4.5.2 Cluster/Network Parallel Execution

Parallel jobs can run across discrete systems in a LAN or nodes within a cluster using the Linda parallel
execution environment. HF, CIS=Direct, and DFT calculations are Linda parallel, including energies, optimiza-
tions, and frequencies. TDDFT energies and gradients and MP2 energies and gradients are also Linda parallel.
Portions of MP2 frequency and CCSD calculations are Linda parallel, but others are only SMP-parallel.
For a Linda parallel job to execute successfully, the following conditions must be true:
♢ You have already executed the appropriate Gaussian 16 initialization file ($g16root/g16/bsd/g16.login or
$g16root/g16/bsd/g16.profile). Test this by running a serial Gaussian 16 calculation on the master node.
♢ The directory $g16root/g16 is accessible on all nodes.
♢ The LD_LIBRARY_PATH environment variable is set to locate the Linda shared libraries.
♢ Local scratch space is available on each node if needed (via the GAUSS_SCRDIR environment variable).
♢ All nodes on which the program will run are trusted by the current host. You should be able to login
remotely with the rsh or ssh command without having to give a password to each of them. Contact your
system administrator about configuring security for the nodes in the network.
Each of these nodes needs to have some access to the Gaussian 16 directory tree. The recommended
configuration is to have G16 on each system that will be used for the parallel job. Note that the Linda binaries
need to have the same path on each machine. If this is not feasible, the G16 tree can be made accessible via an
NFS-mounted disk which is mounted in an identical location on all nodes.
For MP2 calculations, each node must also have some local disk where Gaussian 16 can put temporary
files. This is defined as usual via the GAUSS_SCRDIR environment variable, which should be set in the .cshrc
or .profile for your account on each node.
The %LindaWorkers directive is used to specify computers where Linda worker processes should run. It
has the following syntax:
%LindaWorkers=node1[:n1][,node2[:n2]] [· · · ]
This lists the TCP node name for each node to use. By default, one Linda worker is started on each node,
but the optional value allows this to be varied. A worker is always started on the node where the job is started
(the master node) whether or not it appears in the node list. For example, the following directive causes a
 38 Chapter 4. Running Gaussian 16

network parallel job to be run across the specified 5 nodes. Nodes hamlet and ophelia will each run two worker
processes.
%LindaWorkers=hamlet:2,ophelia:2,laertes,horatio,lear
By default, Linda uses rsh to communicate between nodes. You can use ssh instead by including the
following Link 0 option within the job file:
%UseSSH
Finally, you can also create a configuration file on the master node named .tsnet.config which contains the
following line:
Tsnet.Node.lindarsharg: ssh
This will cause ssh to be used instead. This file can be placed in your home directory or in the directory
from which you launch calculations. The %UseRSH directive is also supported; its purpose is to specify the
use of rsh when ssh has been made the default in Default.Route (see below).
Note that in all cases passwordless ssh logins must already be configured from the master to all worker
nodes.
A few Linda options that are sometime useful are:

-v Display verbose messages

-vv Display very verbose messages

You can use the GAUSS_LFLAGS environment variable to set them. For example, one could turn on very
verbose Linda output using:
$ export GAUSS_LFLAGS="-vv"
The verbose option may also be set by including the %DebugLinda link 0 command.
There are many other Linda options but most of them are not used by Gaussian. The -opt option form can
be used in GAUSS_LFLAGS to invoke any valid .tsnet.config file directive. Note that Gaussian 16/Linda does
not use the native Linda resources minworker and maxworker.

4.5.3 Combining Shared-Memory and Network/Cluster Parallelism

The following link 0 commands start a four-way parallel worker on hosts norway and italy and two such
worker processes on spain:

%CPU=0-3
%LindaWorkers=norway,italy,spain:2

These link 0 commands are appropriate when norway and italy are 4 processor/core computers, and spain
is an 8 processor/core computer.
It is always best to use SMP-parallelism within nodes and Linda only between nodes. For example on a
cluster of 4 nodes, each with a dual quad-core EM64T, one should use the following (rather than using more
than one Linda worker per node):

%CPUs=0-7
%LindaWorkers=node1,node2,node3,node4
 4.6 Using GPUs 39

4.5.4 Starting and Monitoring Parallel Gaussian 16 Jobs

Once the proper setup is completed, the g16 command is used as usual to initiate a parallel Gaussian 16
job:
$ g16 input.gjf &
In the case of distributed parallel calculations, Gaussian 16 will start the master and worker processes as
needed.
Linda parallel links have filenames of the form *.exel. Using the top or other commands on worker nodes
will let you see lxxx.exel when it starts.
The relevant measure of performance for a parallel calculation is the elapsed or wall clock time. The
easiest way to check this is to use an external monitor like time, times, or timex, e.g.
$ times g16 input.gjf &
This command will report elapsed, CPU and system times for the Gaussian job. Note that the last two are
relevant only on the master node, and similar amounts of CPU and system time are expended on each node.
The parallel speedup is the ratio of the elapsed time running a serial job and the elapsed time for the parallel
job.

4.6 Using GPUs

Gaussian 16 can use NVIDIA K40, K80 and P100 GPUs under Linux (the latter starting with Rev. B.01).
Earlier GPUs do not have the computational capabilities or memory size to run the algorithms in Gaussian 16.

4.6.1 Allocating Memory for Jobs

Allocating sufficient amounts of memory to jobs is even more important when using GPUs than for CPUs,
since larger batches of work must be done at the same time in order to use the GPUs efficiently. The K40 and
K80 units can have up to 16 GB of memory. Typically, most of this should be made available to Gaussian.
Giving Gaussian 8-9 GB works well when there is 12 GB total on each GPU; similarly, allocating Gaussian
11-12 GB is appropriate for a 16 GB GPU. In addition, at least an equal amount of memory must be available
for each CPU thread which is controlling a GPU.

4.6.2 About Control CPUs

When using GPUs, each GPU must be controlled by a specific CPU. The controlling CPU should be as
physically close as possible to the GPU it is controlling. GPUs cannot share controlling CPUs. Note that CPUs
used as GPU controllers cannot be used as compute nodes as well.
The hardware arrangement on a system with GPUs can be checked using the nvidia-smi utility. For
example, this output is for a machine with two 16-core Haswell CPU chips and four K80 boards, each of which
has two GPUs:

GPU0 GPU1 GPU2 GPU3 GPU4 GPU5 GPU6 GPU7 CPU Affinity
GPU0 X PIX SOC SOC SOC SOC SOC SOC 0-15 cores on first chip
GPU1 PIX X SOC SOC SOC SOC SOC SOC 0-15
GPU2 SOC SOC X PIX PHB PHB PHB PHB 16-31 cores on second chip
GPU3 SOC SOC PIX X PHB PHB PHB PHB 16-31
GPU4 SOC SOC PHB PHB X PIX PXB PXB 16-31
 40 Chapter 4. Running Gaussian 16

GPU5 SOC SOC PHB PHB PIX X PXB PXB 16-31

GPU6 SOC SOC PHB PHB PXB PXB X PIX 16-31
GPU7 SOC SOC PHB PHB PXB PXB PIX X 16-31

The important part of this output is the CPU affinity. This example shows that GPUs 0 and 1 (on the first
K80 card) are connected to the CPUs on chip 0 while GPUs 2-7 (on the other two K80 cards) are connected to
the CPUs on chip 1.

4.6.3 Specifying GPUs & Control CPUs for a Gaussian Job

The GPUs to use for a calculation and their controlling CPUs are specified with the %GPUCPU Link 0
command. This command takes one parameter:
%GPUCPU=gpu-list=control-cpus
where gpu-list is a comma-separated list of GPU numbers, possibly including numerical ranges (e.g., 0-4,6),
and control-cpus is a similarly-formatted list of controlling CPU numbers. The corresponding items in the two
lists are the GPU and its controlling CPU.
For example, on a 32-processor system with 6 GPUs, a job which uses all the CPUs – 26 CPUs doing parts
of the computation and 6 CPUs used for controlling GPUs – would use the following Link 0 commands:
%CPU=0-31 Control CPUs are included in this list.
%GPUCPU=0,1,2,3,4,5=0,1,16,17,18,19
These command state that CPUs 0-31 will be used in the job (although not all of them will be used for
computation). GPUs 0 through 5 will be used, with GPU0 controlled by CPU 0, GPU1 controlled by CPU
1, GPU2 controlled by CPU 16, GPU3 controlled by CPU 17, and so on. Note that the controlling CPUs are
included in %CPU.
In the preceding example, the GPU and CPU lists could be expressed more tersely as:

%CPU=0-31
%GPUCPU=0-5=0-1,16-19

Normally one uses consecutive processors in the obvious way, but things can be associated differently
in special cases. For example, suppose the same machine already had a job using 6 CPUs, running with
%CPU=16-21. Then, in order to use the other 26 CPUs with 6 controlling GPUs, you would specify:

%CPU=0-15,22-31
%GPUCPU=0-5=0-1,22-25

This job would use a total of 26 processors, employing 20 of them for computation, along with the six
GPUs controlled by CPUs 0, 1, 22, 23, 24 and 25 (respectively).
In [REV B], the lists of CPUs and GPUs are both sorted and then matched up. This ensures that the the
lowest numbered threads are executed on CPUs that have GPUs. Doing so ensures that if a part of a calcula-
tion has to reduce the number of processors used (i.e., because of memory limitations), it will preferentially
use/retain the threads with GPUs (since it removes threads in reverse order).

4.6.4 GPUs and Overall Job Performance

GPUs are effective for larger molecules when doing DFT energies, gradients and frequencies (for both
ground and excited states), but they are not effective for small jobs. They are also not used effectively by
 4.7 g16 Command Line Options 41

post-SCF calculations such as MP2 or CCSD.

Each GPU is several times faster than a CPU. However, on modern machines, there are typically many
more CPUs than GPUs. The best performance comes fromm using all the CPUs as well as the GPUs.
In some circumstances, the potential speedup from GPUs can be limited because many CPUs are also used
effectively by Gaussian 16. For example, if the GPU is 5x faster than a CPU, then the speedup of using the
GPU versus the CPU alone would be 5x. However, the potential speedup resulting from using GPUs on a larger
computer with 32 CPUs and 8 GPUs is 2x:
Without GPUs: 32*1 = 32
With GPUs: (24*1) + (8*5) = 64 Remember that control CPUs are not used for computation.
Speedup: 64/32 = 2

Allocation of memory
GPUs can have up to 16 GB of memory. One typically tries to make most of this available to Gaussian.
Be aware that there must be at least an equal amount of memory given to the CPU thread running each GPU
as is allocated for computation. Using 8-9 GB works well on a 12 GB GPU, or 11-12 GB on a 16 GB GPU
(reserving some memory for the system). Since Gaussian gives equal shares of memory to each thread, this
means that the total memory allocated should be the number of threads times the memory required to use a
GPU efficiently. For example, when using 4 CPUs and 2 GPUs each with 16 GB of memory, you should use 4
× 12 GB of total memory. For example:

%Mem=48GB
%CPU=0-3
%GPUCPU=0-1=0,2

You will need to analyze the characteristics of your own environment carefully when making decisions
about which processors and GPUs to use and how much memory to allocate.

4.6.5 GPUs in a Cluster

GPUs on nodes in a cluster can be used. Since the %CPU and %GPUCPU specifications are applied to
each node in the cluster, the nodes must have identical configurations (number of GPUs and their affinity to
CPUs); since most clusters are collections of identical nodes, this is not usually a problem.

4.7 g16 Command Line Options

The g16 command accepts the following options on all platforms:

Option Description Example

-r=list Route section default keyword list -r="Int=SuperFine Freq=HPModes"
-m=value Memory amount for Gaussian jobs -m=200GB
-c=list Processor/core list for multiprocessor parallel jobs -c="0-31"
-g=list GPUs=Cores list for GPU parallel jobs -g="0-8=0-6,31,32"
- Command to use for starting workers for network par- -s=ssh
s=command allel jobs: one of ssh or rsh
-w=list List of hostnames for network parallel jobs. -w="apple,banana,cherry"
 42 Chapter 4. Running Gaussian 16

-p Number of processors/cores for multiprocessor paral-

lel jobs. Deprecated; use -c.
-l Number of nodes for network parallel jobs. Depre-
cated; use -w.
-x Complete route for the job (the route is not read from -x="# b3lyp/6-31G(d) opt freq"
the input file).
-y Checkpoint file. -y="$HOME/project3/gfp.chk"
-fchk Generate the specified formatted checkpoint file as -fchk=/plots/job8.fchk
well as a binary one, and update it each time the
checkpoint file is updated.
-z Read-write file. -z=/scratch2/fox7.rwf
-ic Existing checkpoint file from which to read input. -ic=job6
-im Matrix element file from which to read input. -im=fox7.dat
-im4 Matrix element file using 4-byte integers from which -im4=fox12
to read input.
-ir Raw matrix element file from which to read input. -ir=job6
-im4 Raw matrix element file using 4-byte integers from -ir4=job27
which to read input.
-oc Output checkpoint file. Generally redundant with -y.
-om Output matrix element file. -om=job16new_mat
-om4 Output matrix element file using 4-byte integers. -om4=job32mat
-or Output raw matrix element file. -or=job7_raw
-or4 Output raw matrix element file using 4-byte integers. -or4=proteins_rawdat

Note that the quotation marks are often required around option values to avoid modification by the shell.

4.8 Setting Defaults

Default values for the Link 0 commands mentioned here can be set in the Default.Route file. They can
also be set via environment variables and on the command line. The following table lists these equivalences:

Link 0 Default.Route Option Env. Variable Description

%CPU -C- -c=list GAUSS_CDEF Processor/core list for multiprocessor parallel
jobs.
%GPUCPU -G- -g=list GAUSS_GDEF GPUs=Cores list for GPU parallel jobs.
%Mem -M- -m=value GAUSS_MDEF Memory amount for Gaussian jobs.
%NProcShared -P- -p=n GAUSS_PDEF Number of processors/cores for multiprocessor
parallel jobs. Superseded in most cases by %CPU.
%UseRSH -S- rsh -s=rsh GAUSS_SDEF=rsh Use rsh to start workers for network parallel jobs.
%UseSSH -S- ssh -s=ssh GAUSS_SDEF=ssh Use ssh to start workers for network parallel jobs.
%LindaWorkers -W- -w=list GAUSS_WDEF List of hostnames for network parallel jobs.
%DebugLinda GAUSS_LFLAGS=-v Enable verbose Linda output.

Quotation marks will be required for command line argument values whenever special characters are
 4.9 The Default.Route File 43

included within them. Note that the environment variable specifications above use bash syntax.
Full documentation for all Link 0 command is available in Link0.

4.9 The Default.Route File

Depending on the characteristics of a particular computer system, it is sometimes necessary for perfor-
mance reasons to override some of the defaults built into the program. This can be done by creating a cus-
tomization file. On UNIX-based systems, this file is named Default.Route, residing in $g16root/g16. Under
Windows, the Gaussian defaults file is Default.Rou, and it is located in the Gaussian 16W scratch subdirectory
(e.g., C:\G16W\scratch). The format of the file is the same on all computer systems.
The following subsections describe the types of information which can be supplied in the defaults file.

4.9.1 Description
Route Defaults

These parameters are introduced by -#- and have the same form as normal route section commands. For
example, this line will set the default SCF algorithm to the conventional (non-direct) algorithm:
-#- SCF=Conventional
There may be more than one -#- line in the file.
Commands listed in Default.Route change only the defaults; they are overridden by anything specified in
the route section of an input file. Thus, if the Default.Route contains:
-#- MP2=NoDirect
and the route section contains the MP2 keyword, then the conventional MP2 algorithm will be used. However,
if the route section contains the MP2=Direct keyword, then the direct algorithm will be used.
The directive -R- is a synonym for -#-.

Maximum Disk Usage

You will usually want to specify the amount of scratch disk space available via the MaxDisk keyword in
the Default.Route file. For example, the following line sets MaxDisk to 2 GB:
-#- MaxDisk=2GB
The amount of available disk space is given in 8-byte words by default. This value may also be followed
by KB, MB, GB, TB, KW, MW, GW, or TW (without intervening spaces) to specify units of kilo-, mega-,
giga-, or tera-bytes/words.
The scratch disk space is set unlimited by default: i.e., MaxDisk=-1. In other words, it is assumed that
enough disk space is available to perform a given calculation with no redundant work. Thus, specifying the
amount of available memory and disk is by far the most important way of optimizing performance for your
calculations. Doing so allows the program to decide between the various available algorithms, selecting the
optimal one for your particular system configuration. Keep in mind that the more disk space available, the
faster the evaluation, especially for MP2.

Memory Defaults

Gaussian jobs which unwisely use excessive memory can cause severe difficulties on the system. The
memory directive -M- enforces a default dynamic memory limit. For example, the following line sets default
 44 Chapter 4. Running Gaussian 16

memory use to 3GB:

-M- 3GB
The amount of available memory is given in 8-byte words (default); this value may also be followed by
KB, MB, GB, TB, KW, MW, GW, or TW (without intervening spaces) to specify units of kilo-, mega-, giga-,
or tera-bytes or words. The default memory size is 800 MB (100 MW). Note that this limit can be overridden
with the %Mem Link 0 command.
The memory directive -U- sets default memory to use in utilities such as formchk and freqchk.

Organization and Host Names

The host name may be set with -H-; the value specifies the host name to be used in archive entries generated
by Gaussian. The default is the current hostname.
The organization/site name may be set with -O-; the value specifies the site name to be used in archive
entries generated by Gaussian. There is no default.

User Defaults Files

Gaussian users may set their own defaults by creating their own Default.Route file. Gaussian checks the
current working directory for a file of this name when a job is initiated. Settings in the local file take precedence
over those in the site-wide file, and options specified in the route section of the job take precedence over both
of them.

Command Line Options & Environment Variable Equivalents

All of these directives can also be set via environment variables or UNIX/Linux command line arguments.
The environment variable GAUSS_xDEF provides a command line equivalent to -X- in the Default.Route file.
Similarly, the command line argument to g16 -x="value" specifies the same setting. For example, all of the
following have the equivalent effect:

-M- 4GB in Default.Route

export GAUSS_MDEF=4GB
g16 -m="4GB" ···

Order of Priority
The order of priority is:
♢ command line argument
♢ environment variable
♢ Default.Route setting
♢ internal program default

Default.Route Limitations
Not all route section keywords are honored in the Default.Route file. In general, the rule is that options
which are specific to a specific job type are ignored. Thus, Integral=SuperFine, which changes the default
integration grid, will be honored, while Freq=Raman, which specifies a setting for a specific job type, will be
ignored.

4.9.2 Parallel Job Directives

4.9 The Default.Route File 45

Parallel Execution on Shared Memory Multiprocessors

Gaussian defaults to execution on only a single processor. If your computer system has multiple proces-
sors/cores, and parallel processing is supported in your version of Gaussian, you may the specific CPUs on
which to run with the -C- directive. For example, the following directive specifies that the program should run
on the first 5 cores of a hexacore system (reserving one core for other use):
-C- 0,1,2,3,4
The node list can also be specified as a range (e.g., 0-5). Ranges can also be followed by a suffix of the
form /n, which says to use every nth processor in the range (e.g., /2 specifies every second processor/core).
The older -P- directive can be used to specify the total number of processors on which to execute (leaving
the selection of processors to the operating system). Clearly, the number of processors requested should not
exceed the number of processors available, or a substantial decrease in performance will result.

Network/Cluster Parallel Execution

You can specify the list of Linda workers in Default.Route via the -W- directive:
-W- dalton,lavoisier:2,priestley,agassiz:3,curie
This example will use the specified five nodes for parallel execution, placing 2 worker processes on
lavoisier, 3 workers on agassiz, and one worker on each of the other systems. If the master node – the node
where the job is started – is not one of these systems, a worker will also run on that system (making a total of
six nodes).
This directive corresponds to – and can be overridden by – the Link 0 command %LindaWorkers.
The -S- directive specifies which program to use to start worker processes. It takes either rsh (the default)
or ssh as its parameter.

Combining SMP and Network Parallelism

When -W- is combined with -C- or -P-, then an SMP parallel worker process is started on each node in the
node list (or more than one such process when multiple workers are specified for that node). In other words,
these individual worker processes run in parallel according to the SMP-related settings. If the settings are
inappropriate for a listed computer, then the work will fail on that node. For example, the following directives
will start workers as multiprocessors jobs on the specified systems:

-W- alpha,beta,gamma
-C- 0,1,2,3

However, if system beta is a dual-core workstation, that worker process will fail as there is no processor
2 or 3 present on that computer. This mechanism is designed primarily for cluster environments with uniform
nodes.
Note that it is the Default.Route file on the master which is relevant; Default.Route files that may be present
on worker systems are not used.

Parallel Execution on GPUs

The -G- directive sets the default list of GPUs to use. When using GPUs it is essential to have each GPU
controlled by a specific CPU and much preferable if the CPU is physically close to the GPU it is controlling.
The list uses the syntax gpu#(s)=core#(s) to indicate which GPUs to use and the core to which each is pinned.
 46 Chapter 4. Running Gaussian 16

For example, the following directive tells Gaussian to execute on GPU0 through GPU3:
-G- 0,1,2,3=0,1,16,17
GPU0 and GPU1 are pinned to cores 0 and 1, while GPU2 and GPU3 are pinned to cores 16 and 17
(respectively).
Ranges of GPUs and/or cores can be used in this directive. For example, the following is equivalent to the
preceding:
-G- 0-3=0-1,16-17

4.9.3 formchk Directives

The -F- directive sets the default options for the formchk utility. By default formchk produces a formatted
checkpoint file that is backwardly compatible with all previous versions of Gaussian.
The parameter to -F- can be -3 or -2 to create a formatted checkpoint file of the corresponding version
(version 3 is the default). The parameter can also contain -c, which causes the molecular mechanics atom types
to appear in the formatted checkpoint file as strings rather than integers.
The memory directive -U- sets default memory to use in utilities such as formchk and freqchk.

4.9.4 Examples
For a dual-core workstation with 8 GB memory and 1 TB of disk, the default algorithms and memory
allocation are fine. However, MaxDisk and the default CPUs for execution need to be specified:

-C- 0,1
-#- MaxDisk=200GB

On a server with 4 octa-core processors and 256 GB of memory designed to be used for large jobs, 8 cores
should be used by default: the first 8 odd numbered cores starting with core 0. Also, more memory should be
given to each job (2 GB/core):

-M- 16GB
-C- 0-16/2
-#- MaxDisk=500GB

On some older Intel processors (Nehalem and before), there is not enough memory bandwidth to keep all
the CPUs on a chip busy, and it is often preferable to use half the CPUs, each with twice as much memory
as if all were used. For example, on such a machine with 4 12-core chips and 128 GBytes of memory, with
CPUs 0-11 on the first chip, 12-23 on the second, etc., it is better to run using 24 processors (6 on each chip)
and give them 72/24=3GByte memory each, rather than use all 48 with only 1.5GBytes of memory each. The
appropriate directive would be

-M- 72GB
-C- 0-47/2

/2 says to use every other core: i.e., cores 0, 2, 4, 6, 8 and 10 on chip 0, cores 12, 14, 16, 18, 20 and 22 on
chip 1, and so on.

4.9.5 Directive List

 4.10 Running Gaussian Test Jobs 47

Default.Route Link 0 Option Env. Var. Description

-#- -r GAUSS_RDEF Route section keyword list.
-C- %CPU -c GAUSS_CDEF Processor/core list for multiprocessor parallel jobs.
-F- GAUSS_FDEF Options for the formchk utility.
-G- %GPUCPU -g GAUSS_GDEF GPUs=Cores list for GPU parallel jobs.
-H- GAUSS_HDEF Computer hostname.
-M- %Mem -m GAUSS_MDEF Memory amount for Gaussian jobs.
-O- GAUSS_ODEF Organization (site) name.
-P- %NProcShared -p GAUSS_PDEF Number of processors/cores for multiprocessor par-
allel jobs. Superseded in most cases by -C-.
-R- -r GAUSS_RDEF Route section keyword list.
-S- %UseSSH -s GAUSS_SDEF Program to start workers for network parallel jobs:
rsh or ssh.
-U- GAUSS_UDEF Memory amount for utilities.
-W- %LindaWorkers -w GAUSS_WDEF List of hostnames for network parallel jobs.

4.10 Running Gaussian Test Jobs

An extensive set of test jobs for Gaussian are provided, along with their corresponding output files. The
input files are found in directory $g16root/g16/tests/com. One or more subdirectories of $g16root/g16/tests,
named for computer architecture types (e.g., ia64), contain reference output for the various test jobs (gzipped
log files). A script file which runs ranges of test jobs automatically is also provided (described below).
If you build the program from source code under a supported architecture and operating system and using
the specified compiler, libraries and other software (if any), we recommend that you run a few of the test jobs
to verify that the program has been built correctly. However, it is not necessary to run the entire test suite.
You do not need to run any test jobs for binary distributions.
Test job input files have names of the form testnnnn.com. Tests 1, 28, 94, 155, 194, 296, and 302 cover a
range of Gaussian capabilities. Note that some test jobs are intended for fast hardware and are quite expensive
on smaller, slower computer systems. The file $g16root/g16/tests/tests.idx lists what each test job does.

Rename Existing Default.Route File Before Running Test Jobs

If you choose to run some or all of the Gaussian test jobs, you will need to make sure that they run with
the program’s built-in default settings. Therefore, you’ll need to rename both the site-wide Default.Route file
(located in the $g16root/g16 directory) as well as any individual version of the defaults file that you may have
prior to running any test job. Note that certain settings in this file can cause some test jobs to fail.

Examples
The script submit.csh can be used to run test jobs. It accepts two parameters: the numbers of the first
and last jobs to run (by default, all of the tests are run). Note that you should run the test jobs from a separate
directory to prevent them from clobbering the reference output.
The following commands illustrate the recommended procedure for running a test job, using the directory
/chem/newtests as the test job execution area and test job 28 as an example:

$ mkdir /chem/newtests; cd /chem/newtests

$ ln -s $g16root/g16/tests/com .
$ mkdir ‘gau-machine‘
48 Chapter 4. Running Gaussian 16

$ $g16root/g16/tests/submit.csh m n &

After each test job finishes, verify that it completed successfully. Then, compare its current output with
the reference output using the d1 script. For example:

$ $g16root/g16/tests/d1 m n

The d1 script filters out insignificant differences from the output files for the specified test jobs and pipes
the remaining output through more. The differences that appear should be limited to non-substantive items.
II
Part Two

5 List of Gaussian Keywords . . . . . . . . . . . . 51

6 Utility Programs . . . . . . . . . . . . . . . . . . . . . 335

 5. List of Gaussian Keywords

♢Link0 Commands ♢Force ♢Polar

♢# ♢Freq ♢Population
♢ADMP ♢G09Defaults ♢Pressure
♢BD ♢Gen and GenECP ♢Prop
♢BOMD ♢GenChk ♢Pseudo
♢CacheSize ♢Geom ♢Punch
♢CASSCF ♢GFInput ♢QCI
♢CBS Methods ♢GFPrint ♢Restart
♢CBSExtrapolate ♢Gn Methods ♢SAC-CI
♢CCD and CCSD ♢Guess ♢Scale
♢Charge ♢GVB ♢Scan
♢ChkBasis ♢HF ♢SCF
♢CID and CISD ♢Huckel ♢SCRF
♢CIS ♢INDO ♢Semi-Empirical Methods
♢CNDO ♢Integral ♢SP
♢Complex ♢IOp ♢Sparse
♢Constants ♢IRC ♢Stable
♢Counterpoise ♢IRCmax ♢Symmetry
♢CPHF ♢LSDA ♢TD
♢Density ♢MaxDisk ♢Temperature
♢DensityFit and NoDensityFit ♢MINDO3 ♢Test
♢DFT Methods ♢MNDO ♢TestMO
♢DFTB and DFTBA ♢MM Methods ♢TrackIO
♢EET ♢MP Methods ♢Transformation
♢EOMCCSD ♢Name ♢Units
♢EPT ♢NMR ♢Volume
♢External ♢ONIOM ♢W1 Methods
♢ExtraBasis & ExtraDensityBasis ♢Optimization ♢Window Keyword and Frozen Core Options
♢Field ♢Output ♢ZIndo
♢FMM ♢PBC
 52 Chapter 5. List of Gaussian Keywords

5.1 Link 0 Commands

This section lists all Link 0 commands, which are optional and precede the route section.
Link 0 commands may be up to 500 characters in length.
%Mem=N
Sets the amount of dynamic memory used to N 8-byte words (default). This value may also be followed
by KB, MB, GB, TB, KW, MW, GW or TW (without intervening spaces) to specify units of kilo-, mega-,
giga-, or tera-bytes or words. The default memory size is 800 MB. A different default value can be set in
Default.Route with the -M- directive.
%Chk=file
Locates and names the checkpoint file.
%OldChk=file
The contents of the checkpoint file specified by %OldChk are copied to the checkpoint file of the current
job step at the start of the job step. This allows data to be picked up from a previous calculation without
destroying anything on the checkpoint file from it.
%SChk=file
Saves a copy of the checkpoint file when the job step starts. One can usually do the same thing with
%OldChk and %Chk but sometimes it might be convenient to save the intermediate results this way.
%RWF=file
Locates and names a single, unified read-write file (old-style syntax).
%RWF=loc1,size1,loc2,size2,· · ·
An alternate syntax is provided for splitting the read-write file among two or more disks (or file systems).
Each location is followed by a maximum size for the file segment at that location. The size of each file
segment is given in 8-byte words (default). This value may also be followed by KB, MB, GB, TB, KW,
MW, GW or TW (without intervening spaces) to specify units of kilo-, mega-, giga- or tera-bytes or
words. A value of -1 for any size parameter indicates that any and all available space may be used, and
a value of 0 indicates that an existing segment should retain its current size. The locations may be either
directory locations, or full pathnames. Note that directory specifications must include terminal slashes
(on UNIX systems).
%OldMatrix=matfile
Copy the data on the unformatted binary matrix element file matfile to the active checkpoint file at the
start of the job step. This directive is similar %OldChk but takes the data from the specified file. In Rev.
B.01 and later, the file name may be followed by the keyword i4lab to specify that the file uses 4-byte
integers: e.g., %OldMatrix=(myfile,i4lab).
%OldRawMatrix=matfile
Copy the data on the raw binary matrix element file matfile to the active checkpoint file at the start of the
job step. This directive is similar %OldChk but takes the data from the specified file. In Rev. B.01 and
later, the file name may be followed by the keyword i4lab to specify that the file uses 4-byte integers:
e.g., %OldRaw=(myfile,i4lab).
%Int=spec
Locates and names the two-electron integral file(s). The spec parameter may take on either of the forms
used for the read-write file.
 5.1 Link 0 Commands 53

%D2E=spec
Locates and names the two-electron integral derivative file(s). The spec parameter may take on either of
the forms used for the read-write file.
%KJob LN [M]
Tells the program to stop the run after the Mth occurrence of Link N. For example, %KJob L502 2 will
cause the run to terminate after Link 502 has been run for the second time. M may be omitted; it defaults
to 1.
%Save
Causes Link 0 to save scratch files at the end of the run. By default, all non-specified scratch files are
deleted and all named scratch files are saved when the run completes successfully.
%ErrorSave
Causes Link 0 to delete scratch files at the end of a successful run, including any files that were named
explicitly preceding this directive. In other words, if a file is named before %ErrorSave is encountered,
it will not be saved. However, if the directive naming the file appears after the %ErrorSave directive,
the file will be retained. If the job ends abnormally, all files are saved. %NoSave is a synonym for this
directive.
If both %Save and %ErrorSave are specified, then the one appearing latest in the input file takes prece-
dence.
%Subst LN dir
Tells Link 0 to take the executable (.exe file) for a link from an alternate directory. For example %SUBST
L913 /user/chem will cause /user/chem/l913.exe to be run instead of the default executable (in $g16root).
The directory specification should be in the usual format for the machine involved. Only the directory
can be specified; the file name must have the standard form of lnnnn.exe, where nnnn is the Link number.

5.1.1 Parallel Job Directives

%CPU=proc-list
This directive contains a list of processor/core numbers for shared memory parallel processing, with
multiple items are separated by commas. This directive is designed to replace the earlier %NProcShared
and %NProc directives.
A default value can be set in Default.Route with the -C- directive.
%NProcShared=N
Requests that the job use up to N processors/cores on shared memory parallel execution on SMP multipro-
cessor computers. For most purposes, this directive is superceded by %CPU. The value of %NProcShared
overrides the -P- directive in the Default.Route file.
%GPUCPU=gpu-list=core-list
This sets the default list of GPUs to use. When using GPUs it is essential to have each GPU controlled
by a specific CPU and much preferable if the CPU is physically close to the GPU it is controlling. The
list preceding the equals sign indicates the GPUs to use for the calculation. Corresponding items in the
second list specify the core to which each CPU is pinned. For example, the following directive tells
Gaussian to execute on GPU0 through GPU3:
%GPUCPU=0,1,2,3=0,1,16,17
 54 Chapter 5. List of Gaussian Keywords

GPU0 and GPU1 are pinned to cores 0 and 1, while GPU2 and GPU3 are pinned to cores 16 and 17
(respectively).
Ranges of GPUs and/or cores can be used in this directive. For example, the following is equivalent to
the preceding:
%GPUCPU=0-3=0-1,16-17
A default value for %GPUCPU can be set in Default.Route with the -G- directive.
%LindaWorkers=node1[:n1] [,node2[:n2]] · · ·
This lists the TCP node name for each node to use. By default, one Linda worker is started on each
node, but the optional value allows this to be varied. A worker is always started on the node where the
job is started (the master node) whether or not it appears in the node list. A default value can be set in
Default.Route with the -W- directive.
%LindaWorkers may be combined with %NProcShared. In this case, one or more parallel worker pro-
cesses will be run on each node (the number still determined by the values in %LindaWorkers). The
value to %NProcShared specifies the number of SMP processors/cores to use on each system in the
worker node list.
Do not use the obsolete %NProcLinda directive. Gaussian will compute the total number of Linda work-
ers based on the %LindaWorkers input.
%UseSSH
Start Linda workers using ssh rather than rsh. %UseRSH specifies the use of rsh, and it is the default. A
different default value can be set in Default.Route with the -S- directive.
%DebugLinda
Report details concerning the starting and stopping of Linda workers.

5.1.2 Examples
These commands specify a name for the checkpoint file, and an alternate name and directory location for
the read-write file, and cause only the checkpoint file to be saved at the conclusion of the Gaussian job:

%RWF=/chem/scratch2/water Files to be deleted go here.

%NoSave
%Chk=water Files to be saved go here.

The following directive causes a network parallel job to be run across the specified 5 nodes. Nodes hamlet
and ophelia will each run two worker processes.
%LindaWorkers=hamlet:2,ophelia:2,laertes,horatio,lear
The following directives specify that a parallel job will be executed on hosts norway, italy and spain.
Nodes norway and italy will each run one 4-way SMP parallel worker, and spain will run two such workers:

NProcShared=4 Specifies four-way SMP parallelism.

%LindaWorkers=norway,italy,spain:2

These directives make sense when norway and italy are 4 processor/core computers, and spain is an 8
processor/core computer.
 5.3 ADMP 55

5.2 #
The route section of a Gaussian job is initiated by a pound sign (#) as the first non-blank character of a
line. The remainder of the section is in free-field format. For most jobs, all of the information can be placed on
this first line, but overflow to other lines (which may but need not begin with a # symbol) is permissible. The
route section must be terminated by a blank line.
If no keywords are present in the route section, the calculation defaults to HF/STO-3G SP.

5.2.1 Alternate Forms

#N
Normal print level; this is the default.
#P
Additional output is generated. This includes messages at the beginning and end of each link giving
assorted machine-dependent information (including execution timing data), as well as convergence infor-
mation in the SCF.
#T
Terse output: output is reduced to essential information and results.

5.3 ADMP
This keyword requests a classical trajectory calculation [120–123] using the Atom Centered Density Ma-
trix Propagation molecular dynamics model [124–126]. This method provides equivalent functionality to Born-
Oppenheimer molecular dynamics (see the BOMD keyword) at considerably reduced computational cost [126].
ADMP belongs to the extended Lagrangian approach to molecular dynamics using Gaussian basis func-
tions and propagating the density matrix. The best known method of this type is Car-Parrinello (CP) molecular
dynamics [127], in which the Kohn-Sham molecular orbitals, ψi , are chosen as the dynamical variables to rep-
resent the electronic degrees of freedom in the system. CP calculations are usually carried out in a plane wave
basis (although Gaussian orbitals are sometimes added as an adjunct [128–130]). Unlike plane wave CP, it is
not necessary to use pseudopotentials on hydrogen or to use deuterium rather than hydrogen in the dynamics.
Fictitious masses for the electronic degrees of freedom are set automatically [126] and can be small enough
that thermostats are not required for good energy conservation.
ADMP can be performed with semi-empirical, HF, and pure and hybrid DFT models (see the Availability
tab for more details). It can be applied to molecules, clusters and periodic systems. PBC calculations use only
the Γ point (i.e., no K-integration).

5.3.1 Input
Although most jobs will not require it, ADMP calculations can accept some input. The first section below
provides the optional initial Cartesian velocities for the ReadVelocity and ReadMWVelocity options.

Initial velocity for atom 1: x y z Optional initial Cartesian velocities

Initial velocity for atom 2: x y z (ReadVelocity and ReadMWVelocity options)
···
Initial velocity for atom N: x y z
···
 56 Chapter 5. List of Gaussian Keywords

First, the initial velocity for each atom is read if the ReadVelocity or ReadMWVelocity option is included.
Each initial velocity is specified as a Cartesian velocity in atomic units (Bohr/sec) or as a mass-weighed Carte-
sian velocity (in amu1/2 *Bohr/sec), respectively. One complete set of velocities is read for each requested
trajectory computation.
This information (if present) may be immediately followed by the Morse parameters for each diatomic
product (no intervening blank line):

Atom1, Atom2, E0 , Len, De , Be

···
Terminate entire trajectory input subsection with a blank line.

The Morse parameter data is used to determine the vibrational excitation of diatomic fragments using the
EBK quantization rules. It consists of the atomic symbols for the two atoms, the bond length between them
(Len, in Angstroms), the energy at that distance (E0 in Hartrees), and the Morse curve parameters De (Hartrees)
and Be (Angstroms−1 ). This input subsection is terminated by a blank line.

5.3.2 Options
MaxPoints=n
Specifies the maximum number of steps that may be taken in each trajectory (the default is 50). If a
trajectory job is restarted, the maximum number of steps will default to the number specified in the
original calculation.
Lowdin
Use the Löwdin basis for the orthonormal set. The alternative is Cholesky, which uses the Cholesky basis
and is the default.
NKE=N
Set the initial nuclear kinetic energy to N microHartrees. NuclearKineticEnergy is a synonym for this
option. The default is 100000 (corresponding to 0.1 Hartree).
DKE=N
Set the initial density kinetic energy to N microHartrees. DensityKineticEnergy is a synonym for this
option.
ElectronMass=N
Set the fictitious electron mass to |N/10000| amu (the default is N=1000, resulting in a fictitious mass
of 0.1 amu). EMass is a synonym for this option. If N<0, then uniform scaling is used for all basis
functions. By default, core functions are weighted more heavily than valence functions.
FullSCF
Do the dynamics with converged SCF results at each point.
ReadVelocity
Read initial Cartesian velocities from the input stream. Note that the velocities must have the same
symmetry orientation as the molecule. This option suppresses the fifth-order anharmonicity correction.
ReadMWVelocity
Read initial mass-weighted Cartesian velocities from the input stream. Note that the velocities must have
the same symmetry orientation as the molecule. This option suppresses the fifth-order anharmonicity
 5.3 ADMP 57

correction.
StepSize=n
Sets the step size in dynamics to n*0.0001 femtoseconds. The default is 1000 (a step size of 0.1 fem-
toseconds).
BandGap
Whether to diagonalize the Fock matrix in order to report the band gap at each step. The default is
NoBandGap.
Restart
Restart an ADMP calculation from the checkpoint file. Note that options set in the original job will
continue to be in effect and cannot be modified.
ReadIsotopes
This option allows you to specify alternatives to the default temperature, pressure, frequency scale factor
and/or isotopes – 298.15 K, 1 atmosphere, no scaling, and the most abundant isotopes (respectively). It is
useful when you want to rerun an analysis using different parameters from the data in a checkpoint file.
Be aware, however, that all of these can be specified in the route section (Temperature, Pressure and Scale
keywords) and molecule specification (the Iso parameter), as in this example:

#T Method/6-31G(d) JobType Temperature=300.0 · · ·

···

0 1
C(Iso=13)
···

ReadIsotopes input has the following format:

temp pressure [scale] Values must be real numbers.

isotope mass for atom 1
isotope mass for atom 2
···
isotope mass for atom n

Where temp, pressure, and scale are the desired temperature, pressure, and an optional scale factor for
frequency data when used for thermochemical analysis (the default is unscaled). The remaining lines hold
the isotope masses for the various atoms in the molecule, arranged in the same order as they appeared
in the molecule specification section. If integers are used to specify the atomic masses, the program will
automatically use the corresponding actual exact isotopic mass (e.g., 18 specifies 18 O, and Gaussian uses
the value 17.99916).

5.3.3 Availability

Semi-empirical, HF, and DFT methods.

 58 Chapter 5. List of Gaussian Keywords

5.3.4 Related Keywords

BOMD

5.3.5 Examples
The following sample ADMP input file will calculate a trajectory for H2 CO dissociating to H2 + CO,
starting at the transition state:

# B3LYP/6-31G(d) ADMP Geom=Crowd

Dissociation of H2CO --> H2 + CO
0 1
C
O 1 r1
H 1 r2 2 a
H 1 r3 3 b 2 180.
r1 1.15275608
r2 1.74415774
r3 1.09413376
a 114.81897892
b 49.08562961
Final blank line

At the beginning of an ADMP calculation, the parameters used for the job are displayed in the output:
TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ
--------------------------------------------------------------------
INPUT DATA FOR L121
--------------------------------------------------------------------

General parameters:
Maximum Steps = 50
Random Number Generator Seed = 398465
Time Step = 0.10000 femtosec
Ficticious electronic mass = 0.10000 amu
MW individual basis funct. = True
Initial nuclear kin. energy = 0.10000 hartree
Initial electr. kin. energy = 0.00000 hartree
Initial electr. KE scheme = 0
Multitime step - NDtrC = 1
Multitime step - NDtrP = 1
No Thermostats chosen to control nuclear temperature

Integration parameters:

Follow Rxn Path (DVV) = False

Constraint Scheme = 10
Projection of angular mom. = True
Rotate density with nuclei = True
--------------------------------------------------------------------
 5.4 BD 59

TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ

The molecular coordinates and velocities appear at the beginning of each trajectory step (some output digits are
truncated here):
Cartesian coordinates:
I= 1 X= -1.1971360D-01 Y= 0.0000000D+00 Z= -1.0478570D+00
I= 2 X= -1.1971360D-01 Y= 0.0000000D+00 Z= 1.1305362D+00
I= 3 X= 2.8718451D+00 Y= 0.0000000D+00 Z= -2.4313539D+00
I= 4 X= 4.5350603D-01 Y= 0.0000000D+00 Z= -3.0344227D+00
MW Cartesian velocity:
I= 1 X= -4.0368385D+12 Y= 1.4729976D+13 Z= 1.4109897D+14
I= 2 X= 4.4547606D+13 Y= -6.3068948D+12 Z= -2.2951936D+14
I= 3 X= -3.0488505D+13 Y= 6.0922004D+12 Z= 1.8527270D+14
I= 4 X= -1.3305097D+14 Y= -3.1794401D+13 Z= 2.4220839D+14
Cartesian coordinates after ADCart:
I= 1 X= -1.1983609D-01 Y= 4.2521779D-04 Z= -1.0437931D+00
I= 2 X= -1.1859803D-01 Y= -1.5769743D-04 Z= 1.1248052D+00
I= 3 X= 2.8688210D+00 Y= 6.0685035D-04 Z= -2.4129040D+00
I= 4 X= 4.4028377D-01 Y= -3.1670730D-03 Z= -3.0103048D+00
TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ

After the trajectory computation is complete, summary information is displayed in the output for each time step
in the trajectory:
Trajectory summary for trajectory 1
Energy/Fock evaluations 51
Gradient evaluations 51

Trajectory summary
Time (fs) Kinetic (au) Potent (au) Delta E (au) Delta A (h-bar)
0.000000 0.1000000 -114.3576722 0.0000000 0.0000000000000000
0.100000 0.0988486 -114.3564837 0.0000371 -0.0000000000000081
0.200000 0.0967812 -114.3543446 0.0001088 -0.0000000000000104
0.300000 0.0948898 -114.3524307 0.0001313 -0.0000000000000115
···

You can also use GaussView or other visualization software to display the trajectory path as an animation.

5.4 BD
This method keyword requests a Brueckner Doubles calculation [131–133]. BD gradients are available
[133].

5.4.1 Options
T
Requests a Brueckner Doubles calculation with a triples contribution [132] added. BD-T is a synonym
for BD(T).
TQ
Requests a Brueckner Doubles calculation with triples and quadruples contributions [134] added.
 60 Chapter 5. List of Gaussian Keywords

FC
All frozen core options are available with this keyword; a frozen core calculation is the default. See the
discussion of the FC options for full information.
MaxCyc=N
Specifies the maximum number of cycles.
Conver=N
Sets the convergence calculations to 10−N on the energy and 10−(N−2) on the wavefunction. The default
is N=4 for single points and N=6 for gradients.
TWInCore
Whether to store amplitudes and products in memory during higher-order post-SCF calculations. The
default is to store these if possible, but to run off disk if memory is insufficient. TWInCore causes
the program to terminate if these can not be held in memory, while NoTWInCore prohibits in-memory
storage.
InCore
Forces the in-memory algorithm. This is very fast when it can be used, but requires N 4 /4 words of
memory. It is normally used in conjunction with SCF=InCore. NoInCore prevents the use of the in-core
algorithm.
SaveAmplitudes
Saves the converged amplitudes in the checkpoint file for use in a subsequent calculation (e.g., using a
larger basis set). Using this option results in a very large checkpoint file, but also may significantly speed
up later calculations.
ReadAmplitudes
Reads the converged amplitudes from the checkpoint file (if present). Note that the new calculation can
use a different basis set, method (if applicable), etc. than the original one.
Read
Reads the initial orbitals from the checkpoint file rather than doing an HF calculation. Note that the new
calculation can use a different basis set than the original one.

5.4.2 Related Keywords

OldFCBD
Requests old-style frozen-core BD (the core orbitals are never changed).
NewFCBD
Requests new-style frozen-core BD, in which the core orbitals are updated to conform to the BD condition
T1=0, which means the BD Fock matrix is diagonal for these orbitals. This is the default.

5.4.3 Availability

Analytic energies and gradients for BD, numerical gradients for BD(T), and numerical frequencies for
all methods. The options FC, T and TQ are not available with analytic gradients. Unrestricted open-shell
calculations are available for BD energies and gradients.
 5.5 BOMD 61

5.4.4 Examples
The BD energy appears in the output labeled E(Corr), following the final correlation iteration:
Wavefunction amplitudes converged. E(Corr)= -75.001908213
The energy is given in Hartrees. If triples (or triples and quadruples) were requested, the energy including
these corrections appears after the preceding:

Time for triples= 0.14 seconds.

T4(BD)= -0.12680940D-03
BD(T)= -0.75002034980D+02 Triples-corrected energy.

5.5 BOMD
This keyword requests a classical trajectory calculation [120–123] using a Born-Oppenheimer molecular
dynamics model (first described in [135, 136]; see [137] for an extended review article). The implementation
in Gaussian 16 [138–140] extends the usual methodology by using a very accurate Hessian-based algorithm
that incorporates a predictor step on the local quadratic surface followed by a corrector step. The latter uses
a fifth-order polynomial or a rational function fitted to the energy, gradient, and Hessian at the beginning and
end points of each step. This method for generating the correction step enables an increase in the step size of a
factor of 10 or more over previous implementations.
The selection of the initial conditions using quasi-classical fixed normal mode sampling and the final
product analysis are carried out in the same manner as in the classical trajectory program VENUS [141].
Alternatively, initial Cartesian coordinates and velocities may be read in.
Note that the ADMP method provides equivalent functionality at substantially lower computational cost
at the Hartree-Fock and DFT levels.

5.5.1 Required Input

All BOMD jobs must specify the number of dissociation paths; for many jobs, this value will be zero (a
blank line is also allowed), and no other BOMD input will be used. In this case, the trajectory is integrated for
a fixed number of steps, as specified by the program default of 100 or the value of the MaxPoints option.
If NPath is set to -1, the dissociation pathways will be detected automatically and a gradient criteria
(Hartree/Bohr) will be used in place of the usual fragmentation pathway and stopping criteria.
When the number of dissociation paths is greater than zero, the full BOMD job input has the following
general structure:

NPath Number of dissociation paths (maximum=20)

IFrag1 , · · · , IFragNAtoms Fragmentation information
··· · · · Repeated NPath times
[R1, R2, R3, R4, G5, ITest, IAtom, JAtom, R6 Optional stopping criteria (ReadStop option)
···] · · · Repeated NPath times
[Estart,DelE,SBeta,Ef,DPert,IFlag] Optional simulated annealing params. (SimAnneal)
[Mode-num, VibEng(Mode-num), · · · ] Optional initial normal mode energies (NSample)
[Initial velocity for atom 1: x y z Optional initial velocities (ReadVelocity, ReadMWVelocity)
Initial velocity for atom 2: x y z
62 Chapter 5. List of Gaussian Keywords

···
Initial velocity for atom N: x y z
···] Entire section repeated NTraj times
[Atom1, Atom2, E0 , Len, De , Be Optional Morse parameters for each diatomic product
···]
Terminate subsection with a blank line

The input line(s) following NPath define the fragmentation information for each path. The value in each
position specifies that the corresponding atom belongs to the specified fragment number (i.e., atom i belongs to
fragment number IFragi ). Note that fragment information for each path must begin on a new line, but the ones
for any individual path may be continued over as many lines as necessary.
Stopping criteria are specified next when the ReadStop option is included. Up to six stopping criteria may
be specified for each path. A trajectory is terminated when all of the active criteria are satisfied. However, a
value of zero for any parameter turns off testing for the corresponding stopping criteria. The stopping criteria
tests are defined as follows (default parameter values are in parentheses):
♢ Minimum distance between the centers of mass for any pair of fragments > R1 (18)
♢ Minimum distance between atoms located in different fragments > R2 (20)
♢ Maximum distance between the center of mass and any atom in the same fragment < R3 (0)
♢ The maximum distance between any pair of atoms in the same fragment < R4 (0)
♢ Interfragment gradient < G5 (10−6 )
♢ If ITest=1, distance between atoms IAtom and JAtom > R6 (0). Otherwise, distance between atoms IAtom
and JAtom < R6 (0)
All distances are specified in Bohr, and the units of the gradient G5 are Hartrees/Bohr.
Parameters for simulated annealing/fragmentation follow the stopping criteria in the input stream when
the SimAnneal option is specified:
♢ Estart is the desired initial kinetic energy (Hartrees).
♢ DelE is the energy gain/loss in Hartrees.
♢ SBeta is the Fermi-Dirac inverse temperature (1/Hartrees).
♢ Ef is the Fermi energy (wavenumbers): all modes corresponding to a frequency in wavenumbers below
Ef will be enhanced, while those above Ef will be reduced. The reverse will happen if SBeta is negative.
♢ DPert is the size of the random perturbation.
♢ IFlag determines the algorithm for applying an energy perturbation for simulated annealing (i.e., adding/re-
moving energy from the eigenmodes). It has the following possible values: 0 (weigh each eigencompo-
nent according to its frequency), 1 (add DelE in a random fashion), 2 (combination of 0 and 1), 00 (if
near a transition state, add all energy along that mode), and 10 (ignore any nearby transition state).
The next part of the input specifies how much energy is in each normal mode when the NSample option is
used. For each mode, VibEng is the translational energy in kcal/mol in the forward direction along the transition
vector. If VibEng < 0, then the initial velocity is in the reverse direction. (You can explicitly specify the forward
direction using the Phase option.)
Next, the initial velocity for each atom is read if the ReadVelocity or ReadMWVelocity option is included.
Each initial velocity is specified as a Cartesian velocity in atomic units (Bohr/sec) or as a mass-weighted
 5.5 BOMD 63

Cartesian velocity (in amu1/2 *Bohr/sec), respectively. One complete set of velocities is read for each requested
trajectory computation.
Finally, Morse parameter data can be specified for each diatomic product. The Morse parameter data is
used to determine the vibrational excitation of diatomic fragments using the EBK quantization rules. It consists
of the atomic symbols for the two atoms, the bond length between them (Len, in Angstroms), the energy at
that distance (E0 in Hartrees), and the Morse curve parameters De (Hartrees) and Be (Angstroms−1 ). This input
subsection is terminated by a blank line.

5.5.2 Options

MaxPoints=n
Specifies the maximum number of steps that may be taken in each trajectory (the default is 100). If
a trajectory job is restarted, the maximum number of steps will default to the number specified in the
original calculation.
Phase=(N1, N2[,N3[,N4]])
Defines the phase for the transition vector such that forward motion along the transition vector corre-
sponds to an increase in the specified internal coordinate. If two atom numbers are given, the coordinate
is a bond stretch between the two atoms; three atom numbers specify an angle bend and four atoms define
a dihedral angle.
ReadVelocity
Read initial Cartesian velocities from the input stream. Note that the velocities must have the same
symmetry orientation as the molecule. This option suppresses the fifth-order anharmonicity correction.
ReadMWVelocity
Read initial mass-weighted Cartesian velocities from the input stream. Note that the velocities must have
the same symmetry orientation as the molecule. This option suppresses the fifth-order anharmonicity
correction.
SimAnneal
Use simulated annealing (the initial velocity is randomly generated). Additional parameters are read in,
as described above.
Only one of ReadVelocity, ReadMWVelocity and SimAnneal can be specified.
ReadStop
Read in alternative stopping criteria.
RTemp=N
Specifies the rotational temperature. The default is to choose the initial rotational energy from a thermal
distribution assuming a symmetric top (the temperature defaults to 0 K).
NSample=N
Read in initial kinetic energies for the first N normal modes (the default is 0). The energies for the
remaining modes are determined by thermal sampling by default.
NTraj=N
Compute N trajectories.
Update=n
By default BOMD does second derivatives at every point. Using the Update keyword causes the program
64 Chapter 5. List of Gaussian Keywords

to perform Hessian updates for n gradient points before doing a new analytic Hessian. GradOnly requests
that only gradients be done and that the Hessian be updated all the time (full second derivatives are not
computed). ReCalcFC is a synonym for this option.
RandomVelocity
Randomly generate initial velocities for dynamics without using any second derivative information. This
is the default for GradientOnly dynamics.
StepSize=n
Sets the dynamic step size to n*0.0001, in the appropriate units. The default step size is 0.25 amu1/2 *Bohr
except for GradientOnly calculations where it is 0.025 femtoseconds.
Sample=type
Specifies the type of sampling, where type is one of these keywords: Microcanonical, Fixed, and Lo-
cal. The default is Fixed normal mode energy unless RTemp was specified, in which case Local mode
sampling is implied.
Restart
Restart a trajectory calculation from the checkpoint file. Note that options set in the original job will
continue to be in effect and cannot be modified.
ReadIsotopes
This option allows you to specify alternatives to the default temperature, pressure, frequency scale factor
and/or isotopes – 298.15 K, 1 atmosphere, no scaling, and the most abundant isotopes (respectively). It is
useful when you want to rerun an analysis using different parameters from the data in a checkpoint file.
Be aware, however, that all of these can be specified in the route section (Temperature, Pressure and Scale
keywords) and molecule specification (the Iso parameter), as in this example:

#T Method/6-31G(d) JobType Temperature=300.0 · · ·

···

0 1
C(Iso=13)
···

ReadIsotopes input has the following format:

temp pressure [scale] Values must be real numbers.

isotope mass for atom 1
isotope mass for atom 2
···
isotope mass for atom n

Where temp, pressure, and scale are the desired temperature, pressure, and an optional scale factor for
frequency data when used for thermochemical analysis (the default is unscaled). The remaining lines hold
the isotope masses for the various atoms in the molecule, arranged in the same order as they appeared
in the molecule specification section. If integers are used to specify the atomic masses, the program will
 5.5 BOMD 65

automatically use the corresponding actual exact isotopic mass (e.g., 18 specifies 18 O, and Gaussian uses
the value 17.99916).

5.5.3 Availability
All semi-empirical, HF, CASSCF, CIS, MP2 and DFT methods.

5.5.4 Related Keywords

ADMP

5.5.5 Examples
The following sample BOMD input file illustrates many of the available options. It will calculate a trajec-
tory for H2 CO dissociating to H2 + CO, starting at the transition state. There is one fragmentation pathway: C
and O belong to fragment 1, and the two hydrogens belong to fragment 2.
Stopping criteria are also specified in this example job. The trajectory will be stopped if the distance
between the centers of mass of H2 and CO exceed 13 Bohr, the closest distance between H2 and CO exceeds
11 Bohr, all atoms in a fragment are less than 1.3 Bohr from the center of mass of the fragment, any atom in
the fragment is less than 2.5 Bohr from all other atoms in the fragment, the gradient for the separation of the
fragments is less than 0.0000005 Hartree/Bohr, and the distance between atoms 1 and 3 is greater than 12.8
Bohr.
The initial kinetic energy along the transition vector is 5.145 kcal/mol, in the direction of the products (the
forward direction is characterized by an increase in the larger C-H distance). The Morse parameters for H2
and CO are specified to determine the vibrational excitation of the product diatomics; they were computed in a
previous calculation. The calculation will be carried out at 300 K.

# HF/3-21G BOMD(Phase=(1,3),RTemp=300,NSample=1,ReadStop) Geom=Crowd

HF/3-21G dissociation of H2CO --> H2 + CO

0 1
C
O 1 r1
H 1 r2 2 a
H 1 r3 3 b 2 180.

r1 1.15275608
r2 1.74415774
r3 1.09413376
a 114.81897892
b 49.08562961

1
1 1 2 2
66 Chapter 5. List of Gaussian Keywords

13.0 11.0 1.3 2.5 0.0000005 1 1 3 12.8

1 5.145
C O -112.09329898 1.12895435 0.49458169 2.24078955
H H -1.12295984 0.73482237 0.19500473 1.94603924
Final blank line

Note that all six stopping criteria are used here only for illustrative purposes. In most cases, one or two
stopping criteria are sufficient.
At the beginning of a BOMD calculation, the parameters used for the job are displayed in the output:

TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ-TRJ
-------------------------------------------------------------------
INPUT DATA FOR L118
-------------------------------------------------------------------

General parameters:
Max. points for each Traj. = 100
Total Number of Trajectories = 1
Random Number Generator Seed = 398465
Trajectory Step Size = 0.250 sqrt(amu)*bohr

Sampling parameters:
Vib Energy Sampling Option = Thermal sampling
Vib Sampling Temperature = 300.0 K
Sampling direction = Forward
Rot Energy Sampling Option = Thermal distribution (symmetric top)
Rot Sampling Temperature = 300.0 K
Start point scaling criteria = 1.000D-05 Hartree
···

Reaction Path 1
****************
Fragment 1 center 1 ( C ) 2 ( O )
Fragment 2 center 3 ( H ) 4 ( H )
Termination criteria:
The CM distances are larger than 13.000 bohr
The min atomic distances among fragments are larger than 11.0 bohr
The max atomic and CM distances in frags are shorter than 1.3 bohr
The max atomic distances in fragments are shorter than 2.500 bohr
The change of gradient along CM is less than 5.00D-07 Hartree/bohr
Distance between atom center 1 ( C ) and 3 ( H ) is GE 12.800 bohr

Morse parameters for diatomic fragments:

 5.6 CacheSize 67

E0 Re De Be
C O -112.0932990 1.1289544 0.4945817 2.2407896
H H -1.1229598 0.7348224 0.1950047 1.9460392
---------------------------------------------------------------------

The initial kinetic energies for the normal modes appear at the beginning of each trajectory step:

-------------------------------------------------------
Thermal Sampling of Vibrational Modes
Mode Wavenumber Vib. quant.# Energy (kcal/mol)
-------------------------------------------------------
1 -2212.761 5.14500
2 837.330 0 1.19702
3 1113.182 0 1.59137
4 1392.476 0 1.99064
5 2026.859 0 2.89754
6 3168.689 0 4.52987
-------------------------------------------------------

After the trajectory computation is complete, summary information is displayed in the output:

Trajectory summary for trajectory 1

Energy/gradient evaluations 76
Hessian evaluations 76

Trajectory summary
Time (fs) Kinetic (au) Potent (au) Delta E (au) Delta A (h-bar)
0.000000 0.0214192 -113.0388912 0.0000000 0.0000000000000000
1.169296 0.0293490 -113.0468302 -0.0000091 0.0000000000053006
2.161873 0.0407383 -113.0582248 -0.0000144 0.0000000000045404
···

The information is given for each time step in the trajectory. In addition, the output includes geometrical
parameters for the atoms in each fragment, the distances between fragments, and the relative mass-weighted
velocities for each fragments and between fragments, all reported at each time step. You can also use GaussView
or other visualization software to display the trajectory path as an animation.

5.6 CacheSize
This keyword specifies the default amount of cache per processor to use with various cache-blocking algo-
rithms (in 8-byte words). Setting this value appropriately will maximize the efficiency of relevant algorithms
by matching the batch size to the available cache.
Typically, this keyword is used in Default.Route files. You can use the testrt utility to determine the default
value for the Gaussian binary installed on the current system. On Linux and most other UNIX-based systems,
the cachesize script can be used to determine the optimal value for this parameter (see the examples).
 68 Chapter 5. List of Gaussian Keywords

When Gaussian 16 binaries are built, this value is set correctly for the current version of the various CPU
types, but it may need to be modified for chips released later which might use a different cache-size or inter-core
cache sharing scheme. If you build Gaussian 16 from source code, this value corresponds to the hardware on
the system where the compile takes place.

5.6.1 Examples
The following testrt command output lists the value for the Gaussian 16 binaries:
$ testrt sp
Revision: EM64M-G16RevA.02 9-Aug-2016 NErtGn=1000 NextEG=955 MaxAtm=
250000 MDCach=131072
Remainder of testrt output · · ·
The value of 131,072 corresponds to 128K working precision words, or 1 MB. This Mac OS X system has
a quad-core 64-bit Intel processor with 6 MB of Level 3 cache. A reasonable value for cache use is 50% of the
available cache, so a value of 0.75 MB/core would be a reasonable (50% of 1.5 MB): CacheSize=98304 (value
is in 8-byte words).
On Linux systems, the cache size is recorded in /proc/cpuinfo. The cachesize script in the $g16root/g16/bsd
subdirectory will display the total cache size:
$ $g16root/g16/bsd/cachesize
524288 bytes
This indicates that there is 512 KB of cache on this ancient dual-core system. In this case, due to the age
of this computer, the per-processor cache size is reported. Giving any parameter to this script will display the
CacheSize keyword to use:
$ $g16root/g16/bsd/cachesize 1
CacheSize=32768
This will use 0.25 MB of cache per core.

5.7 CASSCF
This method keyword requests a Complete Active Space Multiconfiguration SCF (MC-SCF) [142–150].
An MC-SCF calculation is a combination of an SCF computation with a full CI involving a subset of the
orbitals; this subset is known as the active space. The number of electrons (N) and the number of orbitals (M)
in the active space for a CASSCF must be specified following the keyword: CASSCF(N,M). Note that options
may be interspersed with N and M in any order.
By default, the active space is defined assuming that the electrons come from the highest occupied orbitals
in the initial guess determinant and that the remaining orbitals required for the active space come from the
lowest virtuals of the initial guess. Thus, for a 4-electron, 6-orbital CAS – specified as CASSCF(4,6) – on a
closed-shell system, the active space would consist of:
♢ Enough occupied orbitals from the guess to provide 4 electrons. Thus, the 2 highest occupied MOs would
be included.
♢ Enough virtual orbitals to make a total of 6 orbitals. Since 2 occupied orbitals were included, the lowest
4 virtual orbitals would become part of the active space.
Similarly, a 4 electron, 6 orbital CAS on a triplet would include the highest 3 occupied orbitals (one of
 5.7 CASSCF 69

which is doubly occupied and two singly occupied in the guess determinant) and the lowest 3 virtual orbitals.
In Gaussian 16, algorithmic improvements make an active space of up to about 16 orbitals feasible [151].
Normally, Guess=Alter or Guess=Permute is necessary to ensure that the orbitals which are selected in-
volve the electrons of interest and that they are correlated correctly. A prior run with Guess=Only can be used
to quickly determine the orbital symmetries (see the first example below). Alternatively, a full Hartree-Fock
single point calculation may be done, and the subsequent job will include Guess=(Read,Permute) in order to
retrieve and then modify the computed initial guess from the checkpoint file. You need to include Pop=Reg in
the route section of the preliminary job in order to include the orbital coefficient information in the output (use
Pop=Full for cases where you need to examine more than just the few lowest virtual orbitals). Alternatively,
you may use Pop=NBOSave to save the NBOs, which are often the best choice for starting CAS orbitals. You
may also choose to view the orbitals in a visualization package such as GaussView.
CAS is a synonym for CASSCF.
Use #P in the route section to include the final eigenvalues and eigenvectors in addition to the energy and
one-electron density matrix in the CASSCF output.
Note: CASSCF is a powerful but advanced method with many subtleties. We strongly recommend that
you study the cited references before attempting to run production CASSCF calculations. An overview of
the CASSCF method is given in chapter 9 of Exploring Chemistry with Electronic Structure Methods, 3rd ed.
[152]. Relatively straightforward example applications are discussed in references [145, 153–159].

5.7.1 Variations

♢ An MP2-level electron correlation correction to the CASSCF energy may be computed during a CASSCF
calculation by specifying the MP2 keyword in addition to CASSCF within the route section [160].
♢ Calculations on excited states of molecular systems may be requested using the NRoot option. Note that
a value of 1 specifies the ground state, not the first excited state (in contrast to usage with the CIS or TD
keywords).
♢ State-averaged CASSCF calculations may be performed using the StateAverage and NRoot options to
specify the states to be used.
♢ Conical intersections and avoided crossings may be computed by including Opt=Conical in the route
section of a CASSCF job (see the examples) [161–163].
♢ Approximate spin orbit coupling between two spin states can be computed during CASSCF calculations
by including the SpinOrbit option [164–170]. The method used in Gaussian 16 is based on [166]. It is
available for the elements H through Cl. In order to compute the spin orbit coupling, the integrals are
computed in a one-electron approximation involving relativistic terms, and then it uses effective charges
that scale the Z value for each atom to empirically account for 2 electron effects. This value can be
specified for each atom via the molecule specification nuclear parameters list (discussed earlier in this
chapter). Finally, note that such calculations will be state-averaged by default.
♢ The Restricted Active Space variation (RASSCF) [171] is also supported [172]. It is selected via the
RAS option. RASSCF calculations partition the molecular orbitals into five sections:
• The lowest-lying occupieds (doubly occupied in all configurations).
• The RAS1 space of doubly occupied MOs.
• The RAS2 space containing the most important orbitals for the problem.
 70 Chapter 5. List of Gaussian Keywords

• The RAS3 space of weakly occupied MOs.

• The remaining unoccupied orbitals.
Thus, the active space in CASSCF calculations is divided into three parts in a RAS calculations, and
allowed configurations are defined by specifying the minimum number of electrons that must be present
in the RAS1 space and the maximum number that may be in the RAS3 space, in addition to the total
number of electrons in the three RAS spaces. See the discussion of the RAS option for a description of
how to specify these values.

5.7.2 Options

NRoot=j
Requests that the jth root of the CI be used so that an excited state is obtained when j > 1. The option
defaults to the ground state (j=1). The state specified by NRoot is referred to as the “state of interest.”
StateAverage
Used to specify a state-averaged CASSCF calculation. All states up to NRoot are averaged. This option
requires the weighting for the various states to be input in format nF10.8 (no trailing blank line). StateAv-
erage is not allowed in combination with Opt=Conical or CASSCF=SpinOrbit, both of which perform
state-averaged calculations by default.
SpinOrbit
Compute approximate spin orbit coupling between two states, specified on a separate input line. Implies
a state-averaged CASSCF calculation.
RAS=(a,b,c,d)
Requests a RASSCF calculation which allows up to a holes (i.e., excitations from RAS1 into RAS2 or
RAS3) in the b orbitals in the RAS1 space, and to c particles in the d orbitals in the RAS3 space (i.e.,
excitations from RAS1 or RAS2 into RAS3). Thus, the minimum number of electrons in RAS2 is 2b-a.
Note that the two CASSCF keyword parameters specify the size of the entire active space: RAS1 + RAS2
+ RAS3 (see the examples).
DavidsonDiag
Requests the use of the Davidson diagonalization method for the CI matrix instead of the Lanczos itera-
tions. This is the default when there are more than six active orbitals.
LanczosDiag
Requests the use of Lanczos iterations when diagonalizing the CI matrix instead of the Davidson method.
Lanczos is the default when there are 6 or fewer active orbitals.
FullDiag
Requests the use of the full (Jacobi) diagonalization method for the CI matrix instead of Lanczos or
Davidson iterations. The default is full diagonalization if there are 6 or fewer active orbitals and David-
son otherwise. NoFullDiag suppresses the use of the full diagonalization method.
The full Jacobi diagonalization method must be used if quadratic convergence is required (see the QC op-
tion below) and when the CI eigenvector is unknown (in the latter case, specify FullDiag for calculations
involving more than 6 active orbitals).
StateGuess=k
Set the starting vector for the Lanczos method to configuration k. For example, this option can be useful
5.7 CASSCF 71

for selecting a configuration of the correct symmetry for a desired excited state (different from that of the
ground state). In such cases, running a preliminary calculation to determine the orbital symmetries may
be required.
k may also be set to the special value Read, which says to read in the entire eigenvector from the input
stream (format: NZ, (Ind(I), C(Ind(I)), I=1, NZ).
The default diagonalization method is most efficient if the size of the CI problem is greater than about
50, or the user can identify one or more dominant components in the eigenvector from the onset of the
calculation, via the initial trail vector. By default, the starting vector is initialized in j+1 positions, where
j is the value given to the NRoot option (or its default value). The positions correspond to the lowest j+1
energy diagonal elements of the CI Hamiltonian. This usually results in good convergence for the lowest
j roots.
The StateGuess option (below) may be used to change this default. CASSCF(· · · ,StateGuess=k) sets C(k)
to 1.0. The central requirement for this vector is that it should not be deficient in the eigenvector that is
required. Thus, if the CI eigenvector is dominated by configuration k, setting the StateGuess option to k
will generate a good starting vector (e.g., StateGuess=1 is appropriate if the CI vector is dominated by
the SCF wavefunction). However, if the coefficient of configuration k is exactly zero (e.g., by symmetry)
in the desired root, then that eigenvector will be missing, and the calculation will converge to a higher
state.
OrbRot
OrbRot includes and NoCPMCSCF excludes the orbital rotation derivative contributions from the CP-
MC-SCF equations in an Opt=Conical calculation. OrbRot is the default.
SlaterDet
Use Slater determinants in the CASSCF calculation. This option is needed to locate a conical intersec-
tion/avoided crossing between a singlet state and a triplet state.
SaveGEDensities
Saves ground- and excited-state alpha and beta total and transition density matrices (as is done for CIS).
Forces the use of Slater determinants.
HWDet
Use Hartree-Waller determinants instead of Slater. This is the default for CAS calculations involving 10
or more orbitals. It implies NoFullDiag.
RFO
Requests the RFO quadratic step. At most, one of QC and RFO should be specified.
QC
Requests a quadratically convergent algorithm for the CAS. This option should be used with caution; it
works well only with a very good guess. Only one of QC and RFO should be specified.
UNO
Requests that the initial orbitals for the CAS be produced from the natural orbitals generated from a pre-
vious UHF calculation [173, 174]. Normally used with Guess=Read.
The UNO guess must be used with caution. Often, some of the natural orbitals which have modest occu-
pation are not the important ones for the process of interest. Consequently, unless the entire valence space
is being correlated (which is usually prohibitively expensive), one normally runs one job which does a
 72 Chapter 5. List of Gaussian Keywords

UHF calculation with Pop=NaturalOrbitals and then examines the resulting orbitals. The orbitals which
belong in the active space are then selected, and a single-point CASSCF(· · · ,UNO) Guess=(Read, Alter)
calculation is performed. The resulting converged orbitals are then examined to verify that the correct ac-
tive space has been located, and finally an optimization can be run with CASSCF(· · · ,UNO) Guess=Read.
For singlets, this entire process depends on the user being able to coax the UHF wavefunction to converge
to the appropriate broken spin-symmetry (non-RHF) result.
NPairs=n
Number of GVB pairs outside of the CAS active space in a CAS-GVB calculation [175].

5.7.3 Availability and Restrictions

Energies, analytic gradients, and analytic and numerical frequencies. CASSCF may not be combined with
any semi-empirical method. Analytic gradients and frequencies are available only through f functions.
Analytic polarizabilities may not be performed with the CASSCF method. Use CASSCF Polar=Numer.
You can restart a CASSCF calculation by specifying SCF=Restart in the route section. In order to restart
a CASSCF optimization, the keywords CASSCF Opt=Restart Extralinks=L405 must be included in the job’s
route section.
CASSCF frequencies with PCM solvation must be done numerically using Freq=Numer.

5.7.4 Related Keywords

Opt=Conical, MP2, Guess, Pop, SCF

5.7.5 Examples
We will consider several of the most important uses of the CASSCF method in this section.
Preliminary Examination of the Orbitals (Guess=Only). The following route section illustrates one
method of quickly examining the orbitals in order to determine their symmetries and any alterations needed to
produce the desired initial state. We include Pop=Reg to obtain the molecular orbital output in the population
analysis section:
# HF/3-21G Guess=Only Pop=Reg Test
The molecule being investigated is 1,3-cyclobutadiene, a singlet with D2h symmetry. We are going to run
a 4×4 CAS, so there will be four orbitals in the active space: 2 occupied and 2 virtual. We want all four orbitals
to be π orbitals.
The HOMO is orbital 14; therefore, orbitals 13 through 16 will comprise the active space. When we
examine these orbitals, we see that only orbitals 14 and 15 are of the correct type. The molecule lies in the
YZ-plane, so π orbitals will have significantly non-zero coefficients in the X direction. Here are the relevant
coefficients for orbitals 10 and 13-16:

Molecular Orbital Coefficients

10 13 14 15 16
O O O V V
3 1 C 2PX 0.29536 0.00000 0.34716 0.37752 0.00000
7 3PX 0.16911 0.00000 0.21750 0.24339 0.00000
12 2 C 2PX 0.29536 0.00000 0.34716 -0.37752 0.00000
5.7 CASSCF 73

16 3PX 0.16911 0.00000 0.21750 -0.24339 0.00000

21 3 C 2PX 0.29536 0.00000 -0.34716 -0.37752 0.00000
25 3PX 0.16911 0.00000 -0.21750 -0.24339 0.00000
30 4 C 2PX 0.29536 0.00000 -0.34716 0.37752 0.00000
34 3PX 0.16911 0.00000 -0.21750 0.24339 0.00000

Orbital 10 is clearly also a π orbital. If we look at higher virtual orbitals, we will find that orbital 19 is also a π
orbital. We have found our four necessary orbitals, and can now use Guess=Alter to move them into the active
space. Here is the input file for the CASSCF calculation:

# CASSCF(4,4)/3-21G Guess=Alter Pop=Reg Test

1,3-Cyclobutadiene Singlet, D2H, Pi 4×4 CAS

0 1
molecule specification

10,13 Interchange orbitals 10 and 13.

16,19 Interchange orbitals 16 and 19.

CASSCF Energy and the One-Electron Density Matrix. When we run this CASSCF calculation on
cyclobutadiene, we will obtain a prediction for the energy. It appears in the CASSCF output as follows:

TOTAL -152.836259 · · · Energy at each iteration

ITN= 9 MaxIt= 64 E= -152.8402786733 DE=-1.17D-05 Acc= 1.00D-05
ITN= 10 MaxIt= 64 E= -152.8402826495 DE=-3.98D-06 Acc= 1.00D-05
···
DO AN EXTRA-ITERATION FOR FINAL PRINTING

The value of E for the final iteration is the predicted energy: -152.8402826495 Hartrees in this case.
It is also important to examine the one-electron density matrix, which appears next in the output:

Final one electron symbolic density matrix:

1 2 3 4
1 0.191842D+01
2 -0.139172D-05 0.182680D+01
3 0.345450D-05 0.130613D-05 0.172679D+00
4 0.327584D-06 0.415187D-05 0.564187D-06 0.820965D-01
MCSCF converged.

The diagonal elements indicate the approximate occupancies for each successive orbital in the active space.
If any of these values is (essentially) zero, then that orbital was empty throughout the calculation; similarly, if
any of them is essentially 2, then that orbital was doubly occupied throughout the CAS. In either case, there
were no excitations into or out of the orbital in question, and there is probably a problem with the CASSCF
calculation. In our case, the two “occupied” orbitals have values less than 2, and the other two orbitals in the
active space have non-zero occupancies, so things are fine.
74 Chapter 5. List of Gaussian Keywords

CASSCF MP2 Energy. When you run a CASSCF calculation with dynamic correlation (CASSCF MP2
in the route section), the following additional lines will appear in the CASSCF output (with the first one coming
significantly before the second):

MP2 correction to the MCSCF energy is computed Indicates a CASSCF MP2 job.
···
E2 = -0.2635549296D+00 EUMP2 = -0.15310383973610D+03 Electron correlation-corrected energy.

The string EUMP2 labels the energy; in this case, the value is -153.1038397361 Hartrees.
CAS Configuration Information. The beginning of the CASSCF output lists the configurations, in the
following format:

Configuration 1 Symmetry 1 1100

Configuration 2 Symmetry 2 1ab0
Configuration 3 Symmetry 1 1010
Configuration 4 Symmetry 1 a1b0

This is from a CAS(4,4) on a singlet reference, so each configuration indicates the occupation pattern for
the 4 active orbitals. The first line is the reference configuration and in this case has the two lowest active orbitals
doubly occupied, indicated with “1”. In configuration 2, the first active orbital remains doubly occupied, while
a β electron has been excited from the second to the third active orbital indicated by “a” for α and “b” for β . In
configuration 3, the first and third active orbitals are doubly occupied, while configuration 4 shows excitation
of the β electron from the first to the third active orbital. By default, all symmetry types are allowed, and
the symmetry of each configuration is reported. Refer to the symmetry multiplication table printed before the
configuration list for symmetry assignments of the orbitals.
Using CASSCF to Study Excited States. The following two-step job illustrates one method for studying
excited state systems using the CASSCF method. The first step assumes that a preliminary Hartree-Fock
single point calculation has been done in order to examine the orbitals; it takes advantage of the initial guess
computation done by that job, which is retrieved from the checkpoint file:

%chk=CAS1
# CASSCF(2,4) 6-31+G(D) Guess=(Read,Alter) Pop=NaturalOrbital Test Geom=Check

Alter the guess so that the three LUMOs are all the desired symmetry, and run
the CAS

0,1

orbital alterations

--Link1--
%chk=CAS1
%nosave
# CASSCF(2,4,NRoot=2) 6-31+G(D) Guess(Read) Pop(NaturalOrbital) Geom=Check Test

Excited state calculation

5.7 CASSCF 75

0,1

The second job step uses the NRoot option to CASSCF to specify the first excited state. The first excitation
energy for the system will then be computed by taking the energy difference between the two states (see exercise
5 in chapter 9 of Exploring Chemistry with Electronic Structure Methods [176] for a more detailed discussion
of this technique).
Predicting Conical Intersections. Including Opt=Conical keyword in the route section changes the job
from an optimization of the specified state using CASSCF to a search for a conical intersection or avoided
crossing involving that state. The optimized structure will be that of the conical intersection or avoided crossing.
Distinguishing between these two possibilities may be accomplished by examining the final eigenvalues in the
CASSCF output for the final optimization step (it precedes the optimized structure):

FINAL EIGENVALUES AND EIGENVECTORS

VECTOR EIGENVALUES CORRESPONDING EIGENVECTOR

state energy
1 -154.0503161 0.72053292 -0.48879229 · · ·
-0.16028934E-02 0.31874441E-02 · · ·
2 -154.0501151 0.45467877 0.77417416 · · ·

If the two eigenvalues (the first entry in the lines labeled with a state number) are essentially the same,
then the energies of the two states are the same, and it is a conical intersection. Otherwise, it is an avoided
crossing.
Spin Orbit Coupling. Here is the output from a CASSCF calculation where the spin orbit coupling has
been requested with the Spin option (the coupling is between the state specified to the NRoot option and the
next lower state):

****************************
spin-orbit coupling program
****************************
Number of configs= 4
1st state is 1 States for which spin orbit coupling is computed.
2nd state is 2
Transition Spin Density Matrix
1 2
1 .000000D+00 .141313D+01
2 .553225D-01 .000000D+00
magnitude in x-direction= .0000000 cm-1
magnitude in y-direction= .0000000 cm-1
magnitude in z-direction= 55.2016070 cm-1
total magnitude= 55.2016070 cm-1 Spin orbit coupling.
MCSCF converged.

The spin orbit coupling is broken down into X, Y, and Z components, followed by its total magnitude,
which in this case is 55.2016070 cm−1 .
 76 Chapter 5. List of Gaussian Keywords

RASSCF example. Here is an example RASSCF calculation route section:

# CAS(16,18,RASSCF(1,2,3,4)) 6-31G(d)
If this molecule is a neutral singlet, then this route defines the following spaces: RAS1 with 2 orbitals,
3 or 4 electrons in all configurations; RAS2 with 12 orbitals, 12 electrons in the reference configuration; and
RAS3 with 4 orbitals, 0-3 electrons in all configurations. Thus, the RAS2 space will have 9 to 13 electrons in
all configurations. The orbitals taken from the reference determinant for the active space are (assuming a spin
singlet) the 8 highest occupieds and 10 lowest virtuals: i.e., same orbitals as for a regular CAS(16,18).

5.8 CBS Methods

The following method keywords specify various Complete Basis Set (CBS) methods of Petersson and
coworkers for computing very accurate energies [44, 45, 110, 177–181]:
♢ CBS-4M
♢ CBS-QB3
♢ CBS-APNO
The keywords refer to the modified version of CBS-4 [180, 181], CBS-Q//B3 [110, 181] and CBS-APNO
[180] methods, respectively. No basis set should be specified with any of these keywords. The RO prefix may
be added to CBS-QB3 to request the ROCBS-QB3 method [182].
These methods are complex energy computations involving several pre-defined calculations on the speci-
fied system. All of these distinct steps are performed automatically when one of these keywords is specified,
and the final computed energy value is displayed in the output.
Either of the Opt=Maxcyc=n, QCISD=Maxcyc=n or CCSD=Maxcyc=n keywords may be used in con-
junction with any of the these keywords to specify the maximum number of optimization, QCISD, or CCSD
cycles, respectively.

5.8.1 Options
SP
Do only a single-point energy evaluation using the specified compound model chemistry. No zero-point
or thermal energies are included.
NoOpt
Perform the frequencies and single-point energy calculation for the specified model chemistry at the input
geometry. Freq=TProjected is implied. This option is not meaningful or accepted for methods such as
G1, which use different geometries for the frequencies and the single-point steps. StartFreq is a synonym
for NoOpt.
ReadIsotopes
This option allows you to specify alternatives to the default temperature, pressure, frequency scale factor
and/or isotopes – 298.15 K, 1 atmosphere, no scaling, and the most abundant isotopes (respectively). It is
useful when you want to rerun an analysis using different parameters from the data in a checkpoint file.
Be aware, however, that all of these can be specified in the route section (Temperature, Pressure and Scale
keywords) and molecule specification (the Iso parameter), as in this example:

#T Method/6-31G(d) JobType Temperature=300.0 · · ·

 5.8 CBS Methods 77

···

0 1
C(Iso=13)
···

ReadIsotopes input has the following format:

temp pressure [scale] Values must be real numbers.

isotope mass for atom 1
isotope mass for atom 2
···
isotope mass for atom n

Where temp, pressure, and scale are the desired temperature, pressure, and an optional scale factor for
frequency data when used for thermochemical analysis (the default is unscaled). The remaining lines hold
the isotope masses for the various atoms in the molecule, arranged in the same order as they appeared
in the molecule specification section. If integers are used to specify the atomic masses, the program will
automatically use the corresponding actual exact isotopic mass (e.g., 18 specifies 18 O, and Gaussian uses
the value 17.99916).
Restart
Restart from the checkpoint file from a previous CBS calculation. The new job will start after the last
successful calculation of the previous (unfinished) run.

5.8.2 Availability
Energies only.
CBS-4M and CBS-QB3 are available for first and second row atoms; CBS-APNO is available for first row
atoms only.
RO may be combined with CBS-4M and CBS-QB3.
The original CBS-4 model chemistry has been updated with both the new localization procedure and im-
proved empirical parameters [181]. The new version, CBS-4M, (M referring to the use of Minimal Population
localization) is recommended for new studies.

5.8.3 Examples
The output from each step of a CBS method calculation is included in the output file. The final section of
the file contains a summary of the results of the entire run.
CBS Summary Output. Here is the output from a CBS-QB3 calculation on CH2 (triplet state):

Complete Basis Set (CBS) Extrapolation:

M. R. Nyden and G. A. Petersson, JCP 75, 1843 (1981)
G. A. Petersson and M. A. Al-Laham, JCP 94, 6081 (1991)
G. A. Petersson, T. Tensfeldt, and J. A. Montgomery, JCP 94, 6091 (1991)
J. A. Montgomery, J. W. Ochterski, and G. A. Petersson, JCP 101, 5900 (1994)
 78 Chapter 5. List of Gaussian Keywords

Temperature= 298.150000 Pressure= 1.000000

E(ZPE)= 0.016991 E(Thermal)= 0.019855
E(SCF)= -38.936447 DE(MP2)= -0.114761
DE(CBS)= -0.011936 DE(MP34)= -0.018720
DE(CCSD)= -0.002759 DE(Int)= 0.004204
DE(Empirical)= -0.006404
CBS-QB3 (0 K)= -39.069832 CBS-QB3 Energy= -39.066969
CBS-QB3 Enthalpy= -39.066025 CBS-QB3 Free Energy= -39.088192

The temperature and pressure are given first, followed by the components terms of the CBS-QB3 energy.
The second-to-last line gives the CBS-QB3 energy values (reading across): at 0 K and at the specified temper-
ature (298.15 K by default). The final line gives the CBS-QB3 enthalpy (including the thermal correction for
the specified temperature) and the Gibbs free energy computed via the CBS-QB3 method (i.e., the CBS-QB3
energy including the frequency job free-energy correction). All of the energies are in Hartrees.
Rerunning the Calculation at a Different Temperature. The following two-step job illustrates the
method for running a second (very rapid) CBS calculation at a different temperature. This job computes the
CBS-QB3 energy at 298.15 K and then again at 300 K:
The energy labels thus have the following meanings (CBS-QB3 is used as an example):

CBS-QB3 (0 K) Zero-point-corrected electronic energy: E0 = Eelec + ZPE

CBS-QB3 Energy Thermal-corrected energy: E = E0 + Etrans + Erot + Evib
CBS-QB3 Enthalpy Enthalpy computed using the CBS-QB3 predicted energy: H = E + RT
CBS-QB3 Free Energy Gibbs Free Energy computed using the CBS-QB3 predicted energy: G = H - TS

%Chk=cbs
# CBS-QB3 Test

CBS-QB3 on formaldehyde

0 1
molecule specification

--Link1--
%Chk=cbs
%NoSave
# CBS-QB3(Restart,ReadIso) Geom=AllCheck Test

300.0 1.0
isotope specifications

5.9 CBSExtrapolate

This keyword requests a general Complete Basis Set extrapolation of the MP2 energy [44, 45, 177, 178].
 5.10 CCD and CCSD 79

The method requires two parameters: the minimum number of pair natural orbitals and the integration
grid, which are set with the CBSExtrapolate=NMin and Integral=Grid options, respectively.
The minimum number of pair natural orbitals defaults to 5 for the 6-31G**, 6-31G‡ and 6-311G** basis
sets (with or without diffuse functions), and to 10 for the 6-311G basis set with (2df,p) or (3df,p) polarization
functions (again, with or without diffuse functions). NMin must be specified in all other cases, or an error will
result.
The default integration grid is the (99,590) grid; an alternate grid can be specified with the Integral=Grid
keyword. The integration portion is a small part of the total CBS extrapolation computation, so this relatively
large grid was chosen. See the description of the Integral keyword for a full discussion of the available grids.

5.9.1 Options
NMin=N
Specifies N as the minimum number of pair natural orbitals.
MinPopLocal
Use localization based on populations in minimal basis [181]. This is the default.
PopLocal
Use population localization as described in reference [183].
BoysLocal
Use Boys localization [184–186].
NoLocal
Do not use any localization.
NRPopLocal
Newton-Raphson population localization.
NRBoysLocal
Newton-Raphson Boys localization.
NRMinPopLocal
Use 2nd order minimal population analysis.
SaveOrbitals
Save the localized CBS orbitals to the read-write file. Note that they will replace the SCF orbitals.

5.9.2 Availability
Single point energy calculations only, using any electron correlation method.

5.9.3 Related Keywords

Int=Grid, CBS

5.10 CCD and CCSD

These method keywords request coupled cluster calculations [187], using double substitutions from the
Hartree-Fock determinant for CCD [188], or both single and double substitutions for CCSD [189–192]. CC and
QCID are synonyms for CCD. RO may be combined with CCSD for a restricted open-shell energy calculation
[193].
 80 Chapter 5. List of Gaussian Keywords

5.10.1 Options
FC
All frozen core options are available with this keyword; a frozen core calculation is the default. See the
discussion of the FC options for full information.
T
Include triple excitations non-iteratively [190, 194] (CCSD only). CCSD-T is a synonym for CCSD(T).
E4T
Used with the T option to request inclusion of triple excitations for both the complete MP4 as well as
CCSD(T).
T1Diag
Computes the T1 diagnostic of T. J. Lee and coworkers [195] (CCSD only).
Conver=N
Sets the convergence calculations to 10−N on the energy and 10−(N−2) on the wavefunction. The default
is N=7 for single points and N=8 for gradients.
MaxCyc=N
Specifies the maximum number of cycles for CCSD calculations.
TWInCore
Whether to store amplitudes and products in memory during higher-order post-SCF calculations. The
default is to store these if possible, but to run off disk if memory is insufficient. TWInCore causes
the program to terminate if these can not be held in memory, while NoTWInCore prohibits in-memory
storage.
SaveAmplitudes
Saves the converged amplitudes in the checkpoint file for use in a subsequent calculation (e.g., using a
larger basis set). Using this option results in a very large checkpoint file, but also may significantly speed
up later calculations.
ReadAmplitudes
Reads the converged amplitudes from the checkpoint file (if present). Note that the new calculation can
use a different basis set, method (if applicable), etc. than the original one.

5.10.2 Availability
Analytic energies and gradients for CCD and CCSD, numerical gradients for CCSD(T), and numerical
frequencies for all methods.
The restricted open-shell (RO) method is available for CCSD and CCSD(T) energy calculations.

5.10.3 Related Keywords

MP4, Transformation

5.10.4 Examples
The Coupled Cluster energy appears in the output as follows following the final correlation iteration. The
CCSD energy is given in the first line below, and the final line reports the energy with triples included:

Wavefunction amplitudes converged. E(Corr)= -75.001924366

 5.11 Charge 81

···
CCSD(T)= -0.75002048348D+02

The CCSD energy is labeled E(CORR), and the energy including the non-iterative triples contribution is
given in the final line.

5.11 Charge
The Charge keyword requests that a background charge distribution be included in the calculation. The
charge distribution is made up of point charges [196, 197].

5.11.1 Input
By default, the charges are read from the input stream, one per line, in this format:
x y z charge
where x,y,z are the coordinates in the standard orientation (in the units specified by the Units keyword and
defaulting to Angstroms), and charge is the charge.

5.11.2 Options
Angstroms
Indicates that input charge locations are specified in Angstroms.
Bohrs
Indicates that input charge locations are specified in Bohrs.
Check
Reads the background charge distribution from the checkpoint file.

5.11.3 Availability
Single point energies, optimizations and frequencies. Not valid with semi-empirical methods or PBC.

5.11.4 Related Keywords

Units

5.11.5 Examples
To perform geometry optimizations in the presence of background charges, you must use Opt=Z-Matrix
NoSymm keywords and define the input geometry either in traditional Z-matrix coordinates or symbolic Carte-
sian coordinates. Here is an example:

# B3LYP/6=31G(d) Opt=Z-Matrix Charge NoSymm

Water with point charges

0,1
O -0.75 -0.94 0.0
H 0.21 -0.94 0.0
H -1.07 -0.0 0.0
 82 Chapter 5. List of Gaussian Keywords

2.0 2.0 2.0 1.2

2.0 -2.0 2.0 1.1

5.12 ChkBasis
The ChkBasis keyword requests that the basis set be read from the checkpoint file. It is useful in compound
jobs involving general basis sets by allowing them to have only one copy of the basis set in the input stream.
Note, however, that ChkBasis can be used to retrieve whatever basis set exists in a checkpoint file, regardless
of how it was originally specified. ECPs specified in the basis set are also retrieved, as are the choices for pure
vs. Cartesian functions.
By default, ChkBasis will also retrieve any density fitting basis in the checkpoint file. See the examples
for other possibilities.
Of course, no basis set keyword should be specified with ChkBasis.
CheckBasis, CheckPointBasis, ReadBasis, and RdBasis are all synonyms for ChkBasis.

5.12.1 Related Keywords

Gen, GenECP, Pseudo, ExtraBasis, ExtraDensityBasis

5.12.2 Examples
The following route section will retrieve the basis set and density fitting set (if any) from the checkpoint
file and use them for the current job:
# B3LYP/ChkBasis
The following route section will retrieve only the basis set from the checkpoint file, and an automatically
generated density fitting basis will be used:
# B3LYP/ChkBasis/Auto
The following route section will retrieve only the density fitting basis from the checkpoint file:
# B3LYP/6-31G(d)/ChkBasis

5.13 CID and CISD

These method keywords request a Hartree-Fock calculation followed by configuration interaction with
all double substitutions (CID) or all single and double substitutions (CISD) from the Hartree-Fock reference
determinant [198–200]. CI is a synonym for CISD.

5.13.1 Options
FC
All frozen core options are available with this keyword; a frozen core calculation is the default. See the
discussion of the FC options for full information.
Conver=N
Sets the convergence calculations to 10−N on the energy and 10−(N−2) on the wavefunction. The default
is N=7 for single points and N=8 for gradients.
 5.14 CIS 83

MaxCyc=n
Specifies the maximum number of cycles for CISD calculations.
SaveAmplitudes
Saves the converged amplitudes in the checkpoint file for use in a subsequent calculation (e.g., using a
larger basis set). Using this option results in a very large checkpoint file, but also may significantly speed
up later calculations.
ReadAmplitudes
Reads the converged amplitudes from the checkpoint file (if present). Note that the new calculation can
use a different basis set, method (if applicable), etc. than the original one.

5.13.2 Availability
Energies, analytic gradients, and numerical frequencies.

5.13.3 Related Keywords

Transformation

5.13.4 Examples
The CI energy appears in the output as follows:

DE(CI)= -.48299990D-01 E(CI)= -.75009023292D+02

NORM(A) = .10129586D+01

The output following the final CI iteration gives the predicted total energy. The second output line displays
the value of Norm(A). Norm(A) - 1 gives a measure of the correlation correction to the wavefunction; the
coefficient of the HF configuration is thus 1/Norm(A). Note that the wavefunction is stored in intermediate
normalization; that is:

ΨCISD = Ψ0 + ∑ Tia Ψ(i → a) + ∑ Tia jb Ψ(i j → ab)

ia ia jb

Wavefunction in Intermediate Normalization

where Ψ0 is the Hartree-Fock determinant and has a coefficient of 1 (which is what intermediate normalization
means). Norm(A) is the factor by which to divide the wavefunction as given above to fully normalize it. Thus:
v( )
u
u
Norm(A) = t 1 + ∑ Tia Tia + ∑ Ti jab Ti jab
ia i jab

Fully Normalized Wavefunction

The coefficient of the Hartree-Fock determinant in the fully normalized wavefunction is then 1/Norm(A), the
coefficient of singly-excited determinant Ψi→a is Tia /Norm(A), and so on.

5.14 CIS
The CIS method keyword requests a calculation on excited states using single-excitation CI (CI-Singles)
[201]. This implementation works for both closed-shell and open-shell systems.
 84 Chapter 5. List of Gaussian Keywords

CIS jobs can include the Density keyword. Without options, this keyword causes the population analysis
to use the current (CIS) density rather than its default of the Hartree-Fock density. Note that Density cannot be
used with CIS(D).
An energy range can be specified for CIS excitation energies using some options found under the procedure-
related options below.
CIS(D) is used to request the related CIS(D) method (i.e. the D option) [202, 203]. You can also follow a
CIS job with a CIS(D) job to compute the excitation energies for additional states (see the examples).

5.14.1 Options
State Selection Options
Singlets
Solve only for singlet excited states. This option only affects calculations on closed-shell systems, for
which it is the default.
Triplets
Solve only for triplet excited states. This option only affects calculations on closed-shell systems.
50-50
Solve for half triplet and half singlet states. This option only affects calculations on closed-shell systems.
Root=N
Specifies the “state of interest” for which the generalized density is to be computed. The default is the
first excited state (N=1).
NStates=M
Solve for M states (the default is 3). If 50-50 is requested, NStates gives the number of each type of state
for which to solve (i.e., the default is 3 singlets and 3 triplets).
Instead of an integer, Read may be specified as this option’s parameter. In this case, the number of states
to compute is read from the input stream. This is typically used in EET calculations.
Add=N
Read converged states off the checkpoint file and solve for an additional N states. This option implies
Read as well. NStates cannot be used with this option.

Energy Range Options

GOccSt=N
Generate initial guesses using only active occupied orbitals N and higher.
GOccEnd=N
Generate initial guesses: if N>0, use only the first N active occupied orbitals; if N<0, do not use the
highest |N| occupieds.
GDEMin=N
Generate guesses having estimated excitation energies ≥ N/1000 eV.
DEMin=N
Converge only states having excitation energy ≥ N/1000 eV; if N=-2, read threshold from input; if N<-2,
set the threshold to |N|/1000 Hartrees.
IFact=N
Specify factor by which the number of states updated during initial iterations is increased.
5.14 CIS 85

WhenReduce=M
Reduce to the desired number of states after iteration M.
The default for IFact is Max(4,g) where g is the order of the Abelian point group. The default for WhenRe-
duce is 2. A larger value may be needed if there are many states in the range of interest.

Density-Related Option

AllTransitionDensities
Computes the transition densities between every pair of states.

Procedure- and Algorithm-Related Options

FC
All frozen core options are available with this keyword; a frozen core calculation is the default. See the
discussion of the FC options for full information.
Direct
Forces solution of the CI-Singles equation using AO integrals which are recomputed as needed. CIS=Direct
should be used only when the approximately 4O2 N2 words of disk required for the default (MO) algo-
rithm are not available, or for larger calculations (over 200 basis functions).
MO
Requests that a CIS calculation use transformed integrals. This was the default for CIS in G09 but is
never the default in G16.
AO
Forces solution of the CI-Singles equations using the AO integrals, avoiding an integral transformation.
The AO basis is seldom an optimal choice, except for small molecules on systems having very limited
disk and memory.
Conver=N
Sets the convergence calculations to 10−N on the energy and 10−(N−2) on the wavefunction. The default
is N=4 for single points and N=6 for gradients.
Read
Reads initial guesses for the CI-Singles states off the checkpoint file. Note that, unlike for SCF, an initial
guess for one basis set cannot be used for a different one.
Restart
Restarts the CI-Singles iterations off the checkpoint file. Also implies SCF=Restart.
RWFRestart
Restarts the CI-Singles iterations off the read-write file. Useful when using non-standard routes to do
successive CI-Singles calculations.
EqSolv
Whether to perform equilibrium or non-equilibrium PCM solvation. NonEqSolv is the default except for
excited state optimizations and when the excited state density is requested (e.g., with the Current or All
options to the Density keyword).
NoIVOGuess
Forces the use of canonical single excitations for the guess. IVOGuess, which uses improved virtual
orbitals, is the default.
 86 Chapter 5. List of Gaussian Keywords

NonAdiabaticCoupling
Requests that the ground-to-excited-state non-adiabatic coupling be computed. NAC is a synonym for
this option. NoNonAdiabaticCoupling and NoNAC suppress this behavior. The default is NoNAC when
computing energies or energies+gradients because the extra cost is non-trivial. The default is NAC during
frequency calculations where the extra cost is negligible.

Debugging Options
ICDiag
Forces in-core full diagonalization of the CI-Singles matrix formed in memory from transformed inte-
grals. This is mainly a debugging option.
MaxDiag=N
Limits the submatrix diagonalized in the Davidson procedure to dimension N. This is mainly a debugging
option. MaxDavidson is a synonym for this option.

5.14.2 Availability
Energies, analytic gradients, and analytic frequencies for CIS (including open shell systems), and energies
for CIS(D).

5.14.3 Related Keywords

ZIndo, TD, MaxDisk, Transformation, Density

5.14.4 Examples
CIS Output. There are no special features or pitfalls with CI-Singles input. Output from a single point
CI-Singles calculation resembles that of a ground-state CI or QCI run. An SCF is followed by the integral
transformation and evaluation of the ground-state MP2 energy. Information about the iterative solution of the
CI problem comes next; note that at the first iteration, additional initial guesses are made, to ensure that the
requested number of excited states are found regardless of symmetry. After the first iteration, one new vector
is added to the solution for each state on each iteration.
The change in excitation energy and wavefunction for each state is printed for each iteration (in the #P
output):

Iteration 3 Dimension 27
Root 1 not converged, maximum delta is 0.002428737687607
Root 2 not converged, maximum delta is 0.013107675296678
Root 3 not converged, maximum delta is 0.030654755631835
Excitation Energies [eV] at current iteration:
Root 1 : 3.700631883679401 Change is -0.001084398684008
Root 2 : 7.841115226789293 Change is -0.011232152003400
Root 3 : 8.769540624626156 Change is -0.047396173133051

The iterative process can end successfully in two ways: generation of only vanishingly small expansion
vectors, or negligible change in the updated wavefunction.
When the CI has converged, the results are displayed, beginning with this banner:
 5.15 CNDO 87

*****************************************************************
Excited States From <AA,BB:AA,BB> singles matrix:
*****************************************************************

The transition dipole moments between the ground and each excited state are then tabulated. Next, the
results on each state are summarized, including the spin and spatial symmetry, the excitation energy, the oscil-
lator strength, and the largest coefficients in the CI expansion (use IOp(9/40=N) to request more coefficients:
all that are greater than 10−N ):

Excitation energies and oscillator strengths:

Symmetry, excitation energy, oscillator strength
Excited State 1: Singlet-A’ 3.7006 eV 335.03 nm f=0.0008
CI expansion coeffs. for each excitation:
8 -> 9 0.69112 Orbital 8 to 9

This state for opt. and/or second-order corr. This is the state of interest.
Total Energy, E(CIS) = -113.696894498 CIS energy is repeated here for convenience.

CI expansion coefficients give the importance of excited determinants in the excited state wavefunction.
Normalization. For closed shell calculations, the sum of the squares of the expansion coefficients is
normalized to total 1/2 (as the beta coefficients are not shown). For open shell calculations, the normalization
sum is 1.
Finding Additional States. The following route will read the CIS results from the checkpoint file and
solve for 6 additional states beyond those predicted in the previous calculation:
# CIS=(Read,Root=2,Add=6)

5.15 CNDO

This method keyword requests a semi-empirical calculation using the CNDO Hamiltonian [204]. No basis
set keyword should be specified.

5.15.1 Availability

Energies, pseudo-analytic gradients, and numerical frequencies.

5.15.2 Examples

The CNDO energy appears in the output file as follows:

SCF Done: E(UCNDO) = -8.08016620373 A.U. after 11 cycles
The energy is as defined by the CNDO model.

5.16 Complex

This keyword allows the molecular orbitals to become complex. It may only be used for closed-shell
singlet states.
 88 Chapter 5. List of Gaussian Keywords

5.16.1 Availability
Analytic energies for Hartree-Fock and MP2 only, analytic HF gradients, and numerical HF frequencies.

5.16.2 Related Keywords

SCF

5.17 Constants
Specifies which set of physical constants to use. Note that using an older set should only be done in order
to compare results with earlier versions of Gaussian.

5.17.1 Options
2010
Constants used in Gaussian 16, taken from [205, 206] and references therein. This is the default.
2006
Constants used in Gaussian 09, taken from [207] and references therein.
1998
Constants used in Gaussian 03 from [208] and references therein.
1986
Constants used in Gaussian 88 through Gaussian 98, from [209, 210].
1979
Constants used in Gaussian 80 through Gaussian 86, mostly from [211].

5.17.2 Current Values

Here are summarized various conversion factors and physical constants used by Gaussian 16 in converting
from standard to atomic units. All quantities used in calculations inside Gaussian are in atomic units; the
conversion factors are used only when processing input or generating printed output. Values without references
are derived from the referenced quantities.
Raw Constants. The constants which are stored directly in the program are:

1 Bohr (a0 ) = 0.52917721092 Å[205, 206]

1 Atomic mass unit (amu, mu ) = 1.660538921 × 10−27 kilograms [205, 206]
1 Electron charge (e) = 1.602176565 × 10−19 Coulombs [205, 206]
= 4.803204 × 10−10 ESU
Planck’s constant (h) = 6.62606957 × 10−34 Joule-secs [205, 206]
Avogadro’s number (NA ) = 6.02214129 × 1023 [205, 206]
1 Kcal-mol−1 = 4.184 Joules-mol−1 [211]
1 Hartree(Eh ) = 4.35974434 × 10−18 Joules [205, 206]
Speed of light (c) = 2.99792458 × 1010 cm-sec−1 [205, 206]
Boltzman constant (k) = 1.3806488 × 10−23 Joules-degree−1 [205, 206]
Inverse fine structure constant (α −1 ) = 137.035999074 [205, 206]
Molar volume of ideal gas at 273.15 K (Vm ) = 0.022710953 m3 [205, 206]
Proton rest mass (m p ) = 1.672621777 × 10−27 kg [205, 206]
 5.18 Counterpoise 89

Electron magnetic moment (µe ) = -9.28476430 × 10−24 J T−1 [205, 206]

Free electron g-factor (ge ) = -2.00231930436153 (dimensionless) [205, 206]

Conversion Factors. The following useful conversion factors are included for your convenience:

Electron mass (me ) = 0.910938291 × 10−30 kg [205, 206]

Proton mass (m p /me ) = 1836.15267245 electron mass [205, 206]
1 Atomic mass unit (amu) = 1.660538921 × 10−27 kg [205, 206]
= 1822.8885 electron mass
1 Electron volt (eV) = 1.602176565 × 10−19 Joules [205, 206]
= 23.06 kcal-mol−1
1 Hartree = 627.5095 kcal-mol−1
= 27.2114 eV
= 219474.63 cm−1 (vibrational freq. au)
1 Debye2 -angstrom−2 -amu−1 (IR intensity unit) = 42.2561 km-mol−1
= 5.82573 × 10−3 cm−2 -atm−1 at STP
Electric field: 1 au = 5.14220652 × 1011 V-m−1 [205, 206]
Electric polarizability: 1 au = 1.6487772754 × 10−41 C2 -m2 -J−1 [205, 206]
1 Bohr-electron (electric dipole moment au) = 8.47835326 × 10−30 C-m [205, 206]
= 2.541746 Debye = 2.541746 × 10−18 esu-cm

5.18 Counterpoise
Counterpoise corrections [212, 213] may be computed using the Counterpoise keyword, which can be
used in an energy calculation, a geometry optimization, a frequency calculation or a BOMD calculation.
The Counterpoise keyword requires an integer value specifying the number of fragments or monomers in
the molecular structure: e.g., Counterpoise=2.
We recommend the new syntax for defining fragments (see Overview of Molecule Specifications), and
that is what is used in the examples.
Chapter 9 of Exploring Chemistry with Electronic Structure Methods [152, pages 440, 442–44, 454–56]
provides an overview of counterpoise corrections, including several examples.

5.18.1 Options
NewGhost
Requests new-style ghost atoms for which integration grid points for DFT quadrature are included.
NewBq is a synonym for NewGhost. This is the default and the recommended method.
OldGhost
Requests old-style ghost atoms. OldBq is a synonym for OldGhost. This option is only useful for
comparison with previous results.

5.18.2 Availability
Cannot be used with ONIOM or SCRF. Counterpoise calculations cannot produce molecular orbitals.
 90 Chapter 5. List of Gaussian Keywords

5.18.3 Examples
Counterpoise Input. The following input is an example of a counterpoise calculation:

# UB3LYP/6-31G(d) Counterpoise=2

Counterpoise on water dimer

1,2 1,2 0,1

O(Fragment=1) 0.00 0.00 0.00
O(Fragment=2) 0.00 0.00 2.98
H(Fragment=1) 0.49 0.76 -0.29
H(Fragment=1) 0.49 -0.76 -0.29
H(Fragment=2) -0.91 0.00 3.24
H(Fragment=2) -0.01 0.00 2.03

The preceding job also illustrates the use of fragment-specific charge and spin multiplicity specifications.
The first pair on the charge and spin line gives the values for the molecule as a whole; they are followed by the
charge and spin for each fragment in fragment number order.
Here is an example counterpoise optimization using ECPs:

# B3LYP/LANL2DZ Counterpoise=2 NoSymm Opt

HBr + HF, optimization with counterpoise correction using ECP basis

0 1 0 1 0 1
H(Fragment=1) 0.00000000 0.00000000 0.58022808
Br(Fragment=1) 0.00000000 0.00000000 -0.83659185
F(Fragment=2) 0.00000000 0.00000000 2.77788358
H(Fragment=2) 0.00000000 0.00000000 3.69953441

Counterpoise Output. Typical output from a Counterpoise calculation follows:

Counterpoise corrected energy = -622.483714884838

BSSE energy = 0.005664641553
sum of fragments = -622.333463706103
complexation energy = -97.84 kcal/mole (raw)
complexation energy = -94.28 kcal/mole (corrected)

These lines give the counterpoise corrected energy and basis set superposition errors, respectively.

5.19 CPHF
This keyword selects the algorithm used for solving the CPHF equations [214–224].

5.19.1 Options
5.19 CPHF 91

Frequency-Dependent Calculations

RdFreq
Perform frequency-dependent (dynamic) CPHF, reading in the incident light frequency for the electro-
magnetic field perturbation. The desired frequency must be provided in the input stream. The default
units for this value are Hartrees. Other units may be specified by including a suffix, one of cm (cm−1 )
and nm (wavelength). This option is relevant for Freq and Polar jobs. It is the default for Freq=ROA.
InputFreq
Read in perturbation frequencies rather than take them from the checkpoint file when doing Geom=AllCheck.
Static
Automatically include the static perturbations when doing dynamic ones. This is the default except for
Polar=OptRot and Freq=ROA. NoStatic says not to perform static perturbations in combination with
dynamic via RdFreq.

Specifying the Integration Grid

Grid=grid
Specify the integration grid for the CPHF portion of the calculation. The syntax is the same as for the
Int=Grid option. The argument to this option may be a grid keyword (Fine, UltraFine, and so on) or a
specific grid.
The default grid is UltraFine. In this case, the default grid for the CPHF is SG1. When a specific
grid is specified to the Int=Grid option, then that grid is also used for the CPHF. Finally, be aware that
Fine is used in the CPHF as the default integration grid for a few DFT jobs including Polar=OptRot,
Freq=Anharmonic and Freq=NNROA.
See the discussion of Int=Grid for full details on grid specification.
OneStep
DFT nuclear 2nd derivatives (ground- or excited-state) should use a grid for CPHF and CPTD one step
smaller than the rest of the calculation.
TwoStep
DFT nuclear 2nd derivatives (ground- or excited-state) should use a grid for CPHF and CPTD two steps
smaller than the rest of the calculation. This is the default.
TauOneStep
DFT 2nd derivatives (ground- or excited-state) should use a grid for CPHF and CPTD one step smaller
than the rest of the calculation for tau-functionals but two steps smaller for GGAs.
PSCFOneStep
TDDFT 2nd derivatives should use a grid for CPHF and CPKS one step smaller than the rest of the
calculation, but ground-state frequencies continue to default to 2 steps.
PSCFTauOneStep
TDDFT 2nd derivatives should use a grid for CPHF and CPKS one step smaller than the rest of the
calculation when using tau functionals, but excited-state frequencies with GGAs and all ground-state
frequencies continue to default to 2 steps.

The step options are primarily useful in Default.Route

 92 Chapter 5. List of Gaussian Keywords

Procedure-Related Options

Conver=N
Set the CPHF convergence criterion to 10−N . N≥10 defaults to CPHF=Separate for the ground-state
CPHF/CPKS. N>=9 defaults to CPHF=Separate for CPCIS/CPTD.
RecursiveDIIS
Solve reduced equations using recursive DIIS. This is the default when the number of right-hand sides
is at least twice the dimension of the reduced matrix and the dimension of the reduced matrix is large
(occurs only for ONIOM(MO:MM) using electronic embedding), or the limit set by MaxInv is exceeded.
Otherwise, the default is NoRecursiveDIIS, which says to invert the reduced A-matrix.
MaxInv=N
Specifies the largest reduced space for in-core inversion during simultaneous solution (up to dimension
N). Larger reduced problems are solved by a second level of DIIS. The default is 5000.
Simultaneous
Use one expansion space for all variables. This is faster than using separate spaces, but is slightly less
accurate. This is the default except when multiple frequencies are specified with RdFreq (see below).
Separate
Use a separate expansion space for each variable in the CPHF (the opposite of Simultaneous). This is the
default and only choice when multiple frequencies are specified with RdFreq.
AO
Solve CPHF in the atomic orbital basis [216, 221–223]. This is the default.
MO
Solve in the molecular orbital basis.
Canonical
Canonical CPHF, the default.
MOD
Use MOD orbital derivatives for SAC-CI gradients (which uses configuration selection).

5.19.2 Related Keywords

SCF

5.20 Density

By default, population and other analysis procedures use the SCF density (i.e., the Hartree-Fock density
for post-SCF methods; the DFT density for DFT jobs, and the CASSCF density for CAS jobs). The generalized
densities for the MP2, MP3, MP4(SDQ), QCISD, CCD, CCSD, CID, and CISD, BD, CIS, TD and SAC-CI
methods are available. These are based on the Z-Vector [225–228], and hence yield multipole moments which
are the correct analytical derivatives of the energy. The unrelaxed densities at second order (not the same as
MP2) can also be used but are not recommended.
The options of the Density keyword select which density to analyze. The Density keyword without an
option is equivalent to Density=Current.
 5.20 Density 93

5.20.1 Options

Current
Use the density matrix for the current method. This is the default when no option is given to Density.
All
Use all available densities. This is allowed for population analysis but not for electrostatics or density
evaluation. Note that this option does not produce densities for all of the excited states in a CI-Singles
calculation, only the density for the state of interest (see the examples below for a method of doing the
former).
SCF
Use the SCF density. HF is a synonym for SCF.
MP2
Use the generalized density corresponding to the second-order energy.
Transition=N or (N,M)
Use the CIS transition density between state M and state N. M defaults to 0, which corresponds to the
ground state.
AllTransition
Use all available CIS transition densities.
CI
Use the generalized density corresponding to the CI energy.
CC
Use the generalized density corresponding to the QCI (or coupled cluster) energy. QCI is a synonym for
CC.
RhoCI
Use the one-particle density computed using the CI wavefunction for state N. This is not the same as the
CI density [228], and its use is discouraged! Chapter 9 of Exploring Chemistry with Electronic Structure
Methods discusses this issue [176].
Rho2
Use the density correct to second-order in Møller-Plesset theory. This is not the same as the MP2 density,
and its use is discouraged! [228]
CIS=N
Use the total unrelaxed CIS density for state N. Note that this is not the same as the density resulting
from CIS(Root=N,· · · ) Density=Current, which is to be preferred [228].
Checkpoint
Recover the density from the checkpoint file for analysis. Implies Guess=Only ChkBasis: the calculation
does not recompute new integrals, SCF, and so on, and retrieves the basis set from the checkpoint file.

5.20.2 Related Keywords

Guess, ChkBasis
 94 Chapter 5. List of Gaussian Keywords

5.20.3 Examples
The following route section specifies a TD-DFT calculation which predicts the first six excited states of the
molecule under investigation. The population and other analyses will use the TD-DFT density corresponding
to the lowest excited state:

%Chk=benzene
# TD(NStates=6) B3LYP/6-31+G(d,p) Density=Current Pop=NBO

The following route section may be used to rerun the post-TD analyses for another excited state:

%Chk=benzene
# TD(Read,Root=3) B3LYP/6-31+G(d,p) Density=Current Pop=NBO
Guess=Read Geom=AllCheck

This route picks up the converged TD density and wavefunction from the checkpoint file, and performs
the necessary CPHF calculation to produce the relaxed density for state 3, which is then used in the population
and other analyses.

5.21 DensityFit and NoDensityFit

Enables and controls density fitting for the Coulomb problem for calculations involving pure (non-hybrid)
DFT functionals. Density fitting basis sets are specified as part of the model chemistry within the job’s route
section. A list of built-in density fitting sets is included in the discussion of Basis Sets. DenFit is a synonym for
this keyword.
Including this keyword causes a fitting set to be used if possible for the specified model chemistry. If
no specific fitting set is specified in the route section, then the program will select the standard fitting set
corresponding to the specified basis set, if one exists, or generate one automatically. When DensityFit is
included in the Default.Route file, then /Fit is implied for all (relevant) calculations not specifying a fitting set.
The NoDensity keyword turns off the use of density fitting in pure DFT calculations. Since density fitting is
off by default in the program, this keyword’s only use is to override any DensityFit in Default.Route. NoDenFit
is a synonym for NoDensityFit.
If both a fitting set and NoDensityFit are included in a job’s route section, the latter is ignored, and density
fitting is used.

5.21.1 Options
Iterative
Controls whether a generalized inverse is formed or the fitting equations are solved iteratively. NonItera-
tive is the default except for ADMP and PBC.
InvToler=N
Set the tolerance for a non-trivial eigenvalue of the generalized inverse of the fitting matrix to 10−N .
Convergence=N
Specifies 10−N as the convergence criterion for iterative solution of the fitting equations. Implies Iterative.
The default is 10−6 for ADMP and 10−9 for BOMD.
Coulomb
Coulomb specifies the metric to be used for the fitting method. This is the default.
 5.22 DFT (Density Functional Theory) Methods 95

Overlap
Overlap specifies the metric to be used for the fitting method. The default is Coulomb.
JNormalization
Specifies that the read-in density basis has contraction coefficients corresponding to Coulomb normaliza-
tion. This is the default.
AONormalization
Specifies that the read-in density basis has contraction coefficients corresponding to AO (overlap) nor-
malization. JNormalization is the default.

5.21.2 Availability
Applies only to DFT calculations using pure (non-hybrid) functionals.

5.21.3 Related Keywords

Basis sets, ExtraDensityBasis, Gen, ChkBasis

5.22 DFT (Density Functional Theory) Methods

Gaussian 16 offers a wide variety of Density Functional Theory (DFT) [229–232] models (see also [233–
245] for discussions of DFT methods and applications). Energies [246], analytic gradients, and true analytic
frequencies [247–249] are available for all DFT models.
The self-consistent reaction field (SCRF) can be used with DFT energies, optimizations, and frequency
calculations to model systems in solution.
Pure DFT calculations will often want to take advantage of density fitting. See the discussion in Basis sets
for details.
The same optimum memory sizes given by freqmem are recommended for DFT frequency calculations.
Polarizability derivatives (Raman intensities) and hyperpolarizabilities are not computed by default during
DFT frequency calculations. Use Freq=Raman to request them. Polar calculations do compute them.
Note: The double hybrid functionals are discussed with the MP2 keyword since they have similar compu-
tational cost.

Accuracy Considerations
A DFT calculation adds an additional step to each major phase of a Hartree-Fock calculation. This step is a
numerical integration of the functional (or various derivatives of the functional). Thus in addition to the sources
of numerical error in Hartree-Fock calculations (integral accuracy, SCF convergence, CPHF convergence), the
accuracy of DFT calculations also depends on the number of points used in the numerical integration.
The UltraFine integration grid (corresponding to Integral=UltraFine) is the default in Gaussian 16. This
grid greatly enhances calculation accuracy at reasonable additional cost. We do not recommend using any
smaller grid in production DFT calculations. Note also that it is important to use the same grid for all calcu-
lations where you intend to compare energies (e.g., computing energy differences, heats of formation, and so
on).
Larger grids are available when needed (e.g. tight geometry optimizations of certain kinds of systems).
An alternate grid may be selected with the Integral=Grid option in the route section.
 96 Chapter 5. List of Gaussian Keywords

5.22.1 Background
In Hartree-Fock theory, the energy has the form:
EHF = V + <hP> + 1/2<PJ(P)> - 1/2<PK(P)>
where the terms have the following meanings:

V The nuclear repulsion energy.

P The density matrix.
<hP> The one-electron (kinetic plus potential) energy.
1/2<PJ(P)> The classical coulomb repulsion of the electrons.
-1/2<PK(P)> The exchange energy resulting from the quantum (fermion) nature of electrons.

In the Kohn-Sham formulation of density functional theory [230], the exact exchange (HF) for a single
determinant is replaced by a more general expression, the exchange-correlation functional, which can include
terms accounting for both the exchange and the electron correlation energies, the latter not being present in
Hartree-Fock theory:
EKS = V + <hP> + 1/2<PJ(P)> + EX [P] + EC [P]
where EX [P] is the exchange functional, and EC [P] is the correlation functional.
Within the Kohn-Sham formulation, Hartree-Fock theory can be regarded as a special case of density
functional theory, with EX [P] given by the exchange integral -1/2<PK(P)> and EC =0. The functionals normally
used in density functional theory are integrals of some function of the density and possibly the density gradient:
∫ ( )
EX [P] = f ρα (r), ρβ (r), ∇ρα (r), ∇ρβ (r) dr
where the methods differ in which function f is used for EX and which (if any) f is used for EC . In addition to
pure DFT methods, Gaussian supports hybrid methods in which the exchange functional is a linear combination
of the Hartree-Fock exchange and a functional integral of the above form. Proposed functionals lead to integrals
which cannot be evaluated in closed form and are solved by numerical quadrature.

5.22.2 Keywords: Hybrid Functionals

A number of hybrid functionals, which include a mixture of Hartree-Fock exchange with DFT exchange-
correlation, are available via keywords:

Becke Three-Parameter Hybrid Functionals

These functionals have the form devised by Becke in 1993 [250]:
A*ESlater + (1-A)*EHF Becke + EVW N + C*∆Enon−local
X X + B*∆EX C C
where A, B, and C are the constants determined by Becke via fitting to the G1 molecule set.
There are several variations of this hybrid functional.
♢ B3LYP uses the non-local correlation provided by the LYP expression, and VWN functional III for local cor-
relation (not functional V). Note that since LYP includes both local and non-local terms, the correlation
functional used is actually:
C*ECLY P +(1-C)*EVW
C
N

In other words, VWN is used to provide the excess local correlation required, since LYP contains a local
term essentially equivalent to VWN.
♢ B3P86 specifies the same functional with the non-local correlation provided by Perdew 86, and B3PW91
specifies this functional with the non-local correlation provided by Perdew/Wang 91.
5.22 DFT (Density Functional Theory) Methods 97

♢ O3LYP is a three-parameter functional similar to B3LYP:

A*ELSD HF OPT X +C*∆ELY P +(1-C)EVW N
X +(1-A)*EX +B*∆EX C C
where A, B and C are as defined by Cohen and Handy in reference [251].

Functionals Including Dispersion

♢ APFD requests the Austin-Frisch-Petersson functional with dispersion [252], and APF requests the same
functional without dispersion.
♢ The wB97XD functional uses a version of Grimme’s D2 dispersion model.
The standalone keyword EmpiricalDispersion also allows you to specify a dispersion scheme with various
functionals.

Long-Range-Corrected Functionals
The non-Coulomb part of exchange functionals typically dies off too rapidly and becomes very inaccurate
at large distances, making them unsuitable for modeling processes such as electron excitations to high orbitals.
Various schemes have been devised to handle such cases. Gaussian 16 offers the following functionals which
include long-range corrections:
♢ LC-wHPBE: Recommended version [253] of the long-range-corrected ω PBE functional [254–256]. LC-
wPBE requests the original version.
♢ CAM-B3LYP: Handy and coworkers’ long-range-corrected version of B3LYP using the Coulomb-attenuating
method [257].
♢ wB97XD: The latest functional from Head-Gordon and coworkers, which includes empirical dispersion
[258]. The wB97 and wB97X [259] variations are also available. These functionals also include long-
range corrections.
In addition, the prefix LC- may be added to most pure functionals to apply the long correction of Hirao
and coworkers [260]: e.g., LC-BLYP.

Other Hybrid Functionals

Functionals from the Truhlar Group
♢ MN15 requests the MN15 [261] functional.
♢ M11 [262], SOGGA11X [263], N12SX [264], and MN12SX [264] request these hybrid functionals from
the Truhlar group.
♢ PW6B95 and PW6B95D3 [265].
♢ M08HX: The M08-HX functional [266].
♢ M06 hybrid functional of Truhlar and Zhao [267]. The M06HF [268, 269] and M062X [267] variations are
also available.
♢ M05 [270] and M052X [271].
Functionals Employing PBE Correlation
♢ The 1996 pure functional of Perdew, Burke and Ernzerhof [272, 273] as made into a hybrid functional
by Adamo [274]. The keyword is PBE1PBE. This functional uses 25% exact exchange and 75% DFT
exchange. It is known in the literature as PBE0 [274] and as the PBE hybrid [275].
♢ HSEH1PBE: The recommended version of the full Heyd-Scuseria-Ernzerhof functional, referred to as HSE06
in the literature [253, 276–281].
♢ OHSE2PBE: The initial form of the HS06 functional, referred to as HSE03 in the literature.
98 Chapter 5. List of Gaussian Keywords

♢ OHSE1PBE: The version of the HS06 functional prior to modification to support third derivatives.
♢ PBEh1PBE: Hybrid using the 1998 revised form of PBE pure functional (exchange and correlation) [282].
Becke One-Parameter Hybrid Functionals
The B1B95 keyword is used to specify Becke’s one-parameter hybrid functional as defined in the original
paper [283].
The program also provides other, similar one parameter hybrid functionals implemented by Adamo and
Barone [284]. In one variation, B1LYP, the LYP correlation functional is used (as described for B3LYP above).
Another version, mPW1PW91, uses Perdew-Wang exchange as modified by Adamo and Barone combined with
PW91 correlation [285]; the mPW1LYP, mPW1PBE and mPW3PBE variations are available.
Revisions to B97
♢ Becke’s 1998 revisions to B97 [286, 287]. The keyword is B98, and it implements fit 2c in reference [287].
♢ Handy, Tozer and coworkers modification to B97: B971 [288].
♢ Wilson, Bradley and Tozer’s modification to B97: B972 [289].
Functionals with τ -Dependent Gradient-Corrected Correlation
♢ TPSSh: Hybrid functional using the TPSS functionals [290, 291].
♢ tHCTHhyb: Hybrid functional using the tHCTH functional [292].
♢ BMK: Boese and Martin’s τ -dependent 2004 hybrid functional [293].
Older Functionals
♢ HISSbPBE requests the HISS functional [294].
♢ X3LYP: Functional of Xu and Goddard [295].
Half-and-Half Functionals
The following functionals, which are included for backward-compatibility only. Note that these are not
the same as the “half-and-half” functionals proposed by Becke [296].
♢ BHandH: 0.5*EHF LSDA + ELY P
X + 0.5*EX C
♢ BHandHLYP: 0.5*EHF LSDA + 0.5*∆EBecke88 + ELY P
X + 0.5*EX X C

User-Defined Hybrid Models

Gaussian 16 can use any model of the general form:
P2 EHF
X + P1 (P4 ESlater
X + P3 ∆Enon−local
x ) + P6 EClocal + P5 ∆ECnon−local
The only available local exchange method is Slater (S), which should be used when only local exchange
is desired. Any combinable non-local exchange functional and combinable correlation functional may be used
(as listed previously).
The values of the six parameters are specified with various non-standard options to the program:
♢ IOp(3/76=mmmmmnnnnn) sets P1 to mmmmm/10000 and P2 to nnnnn/10000. P1 is usually set to either 1.0
or 0.0, depending on whether an exchange functional is desired or not, and any scaling is accomplished
using P3 and P4 .
♢ IOp(3/77=mmmmmnnnnn) sets P3 to mmmmm/10000 and P4 to nnnnn/10000.
♢ IOp(3/78=mmmmmnnnnn) sets P5 to mmmmm/10000 and P6 to nnnnn/10000.
For example, IOp(3/76=1000005000) sets P1 to 1.0 and P2 to 0.5. Note that all values must be expressed
using five digits, adding any necessary leading zeros.
Here is a route section specifying the functional corresponding to the B3LYP keyword:
#P BLYP IOp(3/76=1000002000) IOp(3/77=0720008000) IOp(3/78=0810010000)
 5.22 DFT (Density Functional Theory) Methods 99

The output file displays the values that are in use:

IExCor= 402 DFT=T Ex=B+HF Corr=LYP ExCW=0 ScaHFX= 0.200000

ScaDFX= 0.800000 0.720000 1.000000 0.810000

where the value of ScaHFX is P2 , and the sequence of values given for ScaDFX are P4 , P3 , P6 , and P5 .

5.22.3 Keyword: Pure Functionals

Names for the various pure DFT models are given by combining the names for the exchange and correla-
tion functionals. In some cases, standard synonyms used in the field are also available as keywords. In order to
specify a pure functional, combine an exchange functional component keyword with the one for desired corre-
lation functional. For example, the combination of the Becke exchange functional (B) and the LYP correlation
functional is requested by the BLYP keyword. Similarly, SVWN requests the Slater exchange functional (S)
and the VWN correlation functional, and is known in the literature by its synonym LSDA (Local Spin Density
Approximation). LSDA is a synonym for SVWN. Some other software packages with DFT facilities use the
equivalent of SVWN5 when “LSDA” is requested. Check the documentation carefully for all packages when
making comparisons.

Exchange Functionals

The following exchange functionals are available in Gaussian 16. Unless otherwise indicated, these ex-
change functionals must be combined with a correlation functional in order to produce a usable method.
♢ S: The Slater exchange, ρ 4/3 with theoretical coefficient of 2/3, also referred to as Local Spin Density
exchange [229, 230, 297]. Keyword if used alone: HFS.
♢ XA: The XAlpha exchange, ρ 4/3 with the empirical coefficient of 0.7, usually employed as a standalone
exchange functional, without a correlation functional [229, 230, 297]. Keyword if used alone: XAlpha.
♢ B: Becke’s 1988 functional, which includes the Slater exchange along with corrections involving the gradient
of the density [298]. Keyword if used alone: HFB.
♢ PW91: The exchange component of Perdew and Wang’s 1991 functional [237, 241, 299–301].
♢ mPW: The Perdew-Wang 1991 exchange functional as modified by Adamo and Barone [285].
♢ G96: The 1996 exchange functional of Gill [302, 303].
♢ PBE: The 1996 functional of Perdew, Burke and Ernzerhof [272, 273].
♢ O: Handy’s OPTX modification of Becke’s exchange functional [304, 305].
♢ TPSS: The exchange functional of Tao, Perdew, Staroverov, and Scuseria [290].
♢ RevTPSS: The revised TPSS exchange functional of Perdew et. al. [306, 307].
♢ BRx: The 1989 exchange functional of Becke [308].
♢ PKZB: The exchange part of the Perdew, Kurth, Zupan and Blaha functional [309].
♢ wPBEh: The exchange part of screened Coulomb potential-based final of Heyd, Scuseria and Ernzerhof
(also known as HSE) [253, 280, 310].
♢ PBEh: 1998 revision of PBE [282].

Correlation Functionals

The following correlation functionals are available, listed by their corresponding keyword component, all
of which must be combined with the keyword for the desired exchange functional:
 100 Chapter 5. List of Gaussian Keywords

♢ VWN: Vosko, Wilk, and Nusair 1980 correlation functional(III) fitting the RPA solution to the uniform
electron gas, often referred to as Local Spin Density (LSD) correlation [311] (functional III in this article).
♢ VWN5: Functional V from reference [311] which fits the Ceperly-Alder solution to the uniform electron
gas (this is the functional recommended in [311]).
♢ LYP: The correlation functional of Lee, Yang, and Parr, which includes both local and non-local terms [312,
313].
♢ PL (Perdew Local): The local (non-gradient corrected) functional of Perdew (1981) [314].
♢ P86 (Perdew 86): The gradient corrections of Perdew, along with his 1981 local correlation functional [315].
♢ PW91 (Perdew/Wang 91): Perdew and Wang’s 1991 gradient-corrected correlation functional [237, 241,
299–301].
♢ B95 (Becke 95): Becke’s τ -dependent gradient-corrected correlation functional (defined as part of his one
parameter hybrid functional [283]).
♢ PBE: The 1996 gradient-corrected correlation functional of Perdew, Burke and Ernzerhof [272, 273].
♢ TPSS: The τ -dependent gradient-corrected functional of Tao, Perdew, Staroverov, and Scuseria [290].
♢ RevTPSS: The revised TPSS correlation functional of Perdew et. al. [306, 307].
♢ KCIS: The Krieger-Chen-Iafrate-Savin correlation functional [316–319].
♢ BRC: Becke-Roussel correlation functional [308].
♢ PKZB: The correlation part of the Perdew, Kurth, Zupan and Blaha functional [309].
Correlation Functional Variations. The following correlation functionals combine local and non-local
terms from different correlation functionals:
♢ VP86: VWN5 local and P86 non-local correlation functional.
♢ V5LYP: VWN5 local and LYP non-local correlation functional.

Standalone Pure Functionals

The following pure functionals are self-contained and are not combined with any other functional keyword
components:
♢ VSXC: van Voorhis and Scuseria’s τ -dependent gradient-corrected correlation functional [320].
♢ HCTH/*: Handy’s family of functionals including gradient-corrected correlation [288, 321, 322]. HCTH
refers to HCTH/407, HCTH93 to HCTH/93, HCTH147 to HCTH/147, and HCTH407 to HCTH/407.
Note that the related HCTH/120 functional is not implemented.
♢ tHCTH: The τ -dependent member of the HCTH family [292]. See also tHCTHhyb below.
♢ B97D: Grimme’s functional including dispersion [323]. B97D3 requests the same but with Grimme’s D3BJ
dispersion [324].
♢ M06L [325], SOGGA11 [326], M11L [327], MN12L [328] N12 [329] and MN15L [330] request these pure
functionals from the Truhlar group.

5.22.4 Empirical Dispersion

The EmpiricalDispersion keyword enables empirical dispersion. It takes the following options:
PFD
Add the Petersson-Frisch dispersion model from the APFD functional [252].
GD2
Add the D2 version of Grimme’s dispersion [323]. The table below gives the list of functionals in
5.22 DFT (Density Functional Theory) Methods 101

Gaussian 16 for which GD2 parameters are defined. The functionals highlighted in bold include this
dispersion model by default when the indicated keyword is specified (e.g., B2PLYPD). For the rest of the
functionals, dispersion is requested with EmpiricalDispersion=GD2.

Functional S6 SR6
B97D 1.2500 1.1000
B2PLYPD 0.5500 1.1000
mPW2PLYPD 0.4000 1.1000
PBEPBE 0.7500 1.1000
BLYP 1.2000 1.1000
B3LYP 1.0500 1.1000
BP86 1.0500 1.1000
TPSSTPSS 1.0000 1.1000

The damping function used by this model also contains a D6 parameter with a fixed value of 6.0.
You can use this empirical dispersion method with other functionals by defining the values of the SR6
and S6 parameters (the value of SR6 is always 1.1). This is done using an environment variable with the
name GAUSS_DFTD3_S6. The value of the environment variable sets the corresponding parameter to
value/1,000,000. For example, the command:
export GAUSS_DFTD3_S6=1200000
sets the value of S6 to 1200000/1000000=1.2.
The wB97XD functional – specified as an independent keyword – uses a version of this dispersion model
with values of S6 and SR6 of 1.0 and 1.1, respectively. This functional uses a similar damping function
to that used by the GD3 model, with D6 and IA6 having fixed values of 6.0 and 12, respectively.
GD3
Add the D3 version of Grimme’s dispersion with the original D3 damping function [331]. The table
below gives the list of functionals in Gaussian 16 for which GD3 parameters are defined. For these
functionals, dispersion is requested with EmpiricalDispersion=GD3.

Functional S6 SR6 S8
B2PLYPD3 [332] 0.6400 1.4270 1.0220
B97D3 1.0000 0.8920 0.9090
B3LYP 1.0000 1.2610 1.7030
BLYP 1.0000 1.0940 1.6820
PBE1PBE 1.0000 1.2870 0.9280
TPSSTPSS 1.0000 1.1660 1.1050
PBEPBE 1.0000 1.2170 0.7220
BP86 1.0000 1.1390 1.6830
BPBE 1.0000 1.0870 2.0330
B3PW91 1.0000 1.1760 1.7750
BMK 1.0000 1.9310 2.1680
CAM-B3LYP 1.0000 1.3780 1.2170
LC-wPBE 1.0000 1.3550 1.2790
102 Chapter 5. List of Gaussian Keywords

M05 1.0000 1.3730 0.5950

M052X 1.0000 1.4170 0.0000
M06L 1.0000 1.5810 0.0000
M06 1.0000 1.3250 0.0000
M062X 1.0000 1.6190 0.0000
M06HF 1.0000 1.4460 0.0000

This model also uses an SR8 parameter with a fixed value of 1.0. The damping function used by this
model also contains D6, IA6, D8, and IA8 parameters with fixed values of 6.0, 14, 6.0, and 16, respec-
tively.
You can use this empirical dispersion method with other functionals by defining the values of the SR6
and S8 parameters (the value of S6 is always 1.0). This is done using environment variables with names
of the form GAUSS_DFTD3_param, where param is one of the parameter names. The value of the
environment variable sets the corresponding parameter to value/1,000,000. For example, the command:
export GAUSS_DFTD3_S8=1375000
sets the value of S8 to 1375000/1000000=1.375.
GD3BJ
Add the D3 version of Grimme’s dispersion with Becke-Johnson damping [324]. The table below gives
the list of functionals in Gaussian 16 for which GD3BJ parameters are defined. The functionals high-
lighted in bold include this dispersion model by default when the indicated keyword is specified (e.g.,
B2PLYPD3). For the rest of the functionals, dispersion is requested with EmpiricalDispersion=GD3BJ.

Functional S6 S8 ABJ1 ABJ2

B2PLYPD3 [332] 0.6400 0.9147 0.3065 5.0570
B97D3 1.0000 2.2609 0.5545 3.2297
B3LYP 1.0000 1.9889 0.3981 4.4211
BLYP 1.0000 2.6996 0.4298 4.2359
PBE1PBE 1.0000 1.2177 0.4145 4.8593
TPSSTPSS 1.0000 1.9435 0.4535 4.4752
PBEPBE 1.0000 0.7875 0.4289 4.4407
BP86 1.0000 3.2822 0.3946 4.8516
BPBE 1.0000 4.0728 0.4567 4.3908
B3PW91 1.0000 2.8524 0.4312 4.4693
BMK 1.0000 2.0860 0.1940 5.9197
CAM-B3LYP 1.0000 2.0674 0.3708 5.4743
LC-wPBE 1.0000 1.8541 0.3919 5.0897

You can use this empirical dispersion method with other functionals by defining the values of the S8,
ABJ1 and ABJ2 parameters (the value of S6 is always 1.0). This is done using environment variables
with names of the form GAUSS_DFTD3_param, where param is one of the parameter names. The
value of the environment variable sets the corresponding parameter to value/1,000,000. For example, the
command:
 5.23 DFTB and DFTBA 103

export GAUSS_DFTD3_S8=2375000
sets the value of S8 to 2375000/1000000=2.375.

5.22.5 Availability
Energies, analytic gradients, and analytic frequencies; ADMP calculations.
Third order properties such as hyperpolarizabilities and Raman intensities are not available for functionals
for which third derivatives are not implemented: the exchange functionals G96, P86, PKZB, wPBEh and PBEh;
the correlation functional PKZB; the hybrid functionals OHSE1PBE and OHSE2PBE.

5.22.6 Related Keywords

IOp, Int=Grid, Stable, TD, DenFit, B2PLYP, mPW2LYP

5.22.7 Examples
The energy is reported in DFT calculations in a form similar to that of Hartree-Fock calculations. Here is
the energy output from a B3LYP calculation:
SCF Done: E(RB3LYP) = -75.3197099428 A.U. after 5 cycles

5.23 DFTB and DFTBA

Requests a density-functional-based tight-binding semi-empirical calculation, a method which is parametrized
via the results of DFT calculations:
♢ DFTB uses the tabulated matrix elements as in the original implementation of Elstner and coworkers [333,
334].
♢ DFTBA is a version that uses analytic expressions for the matrix elements rather than tabulated ones [335].
See [336–340] for review articles and calibration studies.

5.23.1 Options
Read
Read values for parameters from the input stream. This is the default.
ChkParameters
Read parameters from the checkpoint file.

5.23.2 Availability
Energies, gradients, and frequencies.
Analytic second derivatives are available when the analytic DFTB parameters (provided with the program)
are used, but are not available when the tabulated parameters from dftb.org are used. This is because the
linear interpolation that is done using the tabulated parameters give discontinuous first derivatives at first points,
so the second derivatives do not always exist. If you want to ignore this potential problem and compute second
derivatives using the tabulated parameters, then Freq=Numer must be specified in the job’s route section.

Parameter Files
DFTBA is parametrized for all pairs of H, C, N, and O. It is also parametrized for the metals Sc, Ti, Fe,
Co, and Ni but only with H, C, N, and O. That is, Fe5 CO and Sc5 CO are supported, but Fe4 ScCO is not.
 104 Chapter 5. List of Gaussian Keywords

The DFTB parameter files are copyright by Professor Elstner and must be obtained from him.

5.23.3 Examples
The following input file format runs a DFTBA calculation using the parameter set provided with Gaussian:

# DFTBA OPT FREQ

Ala3 DFTB frequencies

0,1
C,0,-4.5929012011,1.0163256276,1.6498020765
O,0,-5.6641782096,0.9622594116,2.2369288649
H,0,-5.788876035,3.2375262156,-2.1703220199
N,0,-4.4446298947,1.4038535552,0.3517633631
Molecule specification continues · · ·

@GAUSS_EXEDIR:dftba.prm

For DFTB, the same format of parameter files is used as in other programs: one file for each pair of
elements, with the order of the two elements being significant. Accordingly, a calculation on H2 CO would use
a parameter input section something like this:

@cc.prm
@oo.prm
@hh.prm
@co.prm
@oc.prm
@ch.prm
@hc.prm
@oh.prm
@ho.prm

The energy appears in the output as follows:

SCF Done: E(RDFT-SCTBA) = -33.9465130617 A.U. after 11 cycles

5.23.4 Modifying Slater-Koster Files

DFTB Parameter (.skf) Files and Gaussian

The handling of DFTB input files has been modified for compatibility with the files provided by Elstner:
HTML data at the end of the file is ignored. Also, multipliers – e.g. 10*1.0 – are now accepted.

Modifying Slater-Koster files (.skf) from dftb.org for use with Gaussian

The first line of each file must be edited to identify the two elements involved. For example, in the file
H-S.skf the first line should contain the atomic numbers, so it goes from dftb.org format:
2.000000000000E-02, 500
 5.24 EET 105

to Gaussian format:
0.02, 500 1 16 Add atomic numbers for hydrogen and sulfur.
The second field in the first line of each file should contain the number of lines in the file containing grid
points for the Hamiltonian and overlap integrals. However, these values are often just placeholders of 500 (as
above) or 600. Many of the files – especially older ones – actually supply some other number of points. If you
count the number of lines between the one with the first point and the last line before Spline, this will yield
the required value:
2.000000000000E-02, 601 1 6 The next line is line 1.
0.000000000000E+00 0.000000000000E+00 0.000000000000E+00 0.000000000000E+00
0.000000000000E+00 0.000000000000E+00 0.000000000000E+00 0.000000000000E+00
-1.668269422592E-05 1.066481969438E-06 0.000000000000E+00 0.000000000000E+00
···
0.000000000000E+00 0.000000000000E+00 0.000000000000E+00 0.000000000000E+00
0.000000000000E+00 0.000000000000E+00 4.881740699644E-05 -7.526317479277E-06
Spline The preceding line is the last one to count.
30 3.5

You would then edit the first line to reflect the actual number of points:
0.02, 601 1 16 Some of the files involving hydrogens are links rather than separate files because they are
the same as the corresponding file with the order of the elements reversed. For example, H-C.skf is a link to
C-H.skf. However, Gaussian expects both files to be provided, differing only in the order of the atomic numbers
on the first line.

5.24 EET
Energy transfer from a photoexcited donor molecule to a nearby ground-state acceptor molecule is a pro-
cess of fundamental interest in many fields of science, including polymer photophysics, surface photochemistry,
photochemical synthesis and molecular device engineering. It is usually known as electronic energy transfer
(EET) or resonance energy transfer (RET). The fundamental theoretical treatment was presented by Förster in
1948 [341], and it EET analysis computes the excitation energy transfer rate between molecules (or parts of
molecules) from the overlap of the fluorescence spectrum of the donor molecule/fragment with the absorption
spectum of the acceptor molecule/fragment. However, not all energy transfers are described well by this treat-
ment. Accordingly, there have been many extensions to Förster’s theory, beginning with Dexter [342]. In recent
years, a variety of new models have built upon these foundations; see [343] for a review.
In Gaussian 16, the EET analysis is a quantum mechanical model for EET based on a DFT description
of the wavefunction, incorporating a time-dependent variational approach [344, 345]. EET is available in the
gas phase and in solution. Indeed, Förster’s original theory recognizes the importance of solvent effects. The
implementation in solution in Gaussian 16 is the formulation of Iozzi, Mennucci, Tomasi and Cammi [346],
a model that differs from its predecessors (e.g., [347]) in that it incorporates solvent effects by adding the
appropriate operators to the Hamiltonian and the linear response equations; in this way, solvation is present in
all steps of the quantum mechanical calculation [348–351]. The solvation cavity for this model is the same for
other employments of IEFPCM [352–354] (rather than a simplistic sphere or multipolar expansion).
The EET keyword performs an excitation energy transfer calculation using the results of the CIS/TDA/TD-
DFT calculation or of an EOM-CCSD calculation. This type of calculation uses the same setup of Guess
 106 Chapter 5. List of Gaussian Keywords

(Fragment=· · · ) but it can also process ONIOM-like link-atom input information to cap the fragments. An
excited-state calculation is performed on each fragment, and all the coupling among all the resulting states are
computed. Solvent effects can be introduced using PCM and a single cavity, or a fragment-pair cavity can be
used to evaluated the solvent-mediated coupling.

5.24.1 Options
Fragment=N
Set up N fragments.
FullSystemCavity
Use the PCM cavity for the whole system when evaluating the EET coupling. This is the default.
FragmentCavity
Set up a PCM cavity for each pair of fragments when evaluating the EET coupling.
NonEqSolv
Force the use of non-equilibrium solvation for the solvent-mediated term of the coupling.
EqSolv
Force the use of equilibrium solvation for the solvent-mediated term of the coupling.
The default choice of equilibrium vs non-equilibrium is such that the EET is consistent with what has been
done in L913/L914.

5.24.2 Examples
The following simple input file performs an EET calculation on formaldehyde dimer, treating each molecule
as a separate fragment. This job models the EET for a single excited state.

# td(nstates=1) b3lyp/6-31G(d) eet(fragment=2)

EET in gas phase (Closed shell fragments done as closed shell)

Full : H2CO ... H2CO
Frag 1: H2CO
Frag 2: H2CO

0 1 0 1 0 1
C(fragment=1) 0.000000 -0.542500 0.000000
O(fragment=1) 0.000000 0.677500 0.000000
H(fragment=1) 0.000000 -1.082500 0.935307
H(fragment=1) 0.000000 -1.082500 -0.935307
C(fragment=2) 2.000000 -0.542500 0.000000
O(fragment=2) 2.000000 0.677500 0.000000
H(fragment=2) 2.000000 -1.082500 0.935307
H(fragment=2) 2.000000 -1.082500 -0.935307

Here is the key part of the EET output:

===============================================================================

Electronic Coupling for Excitation Energy Tranfer

 5.25 EOMCCSD 107

===============================================================================
Separate basis set information will be generated for each pair of fragments.
Using analytical method for overlap contributions to EET.

The minimum distance is a measure of how far the electron moves.

Frag= 2 1 min distance between atoms 5 1 = 2.00 Angs (sum of Rcov=1.520)
excluding hydrogens 5 1 = 2.00 Angs (sum of Rcov=1.520)

End of next line gives value of ω for these two fragments & states.
Frag= 2 State= 1 (w= 3.9574 eV) Frag= 1 State= 1 (w= 3.9574 eV)

delta-w = 0.000000000 eV Energy difference between the two states.

Coulomb = -0.035983294 eV
Exact-exchange = 0.014046399 eV
Exchange-correlation = 0.006375024 eV
w-avg*Overlap = -0.000357708 eV (w-avg=3.957 eV, Ovlp=-0.90389D-04)
Total coupling = -0.015919579 eV Parameter used to compute the rate of EET.

This output will be repeated for each interaction requested by the calculation.

5.25 EOMCCSD
Requests an excited state calculation using the EOM-CCSD method [355–365]. EOM-CCSD is an exten-
sion of CCSD for modeling excited states. It provides CCSD-level accuracy for excited-state calculations and
requires comparable computational cost (scaling as N6 like CCSD) and additional disk space. This method uses
a preliminary CIS calculation to generate the initial guess for the states followed by an EOM-CCSD analysis.
Note: The EOM-CCSD method exploits abelian symmetry (and not higher point groups).
The various solvation methods for EOM developed by Caricato [360, 366, 367] are available; see the
SCRF=PTED option for details.

5.25.1 Options
State Selection and Specification
NStates=N
Try to solve for the lowest N states in EOM. It is a good idea to set N to be larger than the desired number
of states to take account of likely state reordering between the CIS and EOM portions.
NStPIR=K
Number of states per symmetry type to solve for in the EOM. The default is 2. Note that the symmetry
types correspond to the largest abelian subgroups. If K is less than zero, then a separate blank line-
terminated input section is read specifying the number of states for each symmetry type (irreducible
representation). The symmetry ordering can be determined quickly by running a preliminary job with
the %KJob L301 Link 0 command. We recommend that you also specify NCISState with a reasonable
number of states for the CIS (see below).
Only one of NState and NStPIR should be used to specify the desired number of states. If both are
specified, then NState takes precedence. If nothing is specified, then NStPIR=2 is the default.
Singlets
Solve for singlet excited states. This option only affects calculations on closed-shell systems, for which
108 Chapter 5. List of Gaussian Keywords

it is the default.
Triplets
Solve for triplet excited states. This option only affects calculations on closed-shell systems. Must be
combined with Singlets to solve for both kinds of states.
NCISState=M
Total number of states to be generated as guesses by CIS. The default with NState is N*Irr.Reps.; with
NStPIR, it is (K+2)*Irr.Reps.
Root=N
Specifies the state of interest. The default is the first excited state (N=1).

Procedure-Related Options

MaxCyc=N
Specifies the maximum number of cycles for the calculation.
Convergence=N
Sets the convergence calculations to 10−N on the energy and 10−(N−2) on the wavefunction. The default
is N=7.
CCConvergence=N
Use 10−N as the convergence on the CCSD and ground-state Z-vector iterations. CCSDConvergence is
a synonym for this option. The default is N=8.
LRTransitionDensities
Requests linear response transition densities [355, 357, 358] in addition to EOM-style (unrelaxed) ones.
This formalism is more rigorous than the default EOM-CCSD, but it is also computationally more expen-
sive. Note that the two formalisms are equivalent when CCSD provides the exact wavefunction (i.e., the
two electron system). Applies only to singlet closed shell and open shell systems.
EnergyOnly
Save time by computing only right eigenvectors, which are sufficient for excitation energies but not for
transition densities.

Reading/Saving Amplitudes

Amplitudes are saved by default for use in a subsequent calculation. They may be optionally read-in from
a previous calculation. The number of states can be increased in the subsequent calculation. The CIS for the
guess also reads in vectors and automatically adds states if more guesses are required (provided there is no
change in the basis set).
TWInCore
Forces the program to store amplitudes and products in memory during higher-order post-SCF calcula-
tions. The default is to do so if possible, but to run off disk if memory is insufficient. TWInCore causes
the program to terminate if these can not be held in memory, while NoTWInCore prohibits in-memory
storage.
SaveAmplitudes
Saves the converged amplitudes in the checkpoint file for use in a subsequent calculation (e.g., using a
larger basis set). Using this option results in a very large checkpoint file, but also may significantly speed
up later calculations.
 5.25 EOMCCSD 109

ReadAmplitudes
Reads the converged amplitudes from the checkpoint file (if present). Note that the new calculation can
use a different basis set, method (if applicable), etc. than the original one.
ReadGroundStateAmplitudes
Reads in only the ground-state (and Z-vector) amplitudes and not the excited state amplitudes. This
option is useful when going from an EOM calculation on singlets to one on triplets. ReadGSAmplitudes
is a synonym for this option.
NewCIS
Do a new CIS calculation from scratch when reading EOM amplitudes. This option is needed when
reading in singlet states but calculating both singlets and triplets. It is also needed when using a different
basis set than was used for a prior calculation retrieved with ReadAmplitudes.

5.25.2 Availability
Energies and gradients.

5.25.3 Examples
Using EOM-CCSD. It is often useful to perform a preliminary, smaller EOM-CCSD calculation which
solves for a large number of states, and then run a more accurate calculation on the states of interest. The
following route sections illustrate this approach:

First calculation:
%Chk=my_eom
# EOMCCSD(NStates=10,EnergyOnly)/Aug-CC-PVDZ

Second calculation:
%Chk=my_eom
# EOMCCSD(NStates=2,ReadAmplitudes,NewCIS)/Aug-CC-PVQZ

Here is some example output from an EOM-CCSD calculation. This header introduces the results section:

==============================================

EOM-CCSD transition properties

==============================================

Next comes the transition electric dipole moment, separated into left and right sections. The dipole and
oscillator strengths reported at the end of each line are identical in the two sections as the former is the product
of the two:
Ground to excited state transition electric dipole moments (Au):
state X Y Z Dip. S. Osc.
1 0.0000 0.0000 -0.3969 0.1601 0.0614
2 0.0000 0.3963 0.0000 0.1638 0.0756
3 0.0000 1.3681 0.0000 1.9183 1.0604
Excited to ground state transition electric dipole moments (Au):
 110 Chapter 5. List of Gaussian Keywords

state X Y Z Dip. S. Osc.

1 0.0000 0.0000 -0.4034 0.1601 0.0614
2 0.0000 0.4133 0.0000 0.1638 0.0756
3 0.0000 1.4022 0.0000 1.9183 1.0604

For each state, a separate section lists the CI expansion coefficients for excitation along with the corre-
sponding orbital abelian symmetry type, divided by left and right, and then by excitation type:
Excited State 1: Singlet-A1 15.6603 eV 79.17 nm f=0.0614
Right Eigenvector
Alpha Singles Amplitudes
I SymI A SymA Value
4 1 6 1 0.675597 Excitation from orbital 4 (occ.) to 6 (virt.).
3 4 7 4 0.122684
Beta Singles Amplitudes
I SymI A SymA Value
4 1 6 1 0.675597
3 4 7 4 0.122684
Alpha-Beta Doubles Amplitudes Similar information for a double excitation.
I SymI J SymJ A SymA B SymB Value
4 1 4 1 6 1 6 1 -0.118378
Left Eigenvector
Alpha Singles Amplitudes
I SymI A SymA Value
4 1 6 1 0.676418
3 4 7 4 0.121856
Beta Singles Amplitudes
I SymI A SymA Value
4 1 6 1 0.676418
3 4 7 4 0.121856
Alpha-Beta Doubles Amplitudes
I SymI J SymJ A SymA B SymB Value
4 1 4 1 6 1 6 1 -0.107806
Total Energy, E(EOM-CCSD) = -74.4340926881 Total energy reported for state of interest.

5.25.4 Related Keywords

CCSD, CIS, SAC-CI, SCRF

5.26 EPT
This method keyword requests an electron propagator theory [368] calculation of correlated electron affini-
ties and ionization potentials [369–383]. Gaussian 16 includes the renormalized partial third order approxima-
tion – P3+ – method of Ortiz [384]. It also includes algorithmic improvements for significant speedup of the
diagonal, second-order self-energy approximation (D2) component of composite electron propagator (CEP)
methods as described in [385]. These models combine a relatively inexpensive D2-level calculation using a
large basis set (e.g., augmented quadruple or triple zeta) with a more expensive P3+ or OVGF calculation with
a smaller basis set (e.g., triple or double zeta) to produce high accuracy predictions.
 5.26 EPT 111

For reviews of EPT methods and applications, see [343, 386].

EPT calculations default to storage of <ia||bc> integrals, but can be run with Trans=Full to save CPU time
at the expense of disk usage or with Trans=IJAB to save on disk space at the expense of CPU time. In the latter
case, electron affinities are not computed.
By default, only ionization potentials which are < 20 eV are computed.
Use the ReadOrbitals option to specify the starting and ending orbitals to refine as input.
OVGF is a synonym for this keyword.

5.26.1 Options
OVGF
Use the Outer Valence Green’s Function propagator. This is the default.
P3
Use the P3 and P3+ propagators.
OVGF+P3
Use both propagator methods.
D2
Perform the second-order electron propagator using code that is very efficient for this case. D2 does both
attachment (electron affinities) and detachment (ionization potentials) from all orbitals, while the D2IA
does only ionization from active (non-frozen-core) orbitals, (which is even less expensive). Often used
as part of a compound method in conjection with a higher-order EPT calculation using a smaller basis
set. EP2 and EP2IA are synonyms for these options (respectively).
FC
All frozen core options are available with this keyword; a frozen core calculation is the default. See the
discussion of the FC options for full information.
ReadOrbitals
Specify starting and ending orbitals to refine, in a separate, blank-terminated input section. For unre-
stricted calculations, separate ranges are specified for alpha and beta orbitals (on the same input line).
Orbital numbering starts with the first active orbital after the frozen core. For example, using the default
frozen core for ethene, the input 3 8 will skip the two 2s valence orbitals (in addition to the two frozen 1s
cores), resulting in the HOMO being labeled as orbital 6 in the output.
ForceSort
Forces sorting of intermediate quantities to be done even when it is not necessary. This option appears in
some Gaussian test jobs, but it is not useful for production calculations.

5.26.2 Availability
Single-point energy calculations using HF for the reference method.

5.26.3 Examples
For EPT=OVGF calculations, the results for each orbital appear as follows:
3 OVGF renormalized results based on the 3rd order
Method Orbital HF-eigenvalue 3rd-order Pole strength
A: 2 -14.81277 -14.16283 0.93047 OVGF-A results
 112 Chapter 5. List of Gaussian Keywords

B: 2 -14.81277 -14.26825 0.92594 OVGF-B results

C: 2 -14.81277 -14.28318 0.92723 OVGF-C results

Summary of results for alpha spin-orbital 2 OVGF:

Koopmans theorem: -0.54436D+00 au -14.813 eV
Converged second order pole: -0.51494D+00 au -14.012 eV 0.921 (PS)
Converged third order pole: -0.52613D+00 au -14.317 eV 0.929 (PS)
OVGF-von Niessen (OVGF-N) result:
Outer Valence Approximation: -0.52435D+00 au -14.268 eV 0.926 (PS)

The second section gives the estimate of ionization potential/electron affinity for the specified orbital
(which property is given depends on whether the orbital is occupied or not, respectively) with the specified
propagator. The pole strength is a measure of how easy it is to make this excitation, with 1.0 as the maximum
value. Note that orbitals are listed in the output in order of symmetry (and not necessarily in numerical order).
For EPT=P3 calculations, the results for each orbital appear as follows:
Summary of results for alpha spin-orbital 5 P3:
Koopmans theorem: 0.16053D+00 au 4.368 eV
Converged second order pole: 0.13657D+00 au 3.716 eV 0.978 (PS)
Converged 3rd order P3 pole: 0.13578D+00 au 3.695 eV 0.974 (PS) P3 propagator result
Renormalized (P3+) P3 pole: 0.13584D+00 au 3.696 eV 0.974 (PS) P3+ propagator result

Results are given for both the original and renormalized formulations of P3.
For EPT=D2 calculations, the results for each orbital appear as follows:
Converged 2nd order pole for alpha spin-orbital 2 -0.85777 au -23.341 eV
Converged 2nd order pole for alpha spin-orbital 3 -0.51494 au -14.012 eV
Converged 2nd order pole for alpha spin-orbital 4 -0.51494 au -14.012 eV
Converged 2nd order pole for alpha spin-orbital 5 -0.51494 au -14.012 eV
···

5.27 External

Requests a calculation using an external program. This mechanism is primarily intended to facilitate the
use of external programs to provide the low-level calculations in ONIOM calculations, but can also be used
to conduct geometry optimizations using Gaussian’s optimizer with external programs providing the function
values and derivatives.
Gaussian uses a standardized interface to run an external program to produce an energy (and optionally
a dipole moment or forces) at each geometry. A text file is produced with the current structure, and a script
named Gau_External is run by default (see below for information on specifying an alternate script). This script,
which is provided by the user, is expected to:
♢ Convert the text file – referred to as the “input file” – into input for another program.
♢ Run that program.
♢ Convert the results into a standard text form for recovery by Gaussian. The converted file for use by Gaussian
is referred to as the “output file.”
You may specify a different script by including its name as the option to the External keyword: e.g.,
External=MyScript.
 5.27 External 113

5.27.1 Script Invocation

By default, the Gau_External script is passed six parameters:
$ Gau_External layer InputFile OutputFile MsgFile FChkFile MatElFile
The parameters are defined as follows:

layer A key letter indicating whether the computation is being performed on the real
system (R), the model system of a 2-layer ONIOM or the middle layer of a 3-layer
ONIOM (M), or the model system of a 3-layer ONIOM (S).
InputFile The name of the file Gaussian has prepared as input for the external program.
OutputFile The name of the file which should be read in after the external program completes.
MsgFile The name of a file for messages; if the script creates this file, then its contents are
copied to the Gaussian output file.
FChkFile A formatted checkpoint file. If the appropriate options are set to link 402, then this
file is created from the read-write file before starting the external script, and may
be read to import results after the script finishes instead of Gaussian input being
provided via OutputFile. The output formatted checkpoint file can contain an initial
two blank lines plus the data to be updated in the usual format; it does not need to
contain any information which is to remain unchanged.
MatElFile Matrix element file. This is a Fortran unformatted file designed to export data such
as the overlap and Core Hamiltonian matrix and two-electron integrals in an exten-
sible format. The structure is documented in Interfacing to Gaussian 16.

All of these files are deleted by Gaussian once the results have been recovered.
Additional arguments to the script may also be included:
External="RunTink Amber"
In this example, the actual command would be:
$ RunTink Amber layer InputFile OutputFile MsgFile FChkFile MatElFile
The specified script is always passed the parameters mentioned above as its final six arguments.

5.27.2 File Formats

Input File Format
The input file has the following format:
#atoms derivatives-requested charge spin
atomic# x y z MM-charge Repeated for each atom.
The first line specifies the number of atoms in the molecule, what derivatives are to be computed (0=energy
only, 1=first derivatives, 2=second derivatives), and the molecule’s charge and spin multiplicity (format 4I10).
The remaining lines specify the atomic number, coordinates, and molecular mechanics charge for each atom
(format I10, 4F20.12).

Output File Format

The output file is in fixed format and has the following data (all in atomic units):

Items Pseudo Code Line Format

 114 Chapter 5. List of Gaussian Keywords

energy, dipole-moment (xyz) E, Dip(I), I=1,3 4D20.12

gradient on atom (xyz) FX(J,I), J=1,3; I=1,NAtoms 3D20.12
polarizability Polar(I), I=1,6 3D20.12
dipole derivatives DDip(I), I=1,9*NAtoms 3D20.12
force constants FFX(I), I=1,(3*NAtoms*(3*NAtoms+1))/2 3D20.12

The second section is present only if first derivatives or frequencies were requested, and the final section is
present only if frequencies were requested. In the latter case, the Hessian is given in lower triangular form: αi j ,
i=1 to N, j=1 to i. The dipole moment, polarizability, and dipole derivatives can be zero if none are available.

5.27.3 Options
It is also possible to provide one-electron or one- and two-electron integrals and other matrix elements to
an external program and to recover results such as MOs or densities from the other program. Full details and
examples are in the g16/doc subdirectory (doc folder on Windows). Options must follow the name of the script.
Test job 769 serves as an example of some of these options.
InUnf
A Fortran unformatted file will be provided to the external program containing coordinates and one-
electron matrix elements (overlap, core Hamiltonian, etc.). Refer to g16/doc/unfdat.txt for details on
the contents of the file and to g16/doc/rdmat.F for a sample program which reads the file and prints its
contents. 1Elintegrals is a synonym for this option.
2ElIntegrals
The Fortran unformatted file should also contain two-electron integrals. This option implies SCF=Conventional.
InputFchk
A formatted checkpoint file should be generated and provided to the external program.
OutputUnf
A Fortran unformatted file will be provided to the external program and an updated or replaced file with
the same structure will be read by G16 for the results, in lieu of the default text output file expected from
the external program/script.
IOFchk
A formatted checkpoint file will be generated and provided to the external program, and a new .fchk file
will be read to import results afterwards.
ReadInputSection
This option can be used to alter the content of the external text input file that Gaussian 16 automatically
generates for the external script. When the data transfer between Gaussian 16 and the external script is
handled using one of the options above (e.g. IOFchk), the default external text input file is not needed.
With this option, a section (delimited by the usual blank lines) will be read from the Gaussian 16 input
file. The text in this section will be placed in the external text input file instead of the usual content of
such file. This provides additional flexibility to provide extra instructions to the external script.
Files
Include the contents of the specified internal Gaussian file within the generated matrix element file. For
example, the following option:
External=Files=(123,(456,offset=1,integer=27))
 5.28 ExtraBasis & ExtraDensityBasis 115

will cause the contents of internal file 123 (assumed by default to be real values) to be included in the
matrix element file (labeled as “File 123”). The second item in the file list specifies the 27 integers in
internal file 456 starting after the first (8-byte) word (labeled as “File 456 integers section 001”), as well
as any real values following the integers (labeled “File 456 reals section 002”).

5.27.4 Related Info

External scripts may also be specified as one of the models for the ONIOM keyword (see the examples).
The Gaussian stand-alone mm utility program can be run with the -external switch, which causes it to
read and write data in the formats used by the External interface.
See Interfacing to Gaussian 16 for information about exchanging data with other programs.

5.27.5 Examples
The following route section specifies an external script for the low layer of a 3 layer ONIOM calculation:
# ONIOM(B3LYP/6-31G(d):AM1:External="RunTink Amber") Opt
The following route section specifies an external script for the high accuracy layer of a 2 layer ONIOM
job:
# ONIOM(External="RunCC SDT":B3LYP/6-31G(d)) Opt

5.28 ExtraBasis & ExtraDensityBasis

These keywords indicate that additional basis functions are to be added to the basis set or density fitting
basis set specified in the route section for the calculation (respectively). These basis functions appear in a sepa-
rate section in the input stream, using any of the valid formats (which are described in detail in the discussion
of the Gen keyword).
ExtraBasis is most useful for supplying basis functions for elements undefined in a standard basis set. It
cannot be used to replace a definition within a built-in basis set, and attempting to do so will result in an error.
All basis functions specified with this keyword are added to the ones in the basis set specified in the route
section. For these reasons, Gen is often easier to use than ExtraBasis; consult the description for that keyword
before deciding to use this one.
ExtraDensityBasis is ignored if no density fitting basis is specified in the route.

5.28.1 Related Keywords

Gen, Pseudo, GenECP, GFInput, GFPrint

5.28.2 Example
The following job uses the 6-31G(d,p) basis set along with an additional diffuse function on all of the
carbon atoms:

# HF/6-31G(d,p) ExtraBasis · · ·

title section

molecule specification
116 Chapter 5. List of Gaussian Keywords

C 0
SP 1 1.00
0.4380000000D-01 0.1000000000D+01 0.1000000000D+01
****

The following job supplies additional functions for both the basis set and for density fitting:

#p rblyp/6-31g*/dga1 extrabasis extradensitybasis 6d

HCl using the internally stored 6-31g* AO basis & DGA1 fitting set,
adding f functions to the AO basis, and f & g fitting functions

0,1
cl
h,1,1.29

! here are some extra AO polarization functions

cl 0 Additional basis set functions
F 1 1.00 0.000000000000
0.7500000000D+00 0.1000000000D+01
****
h 0
p 1 1.00 0.000000000000
0.1612777588D+00 0.1000000000D+01
****

! here are some extra fitting functions.

cl 0 Additional density fitting functions
f 1
1.5
g 1
1.5
****
h 0
spd 1
0.32
****

The following job reads in extra basis set data from an external file:

# B3LYP/6-31++G(d) ExtraBasis

B3LYP/6-31++G(d) with extra diffuse functions

 5.29 Field 117

molecule specification

@tripleplus.gbs

5.29 Field

The Field keyword requests that a finite field be added to a calculation. In Gaussian, the field can either
involve electric multipoles (through hexadecapoles) or a Fermi contact term. Field requires a parameter in
one of these two formats: M±N or F(M)N, where M designates a multipole, and F(M) designates a Fermi
contact perturbation for atom M (following the ordering in the molecule specification section of the input file).
N*0.0001 specifies the magnitude of the field in atomic units in the first format and specifies the magnitude of
the Fermi contact perturbation in the second format.
Thus, Field=X+10 applies an electric dipole field in the X direction of 0.001 au, while Field=XXYZ-20
applies the indicated hexadecapole field with magnitude 0.0020 au and direction opposite to the default (which
is determined by the standard orientation). Similarly, Field=F(3)27 applies a perturbation of 0.0027 times the
spin density on atom 3.
Note that the coefficients are those of the Cartesian operator matrices; care must be taken regarding the
choice of sign convention when interpreting the results.
All parameters are in the input orientation.
The field specification parameter may be placed among any other options as desired. Archiving is disabled
when Field is specified.

5.29.1 Options

Read
Reads the coefficients of 34 electric multipole components from the input stream in free format.
OldRead
Reads the coefficients of 35 electric multipole components from the input stream, in the old style format
(including the monopole term): using format 3D20.10 (the first component is a charge).
RWF
Takes the 35 multipole components from the read-write file.
ERWF
Extracts only the three electric dipole field components from the read-write file.
Checkpoint
Reads the 35 multipole components from the checkpoint file. Chk is a synonym for Checkpoint. Check-
point is the default with Geom=Check.
NoChK
Prevents the reading of the field from the checkpoint file.
EChk
Extracts only the three electric dipole field components from the checkpoint file.
 118 Chapter 5. List of Gaussian Keywords

5.29.2 Availability
Single-point energy, geometry optimizations, frequencies, and Force and Scan calculations.

5.29.3 Limitations
Note that if symmetry is left on during a GVB calculation, the finite field may not lead to correct numerical
derivatives if the selected field breaks molecular symmetry. To be safe, use Guess=NoSymm whenever using
Field with GVB.
In general, if the electric field causes the wavefunction to have different symmetry than the original
molecule, incorrect numerical derivatives can result. Accordingly, you might want to use NoSymm when
doing numerical derivatives with Field.

5.29.4 Examples
To perform geometry optimizations in the presence of an electric field, you must use Opt=Z-Matrix
NoSymm keywords and define the input geometry either in traditional Z-matrix coordinates or symbolic Carte-
sian coordinates. Here is an example using a Z-matrix:

# RHF/3-21G Field=x+60 Opt=Z-Matrix NoSymm

Z-Matrix optimization

0 1
C
H 1 B1
H 1 B2 2 A1
H 1 B3 2 A2 3 D1
H 1 B4 2 A3 3 D2

B1 1.070000
B2 1.070000
B3 1.070000
B4 1.070000
A1 109.471203
A2 109.471203
A3 109.471231
D1 120.000015
D2 -119.999993

Here is an example using symbolic Cartesian coordinates:

# HF/6-31G(d) Opt=Z-Matrix Field=z-50 NoSymm

Symbolic Cartesian coordinates optimization

 5.30 FMM 119

0 1
O 0 x1 y1 z1
H 0 x2 y2 z2
H 0 x3 y3 z3

x1=0.0
y1=0.0
z1=0.12
x2=0.0
y2=0.75
z2=-0.46
x3=0.0
y3=-0.75
z3=-0.46

5.30 FMM

Force the use of the fast multipole method [280, 387–394] if possible. The use of FMM is automated
in Gaussian 16. Gaussian 16 generally turns on the FMM facility when using it provides even a modest per-
formance gain (say, 1.2x). FMM is enabled for nonsymmetric molecules with 60 atoms or more for both
Hartree-Fock and DFT. For molecules with high symmetry, FMM is enabled for Hartree-Fock and hybrid DFT
above 240 atoms and for pure DFT above 360 atoms. For molecules with low (but non-zero) symmetry, in-
termediate thresholds are used. You will begin to see substantial performance improvements (2x or better) for
systems that are twice as large.
Of course, the exact results will vary from case to case (compact systems show the least speedup; stretched
out linear ones the most), but the defaults are very unlikely to enable FMM when it has a negative effect on
performance and are also as unlikely to fail to enable it when it would be worth a factor of 1.5x or more. Thus,
users are unlikely to need to control FMM by hand except for some very unusual special cases, such as nearly
linear polypeptides and long carbon nanotubes.
The options to FMM are described in Program Development-Related Keywords.

5.30.1 Availability

Energies, gradients and frequencies for HF, pure and hybrid DFT. This keyword may also be used within
method specifications for ONIOM layers.

5.31 Force

This calculation-type keyword requests a single calculation of the forces on the nuclei (i.e., the gradient of
the energy). The dipole moment is also computed (as a proper analytic derivative of the energy for MP2, CC,
QCI and CI) [200, 228].
 120 Chapter 5. List of Gaussian Keywords

5.31.1 Options
EnOnly
Compute the forces by numerically differentiating the energy once. It is the default for all methods for
which analytic gradients are unavailable. Note that this procedure exhibits some numerical instability, so
care must be taken that an optimal step size is specified for each case.
Restart
Restarts numerical evaluation of the forces.
StepSize=N
Sets the step size used in numerical differentiation to 0.0001*N. The units are Angstroms by default un-
less Units=Bohr has been specified. The default step size is 0.01 Å. StepSize is valid only in conjunction
with EnOnly.
NoStep
Can be used with large MM force calculations to avoid the O(N 3 ) work involved in computing the putative
geometry optimization step.

5.31.2 Availability
Analytic gradients are available for all SCF wavefunctions, all DFT methods, CIS, MP2, MP3, MP4(SDQ),
CID, CISD, CCD, CCSD, QCISD, BD, CASSCF, SAC-CI and all semi-empirical methods. For other methods,
the forces are determined by numerical differentiation.

5.31.3 Examples
The forces on the nuclei appear in the output as follows (this sample is from a calculation on water):

***** AXES RESTORED TO ORIGINAL SET *****

-------------------------------------------------------------------
Center Atomic Forces (Hartrees/Bohr)
Number Number X Y Z
-------------------------------------------------------------------
1 8 -.049849321 .000000000 -.028780519
2 1 .046711997 .000000000 -.023346514
3 1 .003137324 .000000000 .052127033
-------------------------------------------------------------------
MAX .052127033 RMS .031211490
-------------------------------------------------------------------
Internal Coordinate Forces (Hartree/Bohr or radian)
Cent Atom N1 Length/X N2 Alpha/Y N3 Beta/Z J
-------------------------------------------------------------------
1 O
2 H 1 -.023347( 1)
3 H 1 -.023347( 2) 2 -.088273( 3)
-------------------------------------------------------------------
MAX .088272874 RMS .054412682
 5.32 Freq 121

The forces are determined in the standard orientation, but are restored to the original (Z-matrix) set of axes
before printing (as noted in the output). This is followed by the corresponding derivatives with respect to the
internal coordinates (lengths and angles used in the Z-matrix) when internal coordinates are in use. The forces
are followed in each case by their maximum and root-mean-square values.

5.32 Freq
This calculation-type keyword computes force constants and the resulting vibrational frequencies. Inten-
sities are also computed. By default, the force constants are determined analytically if possible, by single
numerical differentiation for methods for which only first derivatives are available, and by double numerical
differentiation for those methods for which only energies are available.
Vibrational frequencies are computed by determining the second derivatives of the energy with respect to
the Cartesian nuclear coordinates and then transforming to mass-weighted coordinates. This transformation is
only valid at a stationary point. Thus, it is meaningless to compute frequencies at any geometry other than a
stationary point for the method used for frequency determination.
For example, computing 6-311G(d) frequencies at a 6-31G(d) optimized geometry produces meaningless
results. It is also incorrect to compute frequencies for a correlated method using frozen core at a structure
optimized with all electrons correlated, or vice-versa. The recommended practice is to compute frequencies
following a previous geometry optimization using the same method. This may be accomplished automatically
by specifying both Opt and Freq within the route section for a job.
Note also that the CPHF (coupled perturbed SCF) method used in determining analytic frequencies is
not physically meaningful if a lower energy wavefunction of the same spin multiplicity exists. Use the Stable
keyword to test the stability of Hartree-Fock and DFT wavefunctions.

5.32.1 Calculation Variations

Additional related properties may also be computed during frequency calculations, including the follow-
ing:
♢ When frequencies are done analytically, polarizabilities are also computed automatically; when numerical
differentiation is required (or requested with Freq=Numer), polarizabilities must be explicitly requested
using the Polar keyword (e.g., CCSD Freq Polar).
♢ The VCD option may be used to compute the vibrational circular dichroism (VCD) intensities in addition to
the normal frequency analysis at the Hartree-Fock and DFT levels [395].
♢ The ROA option computes analytic Raman optical activity intensities [396–401]. However, see Polar=ROA
for the recommended method and model chemistries for predicting ROA spectra.
♢ Pre-resonance Raman intensities may be computed by specifying one of the Raman options, and also in-
cluding CPHF=RdFreq within the route and specifying the desired frequency in the input file (see the
examples for additional information).
♢ Frequency-dependent polarizabilities and hyperpolarizabilities may be computed by including CPHF=RdFreq
within the route (subject to their usual availability restrictions).
♢ Vibrational-rotational coupling can be computed using Freq=VibRot [402–410].
♢ The Anharmonic option performs numerical differentiation to compute anharmonic frequencies and zero-
point energies [402–406, 408, 409, 411, 412] and anharmonic vibrational-rotational couplings [407, 410,
 122 Chapter 5. List of Gaussian Keywords

413–416] (as requested). This option is only available for methods with analytic second derivatives:
Hartree-Fock, DFT, CIS and MP2. Full anharmonic IR intensities are computed [416, 417]. The DCPT2
[418, 419] and HDCPT2 [419] methods support resonance-free computations of anharmonic frequencies
and partition functions. Anharmonic VCD and ROA spectra can also be predicted [420]. Calculations in
solution are supported [421].
♢ There are several options for performing an analysis for an electronic excitation using the Franck-Condon
[422–443], Herzberg-Teller method [422, 440–447] or combined Franck-Condon/Herzberg-Teller [440–
443] methods (see the Options and additional input sections). They can be used to predict vibronic
spectra and intensities, as well as resonance Raman spectra [448, 449]. Vibronic computations support
chiral spectroscopies as well (ECD and CPL) [450, 451]. For a tutorial review, see [452].
The keyword Opt=CalcAll requests that analytic second derivatives be done at every point in a geometry
optimization. Once the requested optimization has completed all the information necessary for a frequency
analysis is available. Therefore, the frequency analysis is performed and the results of the calculation are
archived as a frequency job.

5.32.2 Input
The SelectNormalModes and SelectAnharmonicModes options require additional input. The modes to
select are specified in a separate blank-line terminated input section. The initial mode list is always empty.
Integers and integer ranges without a keyword are interpreted as mode numbers; although,This option is
only available for methods with the [not]mode keywords may be used. The keywords atoms and notatoms can
be used to define an atom list whose modes should be included/excluded (respectively). Atoms can also be
specified by ONIOM layer via the [not]layer keywords, which accept these values: real for the real system,
model for the model system in a 2-layer ONIOM, middle for the middle layer in a 3-layer ONIOM, and small
for the model layer of a 3-layer ONIOM. Atoms may be similarly included/excluded by residue with residue
and notresidue, which accept lists of residue names or numbers. Both keyword sets function as shorthand forms
for atom lists.
Here are some examples:

2-5 Includes modes 2 through 5.

atoms=O Includes modes involving oxygen atoms.
1-20 atoms=Fe Includes modes 1 through 20 and any modes involving iron atoms.
layer=real notatoms=H Includes modes for heavy atoms in low layer (subject to default thresh-
old).

5.32.3 Options
Retrieving Force Constants
ReadFC
Requests that the force constants from a previous frequency calculation be read from the checkpoint
file, and the mode and thermochemical analysis be repeated, presumably using a different temperature,
pressure, or isotopes, at minimal computational cost. Note that since the basis set is read from the
checkpoint file, no general basis should be input. If the Raman option was specified in the previous job,
then do not specify it again when using this option.
5.32 Freq 123

Requesting Specific Spectra

Raman
Compute Raman intensities in addition to IR intensities. This is the default for Hartree-Fock. It may
be specified for DFT and MP2 calculations. For MP2, Raman intensities are produced by numerical
differentiation of dipole derivatives with respect to the electric field Raman is equivalent to NRaman for
this method).
NRaman
Compute polarizability derivatives by numerically differentiating the analytic dipole derivatives with
respect to an electric field. This is the default for MP2 if Freq=Raman.
NNRaman
Compute polarizability derivatives by numerically differentiating the analytic polarizability with respect
to nuclear coordinates.
NoRaman
Skips the extra steps required to compute the Raman intensities during Hartree-Fock analytic frequency
calculations, saving 10-30% in CPU time.
VCD
Compute the vibrational circular dichroism (VCD) intensities in addition to the normal frequency analy-
sis. This option is valid for Hartree-Fock and DFT methods. This option also computes optical rotations
(see Polar=OptRot).
ROA
Compute dynamic analytic Raman optical activity intensities using GIAOs [401]. This procedure requires
one or more incident light frequencies to be supplied in the input to be used in the electromagnetic pertur-
bations (CPHF=RdFreq is the default with Freq=ROA). This option is valid for Hartree-Fock and DFT
methods. Note that the Polar=ROA keyword is often a better choice. NNROA says to use the numerical
ROA method from Gaussian 03; this is useful only for reproducing the results of prior calculations.

Anharmonic Frequency Analysis

Anharmonic
Do numerical differentiation along modes to compute zero-point energies, anharmonic frequencies, and
anharmonic vibrational-rotational couplings if VibRot is also specified. This option is only available for
methods with analytic second derivatives: Hartree-Fock, DFT, CIS, and MP2.
ReadAnharm
Read an input section with additional parameters for the vibrational-rotational coupling and/or anhar-
monic vibrational analysis (VibRot or Anharmonic options). Available input options are documented
below following the examples.
ReadHarmonic
Read the central point force constants and normal modes from a previous harmonic frequency calculation
and avoid repeating the calculation at the central point.
ReadDifferentharmonic
Read the central point energy, forces, and force constants from a previous calculation and then compute
3rd and 4th derivatives at the current (presumably lower) level of theory for anharmonic spectra.
SelectAnharmonicModes
124 Chapter 5. List of Gaussian Keywords

Read an input section selecting which modes are used for differentiation in anharmonic analysis. The
format of this input section is discussed above. SelAnharmonicModes is a synonym for this option.

Vibronic Spectra: Franck-Condon, Herzberg-Teller and FCHT

The following options perform an analysis for an electronic excitation using the corresponding method;
these jobs use vibrational analysis calculations for the ground state and the excited state to compute the ampli-
tudes for electronic transitions between the two states. The vibrational information for the ground state is taken
from the current job (Freq or Freq=ReadFC), and the vibrational information for the excited state is taken from
a checkpoint file, whose name is provided in a separate input section (enclose the path in quotes if it contains
internal spaces). The latter will be from a CI-Singles or TD-DFT Freq=SaveNormalModes calculation.
The ReadFCHT option can be added to cause additional input to be read to control these calculations
(see below). In the latter case, the excited state checkpoint file would typically have been generated with
Freq=(SelectNormalModes, SaveNormalModes) with the same modes selected.
FranckCondon
Use the Franck-Condon method [422–439, 441] (the implementation is described in [438–441]). FC is a
synonym for this option. Transitions for ionizations can be analyzed instead of excitations. In this case,
the molecule specification corresponds to the neutral form, and the additional checkpoint file named in
the input section corresponds to the cation.
HerzbergTeller
Use the Herzberg-Teller method [422, 440, 444–447] (the implementation is described in [440]). HT is
a synonym for this option.
FCHT
Use the Franck-Condon-Herzberg-Teller method [440].
Emission
Indicates that emission rather than absorption should be simulated for a Franck-Condon and/or Herzberg-
Teller analysis. In this case, within the computation, the initial state is the excited state, and the final state
is the ground state (although,This option allows you to specify alternatives to the default temperature,
pressure, frequency scale factor the sources of frequency data for the ground and excited state are as
described above: current job=ground state, second checkpoint file=excited state).
ReadFCHT
Read an input section containing parameters for the calculation. Available input options are documented
below following the examples. This input section precedes that for ReadAnharmon if both are present.

Other Calculation Variations and Properties

VibRot
Analyze vibrational-rotational coupling.
Projected
For a point on a mass-weighted reaction path (IRC), compute the projected frequencies for vibrations
perpendicular to the path. For the projection, the gradient is used to compute the tangent to the path. Note
that this computation is very sensitive to the accuracy of the structure and the path [453]. Accordingly,
the geometry should be specified to at least 5 significant digits. This computation is not meaningful at a
minimum.
5.32 Freq 125

TProjected
Perform a projected harmonic frequency analysis if the RMS force is ≥ 1.d-3 Hartree/Bohr and perform
regular harmonic analysis if the RMS force is smaller.
HinderedRotor
Requests the identification of internal rotation modes during the harmonic vibrational analysis [454–
456]. If any modes are identified as internal rotation, hindered or free, the thermodynamic functions
are corrected. The identification of the rotating groups is made possible by the use of redundant inter-
nal coordinates. Because some structures, such as transition states, may have a specific bonding pattern
not automatically recognized, the set of redundant internal coordinates may need to be altered via the
Geom=Modify keyword. Rotations involving metals require additional input via the ReadHinderedRotor
option (see below).
If the force constants are available on a previously generated checkpoint file, additional vibrational/inter-
nal rotation analyses may be performed by specifying Freq=(ReadFC, HinderedRotor). Since Opt=CalcAll
automatically performs a vibrational analysis on the optimized structure, Opt=(CalcAll, HinderedRotor)
may also be used.
ReadHinderedRotor
Causes an additional input section to be read containing the rotational barrier cutoff height (in kcal/mol)
and optionally the periodicity, symmetry number and multiplicity for rotational modes. Rotations with
barrier heights larger than the cutoff value will be automatically frozen. If the periodicity value is neg-
ative, then the corresponding rotor is also frozen. You must provide the periodicity, symmetry and spin
multiplicity for all rotatable bonds contain metals. The input section is terminated with a blank line, and
has the following format:
VMax-value
Atom1 Atom2 periodicity symmetry spin Repeated as necessary.
···

Normal Modes

HPModes
Include the high precision format (to five figures) vibrational frequency eigenvectors in the frequency
output in addition to the normal three-figure output.
InternalModes
Print modes as displacements in redundant internal coordinates. IntModes is a synonym for this option.
SaveNormalModes
Save all modes in the checkpoint file. SaveNM is a synonym for this option. NoSaveNormalModes, or
NoSaveNM, is the default.
ReadNormalModes
Read saved modes from the checkpoint file. ReadNM is a synonym for this option. NoReadNor-
malModes, or NoReadNM, is the default.
SelectNormalModes
Read input selecting the particular modes to display. SelectNM is a synonym for this option. NoSelect-
NormalModes, or NoSelectNM, is the default. AllModes says to include all modes in the output. The
format of this input section is discussed above. Note that this option does not affect the functioning of
126 Chapter 5. List of Gaussian Keywords

SaveNormalModes, which always saves all modes in the checkpoint file.

SortModes
Sort modes by ONIOM layer in the output.
ModelModes
Display only modes involving the smallest model system in an ONIOM calculation.
MiddleModes
Display only modes involving the two model systems in a 3-layer ONIOM.
PrintDerivatives
Print normal mode derivatives of the dipole moment, polarizability, and so on.
PrintFrozenAtoms
By default, the zero displacements for frozen atoms are not printed in the mode output. This option
requests that all atoms be listed.
NoPrintNM
Used to suppress printing of the normal mode components during a frequency calculation. The frequen-
cies and intensities are still reported for each mode.

Geometry-Related Options
ModRedundant
Read-in modifications to redundant internal coordinates (i.e., for use with InternalModes). Note that the
same coordinates are used for both optimization and mode analysis in an Opt Freq, for which this is the
same as Opt=ModRedundant. See the discussion of the Opt keyword for details on the input format.
ReadIsotopes
This option allows you to specify alternatives to the default temperature, pressure, frequency scale factor
and/or isotopes – 298.15 K, 1 atmosphere, no scaling, and the most abundant isotopes (respectively). It is
useful when you want to rerun an analysis using different parameters from the data in a checkpoint file.
Be aware, however, that all of these can be specified in the route section (Temperature, Pressure and Scale
keywords) and molecule specification (the Iso parameter), as in this example:

#T Method/6-31G(d) JobType Temperature=300.0 · · ·

···

0 1
C(Iso=13)
···

ReadIsotopes input has the following format:

temp pressure [scale] Values must be real numbers.

isotope mass for atom 1
isotope mass for atom 2
···
isotope mass for atom n
5.32 Freq 127

Where temp, pressure, and scale are the desired temperature, pressure, and an optional scale factor for
frequency data when used for thermochemical analysis (the default is unscaled). The remaining lines hold
the isotope masses for the various atoms in the molecule, arranged in the same order as they appeared
in the molecule specification section. If integers are used to specify the atomic masses, the program will
automatically use the corresponding actual exact isotopic mass (e.g., 18 specifies 18 O, and Gaussian uses
the value 17.99916).

Algorithm Variations and Execution Options

Analytic
This specifies that the second derivatives of the energy are to be computed analytically. This option is
available only for RHF, UHF, CIS, CASSCF, MP2, and all DFT methods, and it is the default for those
cases.
Numerical
This requests that the second derivatives of the energy are to be computed numerically using analytically
calculated first derivatives. It can be used with any method for which gradients are available and is
the default for those for which gradients but not second derivatives are available. Freq=Numer can be
combined with Polar=Numer in one job step.
FourPoint
Do four displacements instead of two for each degree of freedom during numerical frequencies, polariz-
abilities, or Freq=Anharm. This gives better accuracy and less sensitivity to step size at the cost of doing
twice as many calculations.
DoubleNumer
This requests double numerical differentiation of energies to produce force constants. It is the default
and only choice for those methods for which no analytic derivatives are available. EnOnly is a synonym
for DoubleNumer.
Cubic
Requests numerical differentiation of analytic second derivatives to produce third derivatives. Applicable
only to methods having analytic frequencies but no analytic third derivatives.
Step=N
Specifies the step-size for numerical differentiation to be 0.0001*N (in Angstoms unless Units=Bohr has
been specified). If Freq=Numer and Polar=Numer are combined, N also specifies the step-size in the
electric field. The default is 0.001 Å for Hartree-Fock and correlated Freq=Numer, 0.005 Å for GVB
and CASSCF Freq=Numer, and 0.01 Å for Freq=EnOnly. For Freq=Anharmonic or Freq=VibRot, the
default is 0.025 Å.
Restart
This option restarts a frequency calculation after the last completed geometry. A failed frequency job
may be restarted from its checkpoint file by simply repeating the route section of the original job, adding
the Restart option to the Freq=Numer keyword/option. No other input is required.
Analytic frequencies can be restarted with the Restart keyword provided that the read-write file was
named and saved from the failed job. See the description of that keyword for more information and an
example.
DiagFull
 128 Chapter 5. List of Gaussian Keywords

Diagonalize the full (3Natoms )2 force constant matrix – including the translation and rotational degrees of
freedom – and report the lowest frequencies to test the numerical stability of the frequency calculation.
This precedes the normal frequency analysis where these modes are projected out. Its output reports the
lowest 9 modes, the upper 3 of which correspond to the 3 smallest modes in the regular frequency analy-
sis. Under ideal conditions, the lowest 6 modes reported by this analysis will be very small in magnitude.
When they are significantly non-zero, it indicates that the calculation is not perfectly converged/numeri-
cally stable. This may indicate that translations and rotations are important modes for this system, that a
better integration grid is needed, that the geometry is not converged, etc. The system should be studied
further in order to obtain accurate frequencies. See the examples section below for the output from this
option. DiagFull is the default; NoDiagFull says to skip this analysis.
TwoPoint
When computing numerical derivatives, make two displacements in each coordinate. This is the default.
FourPoint will make four displacements but only works with Link 106 (Freq=Numer). Not valid with
Freq=DoubleNumer.
NFreq=N
Requests that the lowest N frequencies be solved for using Davidson diagonalization. At present, this
option is only available for ONIOM(QM:MM) model chemistries.
WorkerPerturbations
During numerical frequencies using Linda parallelism, run separate displacements on each worker in-
stead of parallelizing each energy+derivative evaluation across the cluster. This strategy is more efficient,
but it requires specifying an extra worker on the master node. It is the default if at least 3 Linda workers
were specified. NoWorkerPerturbations suppresses this behavior.

5.32.4 Availability
Analytic frequencies are available for the AM1, PM3, PM3MM, PM6, PDDG, DFTB, DFTBA, HF, DFT,
MP2, CIS, TD and CASSCF methods.
Numerical frequencies are available for MP3, MP4(SDQ), CID, CISD, CCD, CCSD, EOM-CCSD and
QCISD.
Raman is available for the HF, DFT and MP2 methods.
VCD and ROA are available for HF and DFT methods.
Anharmonic is available for HF, DFT, MP2 and CIS methods.
Freq and NMR can both be on the same route for HF and DFT.

5.32.5 Related Keywords

Polar, Opt, Stable, NMR.

5.32.6 Examples
Frequency Output. The basic components of the output from a frequency calculation are discussed in
detail in chapter 4 of Exploring Chemistry with Electronic Structure Methods [152].
New Gaussian users are often surprised to see that the final part frequency calculation output that looks
that of a geometry optimization at the beginning of a frequency job:
5.32 Freq 129

GradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
Berny optimization.
Initialization pass.

Link 103, which performs geometry optimizations, is executed at the beginning and end of all frequency
calculations. This is done so that the quadratic optimization step can be computed using the correct second
derivatives. Occasionally an optimization will complete according to the normal criterion using the approximate
Hessian matrix, but the step size is actually larger than the convergence criterion when the correct second
derivatives are used. The next step is printed at the end of a frequency calculation so that such problems can be
identified. If you think this concern is applicable, use Opt=CalcAll instead of Freq in the route section of the
job, which will complete the optimization if the geometry is determined not to have fully converged (usually,
given the full second derivative matrix near a stationary point, only one additional optimization step is needed),
and will automatically perform a frequency analysis at the final structure.
Specifying #P in the route section produces some additional output for frequency calculations. Of most im-
portance are the polarizability and hyperpolarizability tensors (the latter in Raman calculations only); although,
they still may be found in the archive entry in normal print-level jobs. They are presented in lower triangular
and lower tetrahedral order, respectively (i.e., αxx , αxy , αyy , αxz , αyz , αzz and βxxx , βxxy , βxyy , βyyy , βxxz , βxyz ,
βyyz , βxzz , βyzz , βzzz ), in the standard orientation:

Dipole = 2.37312183D-16 -6.66133815D-16 -9.39281319D-01

Polarizability= 7.83427191D-01 1.60008472D-15 6.80285860D+00
-3.11369582D-17 2.72397709D-16 3.62729494D+00
HyperPolar = 3.08796953D-16 -6.27350412D-14 4.17080415D-16
5.55019858D-14 -7.26773439D-01 -1.09052038D-14
-2.07727337D+01 4.49920497D-16 -1.40402516D-13
-1.10991697D+01

#P also produces a bar-graph of the simulated spectra for small cases.

Thermochemistry analysis follows the frequency and normal mode data:
Zero-point correction= .023261 (Hartree/Particle)
Thermal correction to Energy= .026094
Thermal correction to Enthalpy= .027038
Thermal correction to Gibbs Free Energy= .052698
Sum of electronic and zero-point Energies= -527.492585 E0 =Eelec +ZPE
Sum of electronic and thermal Energies= -527.489751 E= E0 + Evib + Erot +Etrans
Sum of electronic and thermal Enthalpies= -527.488807 H=E+RT
Sum of electronic and thermal Free Energies= -527.463147 G=H-TS

The raw zero-point energy correction and the thermal corrections to the total energy, enthalpy, and Gibbs free
energy (all of which include the zero-point energy) are listed, followed by the corresponding corrected energy.
The analysis uses the standard expressions for an ideal gas in the canonical ensemble. Details can be found in
McQuarrie [457] and other standard statistical mechanics texts. In the output, the various quantities are labeled
as follows:

E (Thermal) Contributions to the thermal energy correction

130 Chapter 5. List of Gaussian Keywords

CV Constant volume molar heat capacity

S Entropy
Q Partition function

The thermochemistry analysis treats all modes other than the free rotations and translations as harmonic
vibrations. For molecules having hindered internal rotations, this can produce slight errors in the energy and
heat capacity at room temperatures and can have a significant effect on the entropy. The contributions of
any very low frequency vibrational modes are listed separately so that their harmonic contributions can be
subtracted from the totals and their correctly computed contributions included should they be group rotations
and high accuracy is required. Expressions for hindered rotational contributions to these terms can be found in
Benson [458]. The partition functions are also computed, with both the bottom of the vibrational well and the
lowest (zero-point) vibrational state as reference.
Pre-resonance Raman. This calculation type is requested with one of the Raman options in combination
with CPHF=RdFreq. The frequency specified for the latter should be chosen as follows:
♢ Determine the difference in frequency between the peak of interest in the UV/visible absorption spectrum
and the incident light used in the Raman experiment.
♢ Perform a TD calculation using a DFT method in order to determine the predicted location of the same peak.
♢ Specify a frequency for CPHF=RdFreq which is shifted from the predicted peak by the same amount as the
incident light differs from the observed peak.
Pre-resonance Raman results are reported as additional rows within the normal frequency tables:

Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman

scattering activities (A**4/AMU), depolarization ratios for plane
and unpolarized incident light, reduced masses (AMU), force constants
(mDyne/A), and normal coordinates:
1
B1
Frequencies -- 1315.8011
Red. masses -- 1.3435
Frc consts -- 1.3704
IR Inten -- 7.6649
Raman Activ -- 0.0260
Depolar (P) -- 0.7500
Depolar (U) -- 0.8571
RamAct Fr= 1-- 0.0260 Additional output lines begin here.
Dep-P Fr= 1-- 0.7500
Dep-U Fr= 1-- 0.8571
RamAct Fr= 2-- 0.0023
Dep-P Fr= 2-- 0.7500
Dep-U Fr= 2-- 0.8571

Vibration-Rotation Coupling Output. If the VibRot option is specified, then the harmonic vibrational-
rotational analysis appears immediately after the normal thermochemistry analysis in the output, introduced by
5.32 Freq 131

this header:
Harmonic Vibro-Rotational Analysis
If anharmonic analysis is requested as well (i.e., VibRot and Anharmonic are both specified), then the an-
harmonic vibrational-rotational analysis results follow the harmonic ones, introduced by the following header:
Second-order Perturbative Anharmonic Analysis
Anharmonic Frequency Calculations. Freq=Anharmonic jobs produce additional output following the
normal frequency output. (It follows the vibrational-rotational coupling output if this was specified as well.)
We will briefly consider the most important items.
The output displays the equilibrium geometry (i.e., the minimum on the potential energy surface), followed
by the anharmonic vibrationally averaged structure at 0 K:

Internal coordinates for the Equilibrium structure (Se)

Interatomic distances:
1 2 3 4
1 C 0.000000
2 O 1.206908 0.000000
3 H 1.083243 2.008999 0.000000
4 H 1.083243 2.008999 1.826598 0.000000
Interatomic angles:
O2-C1-H3=122.5294 O2-C1-H4=122.5294 H3-C1-H4=114.9412
O2-H3-H4= 62.9605
Dihedral angles:
H4-C1-H3-O2= 180.

Internal coordinates for the vibrationally average structure at 0K (Sz)

Interatomic distances:
1 2 3 4
1 C 0.000000
2 O 1.210431 0.000000
3 H 1.097064 2.024452 0.000000
4 H 1.097064 2.024452 1.849067 0.000000
Interatomic angles:
O2-C1-H3=122.57 O2-C1-H4=122.57 H3-C1-H4=114.8601
O2-H4-H3= 62.8267
Dihedral angles:
H4-C1-H3-O2= 180.

Note that the bond lengths are slightly longer in the latter structure. The predicted coordinates at STP
follow in the output.
The anharmonic zero point energy is given shortly thereafter in the output:

Anharmonic Zero Point Energy

----------------------------
Harmonic : cm-1 = 5008.40626 ; Kcal/mol = 14.320 ; KJ/mol = 59.914
Anharmonic Pot.: cm-1 = -53.31902 ; Kcal/mol = -0.152 ; KJ/mol = -0.638
132 Chapter 5. List of Gaussian Keywords

Watson+Coriolis: cm-1 = -12.83227 ; Kcal/mol = -0.037 ; KJ/mol = -0.154

Total Anharm : cm-1 = 4942.25496 ; Kcal/mol = 14.131 ; KJ/mol = 59.122

The anharmonic frequencies themselves appear just a bit later in this table, in the column labeled E(anharm):
==================================================
Anharmonic Infrared Spectroscopy
==================================================

Units: Transition energies (E) in cm^-1

Integrated intensity (I) in km.mol^-1

Fundamental Bands
-----------------
Mode(n) E(harm) E(anharm) I(harm) I(anharm)
1(1) 2938.531 2788.983 55.17567187 55.41312200
2(1) 1888.862 1864.231 101.42877427 104.63741421
...

Overtones
---------
Mode(n) E(harm) E(anharm) I(anharm)
1(2) 5877.061 5517.149 0.00211652
2(2) 3777.724 3710.383 3.68324904
...

Combination Bands
-----------------
Mode(n) Mode(n) E(harm) E(anharm) I(anharm)
2(1) 1(1) 4827.393 4654.114 1.74785224
3(1) 1(1) 4490.139 4271.343 0.04557003
...

The harmonic frequencies are also listed for convenience.

Vibronic Analysis. The following input file predicts the vibronic spectrum:

%OldChk=excited Excited state calculation.

%Chk=fcht
# Freq=(ReadFC,FCHT,ReadFCHT) Geom=AllCheck · · ·

TimeIndependent ReadFCHT additional input.

Output=Matrix=JK Output Duschinsky matrix and shift vector.
final blank line

The molecule specification is taken from the checkpoint file from the excited state, as are the force con-
stants for the excited states.
FCHT analysis produces many results. The final Duschinsky (state overlap) matrix appears as follows:
Final Duschinsky matrix
5.32 Freq 133

-----------------------
Note: The normal coordinates of the final state (columns) are expressed
in the basis set of the normal coordinates of the initial state (rows)
1 2 3 4 5
1 -0.539484D+00 0.839747D+00 0.139916D-01 -0.147815D-01 0.167387D-02
2 -0.594185D+00 -0.373849D+00 -0.647845D+00 0.757424D-01 -0.627709D-02
3 0.303582D-01 0.276954D-01 0.572527D-02 0.354162D+00 -0.933518D+00
···

Note that this output reports the value of Ji j for each pair of states. Generally, what is plotted is J 2 .
The locations and intensities of the predicted bands are reported as follows:

==================================================
Information on Transitions
==================================================

Energy of the 0-0 transition: 31327.1976 cm^(-1)

NOTE: The energy (transition energy) refers to the relative energy,

with respect to the 0-0 transition energy.
The intensity is the line intensity.
DipStr is the dipole strength.

Energy = 0.0000 cm^-1: |0> -> |0> Frequency and transition (states).
-> Intensity = 7003. (DipStr = 0.9135E-01)

Energy = 457.9310 cm^-1: |0> -> |9^1> Location is 31875 cm−1 .

-> Intensity = 650.2 (DipStr = 0.8360E-02) Intensity in dm3 cm−1 mol−1 ;
··· Dipole strength in au.

The final predicted spectrum follows in a form suitable for plotting:

==================================================
Final Spectrum
==================================================

Band broadening simulated by mean of Gaussian functions with

Half-Widths at Half-Maximum of 135.00 cm^(-1)

Legend:
-------
1st col.: Energy (in cm^-1)
2nd col.: Intensity at T=0K
Intensity: Molar absorption coefficient (in dm^3.mol^-1.cm^-1)
-----------------------------
30327.1976 0.000000D+00
···
31319.1976 0.699549D+04
31327.1976 0.701428D+04
134 Chapter 5. List of Gaussian Keywords

31335.1976 0.699927D+04
···

Resonance Raman Spectra. The following input file computes the resonance Raman intensities from two
previously run frequency calculations.
%Chk=S0_freq Ground state checkpoint file.
# Freq=(FC,ReadFC,ReadFCHT) Geom=AllCheck · · ·

TimeIndependent ReadFCHT additional input.

Spectroscopy=ResonanceRaman Predict resonance Raman spectrum.
Spectrum=(Lower=800.,Upper=2800.,Broadening=Stick) Spectrum specifications.
Intermediate=Source=Chk Get second state data from checkpoint file (named below).
RR=(OmegaMin=55000,OmegaMax=56000,OmegaStep=100) RR analysis parameters: e˛ range and step size.

S2_freq.chk Excited state checkpoint file.

See the section on Freq=ReadFCHT for details about the additional input. For each of the Raman modes,
the following output appears for each point in the specified range of incident energies (omega):
==================================================
Information on Transitions
==================================================

Energy of the 0-0 transition: 54854.2397 cm^(-1)

Alp2: alpha^2, BsAl: beta_s(alpha)^2, BaAl: beta_a(alpha)^2

Energy = 0.0000 cm^-1: |0> -> |0> Relative energy and involved states.
-> Omega = 55000.0 cm^-1, Sigma = 1.1332
Alp2 = 0.33009E+02, BsAl = 0.29859E+03, BaAl = 0.00000E+00

Following this output, the same data is presented in a tabular form:

==================================================
Final Spectrum
==================================================

No band broadening applied (stick spectrum)

Legend:
-------
1st col.: Raman shift (in cm^-1)
2nd col.: Intensity at T=0K for incident energy: 55000.00 cm^-1
3rd col.: Intensity at T=0K for incident energy: 55100.00 cm^-1
4th col.: Intensity at T=0K for incident energy: 55200.00 cm^-1
5th col.: Intensity at T=0K for incident energy: 55300.00 cm^-1
Raman scattering intensity in cm^3.mol^-1.sr^-1
-----------------------------------------------------------------------------
···
1188.0000 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00
5.32 Freq 135

1190.0000 0.134622D-21 0.213038D-21 0.358179D-21 0.644832D-21

1192.0000 0.000000D+00 0.000000D+00 0.000000D+00 0.000000D+00
···

Since no spectral broadening was requested here (Spectrum=Broadening=Stick), the only rows with non-
zero intensities correspond to the Raman active frequencies.
Examining Low-Lying Frequencies. The output from the full force constant matrix diagonalization (the
default Freq=DiagFull), in which the rotational and translational degrees of freedom are retained, appears as
following in the output:

Low frequencies --- -19.9673 -0.0011 -0.0010 0.0010 14.2959

Low frequencies --- 25.6133 385.4672 988.9028 1083.0692

This output is from an Opt Freq calculation on methanol. Ignoring sign, there are 3 low-lying modes,
located at around 14, 19, and 25 wavenumbers (in addition to the three that are ∼0). However, if we rerun
the calculation using tight optimization criteria (Opt=Tight) and a larger integration grid, the lowest modes
become:

Low frequencies --- -7.4956 -5.4813 -2.6908 0.0003 0.0007

Low frequencies --- 0.0011 380.1699 988.1436 1081.9083

The low-lying modes are now quite small, and the lowest frequencies have moved slightly as a result.
This analysis is especially important for molecular systems having frequencies at small wavenumbers. For
example, if the lowest reported frequency is around 30 and there is a low-lying mode around 25 as above, then
the former value is in considerable doubt (as is whether the molecular structure is even a minimum).
Rerunning a Frequency Calculation with Different Thermochemistry Parameters. The following two-step
job contains an initial frequency calculation followed by a second thermochemistry analysis using a different
temperature, pressure, and selection of isotopes:

%Chk=freq
# B3LYP/6-311+G(2d,p) Freq

Frequencies at STP

molecule specification

-Link1-
%Chk=freq
%NoSave
# B3LYP/6-311+G(2d,p) Freq(ReadIso,ReadFC) Geom=Check

Repeat at 300 K

0,1

300.0 1.0
 136 Chapter 5. List of Gaussian Keywords

16
2
3
···

Note also that the freqchk utility may be used to rerun the thermochemical analysis from the frequency
data stored in a Gaussian checkpoint file.

5.32.7 ReadAnharm Input

The following keywords for specifying various aspects of Freq=Anharm calculations are included as ad-
ditional input within the Gaussian input file. They control various aspects of anharmonic frequency analyses.
Note that these keywords are completely different from those supported in Gaussian 09 (a few of these changes
were introduced in Gaussian 09 revision D.01).

Data Sources and Format

The DataSrc, DataAdd and DataMod input items locate the various data required by the anharmonic
frequency analysis. They each take a list of parameters and associated values which specify locations from
which to retrieve different data items. In general, parameters specify what data is to be read and their values
specify the location of that data. The available options for the latter are listed below. Generally, they may be
optionally followed by a format suffix.
Source keywords are used to specify where the data is located:
♢ Src: Use data from the RWF file for the current job. RWF is a synonym.
♢ Chk: Retrieve data from the current checkpoint file (as defined with %Chk or %OldChk).
♢ In: Read data from the input stream.
♢ InChkn: Retrieve data from the nth file in the file list (see the discussion of additional input sections below).
Valid values of n run from 1 to 6.
Format Suffixes are appended directly to the source item, and they specify a non-default format for
various read-in data. For example, InQMW says to read derivative data from the input stream in mass-weighted
normal coordinates. The following suffixes are available:
♢ QMW: Derivatives are with respect to normal modes in mass-weighted normal coordinates. Q is a synonym
for this format suffix.
♢ QMWX: Harmonic derivatives are with respect to normal modes in Cartesian coordinates, and anharmonic
derivatives are with respect to normal modes in mass-weighted normal coordinates. X is a synonym for
this format suffix.
♢ QRedX: Harmonic derivatives are with respect to normal modes in Cartesian coordinates, and anharmonic
derivatives are with respect to normal modes in dimensionless normal coordinates.
By default, QMWX is tried first, followed by QMW.

DataSrc=param: Specify the source(s) of various read-in data. The parameter consists of a keyword indicating
the data to which it applies and a source keyword indicating its location (and possibly its format). The available
parameters are:
♢ source: Sets the data source for all data.
♢ Harm=source: Sets the data source for harmonic data. The default is taken from the source file.
5.32 Freq 137

♢ Anharm=source: Sets the data source for harmonic data. The default is taken from the source file.
♢ Coriolis=source: Sets the data source for the Coriolis couplings. At present, the only supported items are
Src and In, and format suffixes may not be used.
♢ NMOrder=ordering: Specifies the order normal modes are stored in the input source, selected from the
following list. This item may be specified in addition to a source item.
• AscNoIrrep: Ascending order. Do not sort by irreducible representation. This is the default.
• Asc: Ascending order. Sort by irreducible representation if possible.
• Desc: Descending order. Sort by irreducible representation if possible.
• DescNoIrrep: Descending order. Do not sort by irreducible representation.
• Print: Use same order as for printing.
The following DataSrc items are deprecated, and are included only for backward similarity to Gaussian
09 (where they functioned as top-level additional input items).
♢ InDerAU: Use data from the input stream in atomic units.
♢ InDerAJ: Use data from the input stream in attoJoules
♢ InDerRed: Use data from the input stream in reduced form. Reduced is an alternate name for this item.
♢ InDerGau: Use data from the input stream with the layout of the Gaussian output. InGauDer is an alternate
name for this item.

DataAdd=params: Read alternate data to replace or complete the original data. Using this option will replace
the already existing information in the original data with the data specified here.
♢ Freq: Replace harmonic frequencies with values given in the input stream (in cm−1 ). A data source may
also be specified as a parameter: Freq=source, but format suffixes are not allowed.
♢ PESFull=source: Read force constraints from specified specified source.
♢ PESHarm=sources: Read harmonic force constants from specified specified source.
♢ PESAnh=sources: Read anharmonic force constants from specified specified source.
♢ EDipFull=sources: Read the electric dipole from the specified specified source.
♢ EDipHarm=sources: Read the harmonic components of the electric dipole from the specified specified
source.
♢ EDipAnh=sources: Read the anharmonic components of the electric dipole from the specified specified
source.
♢ MDipFull=sources: Read the magnetic dipole from the specified source.
♢ MDipHarm=sources: Read the harmonic components of the magnetic dipole from the specified source.
♢ MDipAnh=sources: Read the anharmonic components of the magnetic dipole from the specified source.
♢ PolFull=sources: Read the polarizability tensor from the specified source.
♢ PolHarm=sources: Read the harmonic components of the polarizability tensor from the specified source.
♢ PolAnh=sources: Read the anharmonic components of the polarizability tensor from the specified source.
♢ MagFFull=sources: Read the magnetic-field properties from the specified source.
♢ MagFHarm=sources: Read the harmonic components of the magnetic-field properties from the specified
source.
♢ MagFAnh=sources: Read the anharmonic components of the magnetic-field properties from the specified
source.
♢ FreqDepPFull=sources: Read the frequency-dependent properties from the specified source.
138 Chapter 5. List of Gaussian Keywords

♢ FreqDepPHarm=sources: Read the harmonic components of the frequency-dependent properties from the
specified source.
♢ FreqDepPAnh=sources: Read the anharmonic components of the frequency-dependent properties from the
specified source.

DataMod=params: Modify the data in various manners.

♢ ScHarm=value: Scales harmonic frequencies with a constant scaling factor (default is 1.0).
♢ NoCor: Discards Coriolis couplings in calculations. By default, all couplings will be retained.
♢ DerOrder=N: Selects the derivatives order to keep. E.g. DerOrder=123 discards all quartic force constants.
♢ DerIndex=N: Sets the maximum number of independent indexes for a derivative. E.g. DerIndex=2 keeps
kii j but discards ki jk .
♢ SkipPT2=what: Selectively removes derivatives based on the parameter, whose possible values are listed
below:
• No: Do not remove the data. This is the default option.
• Modes: Removes the derivatives with respect to any of the normal modes given in the input stream.
• Constants: Removes the derivatives based on the indexes given in the input stream. The input
explicitly specifies the force constants (energy derivatives) to be removed. Each line specifies the
involved normal modes, with the derivative order implied by the number of indexes. For example,
to remove the third derivatives with respect to normal coordinates Q1 Q2 Q5 , the input line would be:
1 2 5
• OptModes: Modify derivatives based on additional instructions in the input stream (see input order-
ing section below).

Tolerances=data: Modify the tolerance threshold to include/discard derivative data.

♢ Gradient=value: Threshold for the energy first derivatives (default is 3.7074×10−3 ).
♢ Hessian=value: Threshold for the energy second derivatives (default is 3.7074×10−5 ).
♢ Cubic=value: Threshold for the energy third derivatives (default is 3.7074×10−5 ).
♢ Quartic=value: Threshold for the energy fourth derivatives (default is 3.7074×10−5 ).
♢ Coriolis=value: Threshold for the Coriolis couplings (default is 1.0×10−3 ).
♢ Inertia=value: Threshold for the principal moments of inertia (default is 1.0×10−4 Å2 ).
♢ Symm=value: Tolerance for anharmonic data with respect to symmetry rules (default is 2%).

Output Control

This section specifies the contents and destination of the calculation output.

Print=items: Include items in the output file. Available items are the following:
♢ InDataX: Include data compatible with DataSrc=InQMWX. The form Print=InDataX=Ext writes the data to
the external file input_data.dat.
♢ InDataNM: Include data compatible with DataSrc=InQMW. The form Print=InDataNM=Ext writes the data
to the external file input_data.dat.
♢ YMatrix: Include the Y matrix (a variant of the χ matrix).
♢ Verbosity=n: Specify the verbosity level. The default is 0.
5.32 Freq 139

♢ ITop=rep: Selects the representation used for rotational spectroscopy. By default, it is defined automatically
by Gaussian from the principal moments of inertia. Available representations are:
• Ir: Ir Representation: Iz < Ix < Iy
• IIr: IIr Representation: Iy < Iz < Ix
• IIIr: IIIr Representation: Ix < Iy < Iz
• Il: Il Representation: Iz < Iy < Ix
• IIl: IIl Representation: Ix < Iz < Iy
• IIIl: IIIl Representation: Iy < Ix < Iz
♢ ZAxisSymm=axis: Sets the Eckart axis to be used as Z for the definition of the reduced Hamiltonians for
the vibrorotational analysis. Available choices are:
• X: Z collinear with X.
• Y: Z collinear with Y.
• Z: Z collinear with Z.
♢ NMOrder=ordering: Specifies the order in which normal modes are listed:
• Asc: Ascending order. Sort by irreducible representation if possible.
• Desc: Descending order. Sort by irreducible representation if possible. This is the default.
• AscNoIrrep: Ascending order. Do not sort by irreducible representation.
• DescNoIrrep: Descending order. Do not sort by irreducible representation.
♢ PT2VarEVec: Include the eigenvector matrix from the diagonalization of the variational matrix.
♢ PT2VarStates: Include the projection of the variational states on the deperturbed ones.
♢ PT2VarProj: Include the projection of the DVPT2 states on the new variational states.
♢ InDataAU: Write data compatible with DataSrc=InDerAU (deprecated).
♢ Polymode: Write data to use in the Polymode program.

Reduced-Dimensionality Schemes

RedDim=items: Specifies which normal modes are active in the analysis. Items are:
♢ Active=n: Activate the n modes specified in the input stream. By default, all modes are active.
♢ Inactive=n: Read list of n inactive modes from the input stream.
♢ Frozen=n: Read n modes to be frozen from the input stream.
♢ MinFreqAc=freq: Sets the normal modes with a frequency above the specified value to be active (default is
0). Only valid if MaxFreqAc>MinFreqAc.
♢ MaxFreqAc=freq: Sets the normal modes with a frequency below the specified value to be active (default is
infinity). Only valid if MaxFreqAc>MinFreqAc.
♢ MinFreqIn=freq: Sets the normal modes with a frequency above the specified value to be inactive (default is
0). Only valid if MaxFreqIn>MinFreqIn.
♢ MaxFreqIn=freq: Sets the normal modes with a frequency below the specified value to be active (default is
infinity). Only valid if MaxFreqIn>MinFreqIn.
♢ MinFreqFr=freq: Sets the normal modes with a frequency above the specified value to be frozen (default is
0). Only valid if MaxFreqFr>MinFreqFr.
♢ MaxFreqFr=freq: Sets the normal modes with a frequency below the specified value to be frozen (default is
infinity).Only valid if MaxFreqFr>MinFreqFr.
140 Chapter 5. List of Gaussian Keywords

Second-Order Vibrational Perturbation Theory (VPT2)

PT2Model=data: Sets the VPT2 model to use. The default is GVPT2.
♢ HDCPT2: Use the Hybrid Degeneracy-Corrected 2nd-order Perturbation Theory.
♢ VPT2: Use the original 2nd-order Vibrational Perturbation Theory. Vibrational spectroscopy intensities are
available for this model.
♢ DVPT2: Use the Deperturbed 2nd-order Vibrational Perturbation Theory. Vibrational spectroscopy inten-
sities are available for this model. The form DVPT2=all selects all possibly resonant terms as Fermi
resonances, and it is equivalent to Resonances=(DFreqFrm=∞,DPT2Var=0).
♢ GVPT2: Use the Generalized 2nd-order Vibrational Perturbation Theory. This is the default. It is similar
to DVPT2, but the removed terms are treated variationally in a second step. Vibrational spectroscopy
intensities are available for this model. The form GVPT2=all selects all possibly resonant terms as Fermi
resonances, and it is equivalent to Resonances=(DFreq12=∞,K12Min=0).
♢ DCPT2: Use the Degeneracy-Corrected 2nd-order Perturbation Theory.

HDCPT2=params: Set the parameters for the model with the Alpha and Beta options (i.e., HDCPT2=Alpha=value),
[ (√ ) ]
which specify values for the corresponding variables in the expression for Λ: Λ = tanh α × k2 ε 2 − β + 1 /2

Resonances=params: Set resonance thresholds and parameters for DVPT2 (Fermi-related items only) and
GVPT2 calculations.
♢ DFreq12=value: Sets the maximum frequency for 1 – 2 Fermi resonances (ωi − (ω j + ωk )). The default is
200 cm−1 .
♢ DFreq22=value: Sets the maximum frequency for 2 – 2 Darling-Dennison resonances (2ωi − (ω j + ωk ) and
2ωi − 2ω j ). The default is 100 cm−1 .
♢ DFreq11=value: Sets the maximum frequency for 1 – 1 Darling-Dennison resonances (ωi ω j ). The default
is 100 cm−1 .
♢ DFreq13=value: Sets the maximum frequency for 1 – 3 Darling-Dennison resonances (ωi − (ω j + ωk + ωl )).
The default is 100 cm−1 .
♢ K12Min=value: Sets the maximum allowed difference between the VPT2 and model variational results
(Martin test). The default is 1 cm−1 .
♢ K22Min=value: Sets the minimum value for off-diagonal 2 – 2 Darling-Dennison term. The default is 10
cm−1 .
♢ K11Min=value: Sets the minimum value for off-diagonal 1 – 1 Darling-Dennison term. The default is 1
cm−1 .
♢ K11MinI=value: Sets the minimum value for the secondary 1 – 1 resonance test, intended to detect critical
cases specific to intensity calculations. The default is 1 cm−1 .
♢ K13Min=value: Sets the minimum value for off-diagonal 1 – 3 Darling-Dennison term. The default is 10
cm−1 .
♢ K13MinI=value: Sets the minimum value for the secondary 1 – 3 resonance test, intended to detect critical
cases specific to intensity calculations. The default is 0.25 cm−1 .
♢ HDCPT2=value: Sets the minimum value for the HDCPT2/VPT2 difference test. The default is 0.1.
♢ NoFermi: Deactivates the search for 1 – 2 Fermi resonances. No12Res is a synonym for this item.
♢ NoDarDen: Deactivates the search for Darling-Dennison (2 – 2, 1 – 1 and 1 – 3) resonances.
5.32 Freq 141

♢ No22Res: Deactivates the search for 2 – 2 Darling-Dennison resonances.

♢ No11Res: Deactivates the search for 1 – 1 Darling-Dennison resonances.
♢ No13Res: Deactivates the search for 1 – 3 Darling-Dennison resonances. 1 – 3 resonances are only available
for 3-quanta transitions.
♢ List=action: Tells Gaussian to read resonance cases from the input stream. action is optional; it defaults to
Replace. Otherwise, it controls the use of the input resonances. The available action keywords are:
• Replace: Discards automatic analysis and only use resonances in the input. This is the default.
• Add: Augments automatic results with input data. A simpler form of this option is Resonances=Add.
• Delete: Remove resonances in the input list from the results of the automatic analysis. A simpler
form of this option is Resonances=Delete.
• Modify: Add or remove resonances starting from the list obtained from the automatic analysis. An
action keyword – ADD or DEL – must precede the resonance data on each input line.
See the Specifying Resonances subsection below for more information.

Spectroscopy
Spectro=MaxQuanta=quanta: Compute transition integrals to states with up to the specified quanta. The default
is 2.

ROA=params: Options related to Raman optical activity. If the keyword is specified, then only those scatter-
ings explicitly requested will be computed. If the ROA is not specified, then intensities are computed for all
supported scatterings.
♢ ICP0: Compute ROA intensity for ICP forward scattering.
♢ ICP90x: Compute ROA intensity for incident circular polarization (ICP) right-angle scattering (polarized).
♢ ICP90z: Compute ROA intensity for ICP right-angle scattering (depolarized).
♢ ICP90*: Compute ROA intensity for ICP right-angle scattering (magic angle).
♢ ICP180: Compute ROA intensity for ICP backward scattering.
♢ SCP0: Compute ROA intensity for scattered circular polarization(SCP) forward scattering.
♢ SCP90x: Compute ROA intensity for SCP right-angle scattering (polarized).
♢ SCP90z: Compute ROA intensity for SCP right-angle scattering (depolarized).
♢ SCP90*: Compute ROA intensity for SCP right-angle scattering (magic angle).
♢ SCP180: Compute ROA intensity for SCP backward scattering.
♢ DCP180: Compute ROA intensity for double circular polarization (DCP) backward scattering.
♢ All: Compute the ROA intensity for all supported scatterings.

Freq=ReadAnharm Additional Input Ordering

The potential input sections for the various Freq=ReadAnharm additional input items should follow the
keyword list section in the following order. Blank lines separate input sections, but each section and its termi-
nating blank line should be included only when the corresponding keyword is specified.

Freq=ReadAnharm input keywords

blank line
checkpoint file list for DataSrc=InChkn or DataAdd=· · · =InChkn
blank line
data for DataSrc=In or DataAdd=· · · =In (harmonic followed immediately by anharmonic)
142 Chapter 5. List of Gaussian Keywords

blank line
data for DataAdd=Freq
blank line
n modes for RedDim=Active
blank line
n modes for RedDim=Inactive
blank line
n modes for RedDim=Frozen
blank line
keyword for DataMod=SkipPT2=OptModes (see below)
modes for DataMod=SkipPT2=Modes or Constants or DataMod=SkipPT2=OptModes
blank line
data for Resonances=List
blank line

DataMod=SkipPT2=OptModes Keywords: Removal of Contributions from Selected Normal Modes

One or more options are specified on a single line with no blank line following. The options available are:
♢ MinInd=n: Controls the minimum number of times a selected normal mode must appear to discard the
derivative. The default is 1. For example, a value of 2 means that ki jk is kept, but kii j and kiii are removed.
♢ EnOrd=mask: Controls the energy derivative orders to consider. The default is 1234 which says to include
all energy derivatives. The value 14 says to only treat the first and fourth energy derivatives and to ignore
the second and third energy derivatives.
Here is an example calculation using DataMod=SkipPT2=OptModes:

# Freq=(Anharm,ReadAnharm) · · ·

Formaldehyde

0 1
C -0.6067825443565 -0.0000000216230 0.0000000000000
O 0.6033290944914 0.0000000215000 0.0000000000000
H -1.1752074085613 0.9201232113261 0.0000000000000
H -1.1752073429832 -0.9201232950844 0.0000000000000

PT2Model=GVPT2 Resonances=(NoDarDen,NoFermi)
DataMod=SkipPT2=OptModes

MinInd=2 EnOrd=34 Control keywords: keep only ki jk for third and fourth derivatives
5 6 Modes for which to remove derivatives
terminating blank line
5.32 Freq 143

Specifying Resonances

For Resonances=Add, Resonances=List=Replace and Resonances=Delete, each line contains the type of
resonance and the indexes of the normal modes involved in the resonances. Supported types are:
♢ 1-2 or 12: 1-2 Fermi resonance. 3 indexes needed, given in the order: ω1 ≈ ω2 + ω3
♢ 1-1 or 11: 1-1 Darling-Dennison resonance. 2 indexes needed, given in the order: ω1 ≈ ω2
♢ 1-3 or 13: 1-3 Darling-Dennison resonance. 4 indexes needed, given in the order: ω1 ≈ ω2 + ω3 + ω4
♢ 2-2 or 22: 2-2 Darling-Dennison resonance. 4 indexes needed, given in the order: ω1 + ω2 ≈ ω3 + ω4
For Resonances=List=Modify, an action must be specified at the beginning of the line, before the reso-
nance type and the normal modes. The available actions are ADD (add resonance) and DEL (remove resonance
if previously identified).

Examples

Example 1: Frequency data calculated in the current job:

%Chk=example1
# B3LYP/6-311+G(d,p) Freq=(Anharmonic,ReadAnharm)

Anharmonic frequencies example 1

molecule specification

DataMod=SkipPT2=Modes Freq=ReadAnharm additional input

RedDim=Inactive=1 # modes to make inactive
PT2Model=GVPT2
Resonances=Add
Print=InDataX=Ext Write data to an external file
blank line
6 Modes to make inactive: RedDim=Inactive
blank line
4 5 Modes for which to discard derivatives: DataMod=SkipPT2=Modes
blank line
1-2 2 3 3 List of additional resonances: Resonances=Add
blank line

Example 2: Frequency data read from input stream. It uses the checkpoint file from Example 1 to retrieve the
molecular geometry and Hessian:

%OldChk=example1
%Chk=example2
# B3LYP/6-311+G(d,p) Freq=(ReadFC,Anharmonic,ReadAnharm) Geom=Check

Anharmonic frequencies example 2

0 1

PT2Model=GVPT2 Freq=ReadAnharm additional input

DataSrc=(InQMWX,NMOrder=Desc) Read harmonic/anharmonic data from input
 144 Chapter 5. List of Gaussian Keywords

DataAdd=Freq Replace harmonic frequencies with input values

RedDim=Inactive=1
blank line
@input_data.dat Data file from previous job with Print=InDataX=Ext
blank line
1198.351 List of harmonic frequencies: DataAdd=Freq
1259.285
1530.636
1814.590
2884.164
2941.556
blank line
6
blank line

Example 3: The following example specifies alternate values for several parameters:

# B3LYP/6-31G(d) Freq=(Anharm,ReadAnharm)

Anharmonic frequencies example 3

molecule specification

Tolerances=Coriolis=0.25 Freq=ReadAnharm additional input

Resonances=(DFreq12=220.0,K12Min=1.1)
DataMod=SCHarm=0.98
blank line

Example 4: Anharmonic VCD and ROA spectra calculation:

%Chk=project4
# Freq=(ROA,VCD,Anharm,ReadAnharm) CPHF=RdFreq · · ·

Anharmonic VCD and ROA spectrum

0 1
molecule specification

589.3nm incident light frequency

PT2Model=GVPT2 ReadAnharm input section

Spectro=MaxQuanta=3
blank line

5.32.8 ReadFCHT Input

The following keywords for specifying various aspects of Freq=FC, HT or FCHT calculations are included
as additional input within the Gaussian input file. They control various aspects of these analyses. Note that
these keywords are different from those supported in Gaussian 09.
5.32 Freq 145

Specifying Calculation Options and Parameters

Transition=type: Specify the type of electronic transition.
♢ Absorption: Absorption. This is the default.
♢ Emission: Emission.

Spectroscopy=type(s): Spectroscopy to simulate. The default is Spectroscopy=OnePhoton. The following

items are available (names may be abbreviated to just the capital letters below: e.g., RR for ResonanceRaman):
♢ OnePhoton: One-photon process. This is the default.
♢ CircularDichroism: Circular Dichroism: electronic circular dichroism (ECD) for absorption and circularly
polarized luminescence (CPL) for emission.
♢ OnePhotonAbsorption: One-photon absorption. Implies Transition=Absorption.
♢ OnePhotonEmission: One-photon emission. Implies Transition=Emission.
♢ ElectronicCircularDichroism: Electronic circular dichroism. Implies Transition=Absorption.
♢ CircularlyPolarizedLuminescence: Circularly polarized luminescence. Implies Transition=Emission.
♢ ResonanceRaman: Vibrational Resonance Raman. Options are specified via a separate item (see below).

ResonanceRaman=options: The following RR-specific options are available:

♢ CombOnly: Compute only combination bands.
♢ NoComb: Skip computation of combination bands.
♢ aMean=coeff : Set the coefficient of the mean polarizability. The default is 45.
♢ Damping=value: Damping constant or lifetime of intermediate states (in cm−1 ). The default is 500 cm−1 .
♢ dAnti=coeff : Set the coefficient of the antisymmetric anisotropy. The default is 5.
♢ gSymm=coeff : Set the coefficient of the symmetric anisotropy. The default is 7.
♢ Omega=value: Incident energy (in cm−1 ). By default, it is calculated as the difference in energy between
the vibrational fundamental states of the initial and intermediate states.
♢ OmegaList: Reads a list of incident energies (in cm−1 ) in the input stream to build an energy profile.
♢ OmegaMax=value: Maximum energy (in cm−1 ) for the incident energy profile.
♢ OmegaMin=value: Minimum energy (in cm−1 ) for the incident energy profile.
♢ OmegaNum=n: Number of energies in the incident energy profile.
♢ OmegaStep=value: Energy interval (in cm−1 ) between two energies for the incident energy profile.
♢ Scattering=params: Scattering geometry for the Resonance Raman simulation. Available items are (note
that the asterisks below are part of the parameter names):
• ICP0: Compute RR intensity for Incident Circular Polarization (ICP) forward scattering.
• ICP90x: Compute RR intensity for ICP right-angle scattering (polarized).
• ICP90z: Compute RR intensity for ICP right-angle scattering (depolarized).
• ICP90*: Compute RR intensity for ICP right-angle scattering (magic angle).
• ICP180: Compute RR intensity for ICP backward scattering.
• SCP0: Compute RR intensity for Scattered Circular Polarization (SCP) forward scattering.
• SCP90x: Compute RR intensity for SCP right-angle scattering (polarized).
• SCP90z: Compute RR intensity for SCP right-angle scattering (depolarized).
• SCP90*: Compute RR intensity for SCP right-angle scattering (magic angle).
• SCP180: Compute RR intensity for SCP backward scattering.
146 Chapter 5. List of Gaussian Keywords

• DCP180: Compute RR intensity for Double Circular Polarization (DCP) forward scattering.
• All: Compute the RR intensity for all supported scatterings.

Temperature: Specify temperature and related parameters:

♢ Value=temp: Temperature of simulation in K. The default is the value specified to Gaussian with the Temp
keyword or via additional input; the Gaussian default is 298.15 K.
♢ MinPop=ratio: Minimum ratio between the Boltzmann populations of any vibrational initial state and the
fundamental state for the former to be considered in the calculations. In other words, this item specifies
the fraction of a vibrational state that must be populated in order for it to be treated as the starting point
of a transition. The default value is 0.1 (10%).

TransProp=definition: Definition of the transition dipole moment(s). The first three items effectively select
among Franck-Condon, Herzberg-Teller and FCHT analyses. However, the corresponding options to the Freq
keyword are preferable. The following items are available:
♢ FC: The dipole moment is assumed constant during the electronic transition. This selection describes dipole-
allowed transitions well. It is the default.
♢ FCHT: Computes zeroth- and first-order terms of the Taylor expansion of the transition dipole moment
about the equilibrium geometry. It is needed to correctly treat weakly-allowed electronic transitions or
CD spectra.
♢ HT: Implements linear variation of the dipole moment with respect to the normal mode. This item corre-
sponds to the first-order term of the Taylor expansion of the transition dipole moment about the equilib-
rium geometry.
♢ DipA=source: Explicit definition of the transition dipole moment dA . The following options for the data
source are available:
• Auto: Gaussian will choose the definition depending on the simulation parameters. This is the
default.
• Read: Read data from main input source (see “Data Sources” below).
• Input: Read data from input stream.
♢ DipB=source: Definition of the transition dipole moment dB . This item accepts the same data source options
as DipA.
♢ EDip=source: Definition of the transition electric dipole moment. This item accepts the same data source
options as DipA.
♢ MDip=source: Definition of the transition magnetic dipole moment. This item accepts the same data source
options as DipA.
♢ NoUse: Discard the transition dipole read in the data source and replace it with a unitary one. This is
the default behavior for electronic transition with a change in multiplicity or charge. Keyword is not
supported for HT and FCHT calculations.

Method=method: Selects the representation model for the electronic transition. The non-default options specify
methods for approximating the excited state frequencies based on the ground state. These are not generally
preferable to modeling the excited state explicitly. The following methods are available:
♢ AdiabaticHessian: Both PESs – ground state and excited state – are calculated at the harmonic level about
their respective minimum. This is the default.
5.32 Freq 147

♢ AdiabaticShift: Both PESs are calculated at the harmonic level about their respective minimum, but the PES
of the final state is assumed to be the same as the initial state. Only the equilibrium geometry of the final
state is calculated.
♢ VerticalHessian: The PES of the final state is evaluated about the equilibrium geometry of the initial state.
♢ VerticalGradient: The PES of the final state is evaluated about the equilibrium geometry of the initial state,
but the PES of the final state is assumed to be the same as the initial state. Only the energy gradient of the
final state is calculated about the equilibrium geometry of the initial state. (This method is also known as
the linear coupling model.)
For emission spectra, the form VerticalGradient=Abs causes Gaussian to compute the 0-0 transition en-
ergy in the same way as absorption spectra in order to get the correct 0-0 transition energy. It is needed
when the emission spectrum is incorrectly computed as an absorption spectrum (equilibrium geometry
of the ground state, frequencies of the ground state and forces of the excited state).

Prescreening=params: Sets the prescreening criteria for choosing the most intense transitions. Only available
for the time-independent framework. Available parameters:
♢ MaxC1=n: Maximum quantum number reached in C1 (Cmax
1 ). The default is 20.
♢ MaxC2=n: Maximum quantum number reached by both modes involved in the combination bands in C2
(Cmax
2 ). The default is 13.
♢ MaxInt=millions: Maximum number of integrals to compute for each class above C2 (Nmax
I ), in units of one
million. The default value is 100 (100,000,000).

TimeIndependent: Use the time-independent framework. This is the default for one-photon spectroscopy. TI is
a synonym for this item.

TimeDependent=params: Compute the band shape using the path-integral approach instead of the sum-over-
states approach. This is the default for Resonance Raman spectroscopy. TD is a synonym for this item. Avail-
able parameters are:
♢ 2NStep=m: Use 2m steps for the integration. m defaults to 18 for OPA, OPE, ECD and CPL and 12 for RR.
♢ 2NStepWin=k: Set the number of steps in which the correlation function X(t) is actually computed to as 2k .
The function is 0 outside this range. Note that k must be ≤ m from 2NStep above. By default, k is set
equal to m.
♢ GauHWHM=n: Inhomogenous broadening, applied as a dephasing (in cm−1 ). The default is 135 cm−1 .
♢ LorHWHM=n: Homogenous broadening, applied as a dephasing (in cm−1 ). The default is 0 cm−1 .
♢ Time=seconds: Time interval ∆t in seconds. The default value is 2m ×10−17 , where m is from 2NStep above.

Termination=DeltaSP=value: Sets the termination criteria. Set the minimum difference between two consecu-
tive classes of the final state to continue the calculation. The default is 0.0 (always continue).

Data Sources
The items in this section specify the locations and methods for obtaining various data used by the FCHT
analysis.

Initial=items: Data source(s) and/or parameters for the initial state.

148 Chapter 5. List of Gaussian Keywords

Final=items: Data source(s) and/or parameters for the final state.

Intermediate=items: Data sources(s) and/or parameters related to the intermediate state. Only valid for Reso-
nance Raman.
The following parameters are available for the three preceding items:
♢ Source=source: Data source for the state:
• Calc: Current calculation. This is the default for Absorption spectra.
• Chk: Checkpoint file (the filename is given in the input stream). This is the default for Emission
spectra.
• LogFile: Gaussian output filename (the filename is given in the input stream).
♢ Freq=params: Source and handling of vibrational frequency data:
• Read: Read frequencies from the main data source. This is the default.
• Input: Read frequencies from the input stream.
• Scale: Scale frequencies using a mode-specific extrapolated scaling factor based on the Duschinsky
transformation. The reference state used is the other electronic state. For example, Final=Freq=Scale
uses the input initial state frequencies to scale those of the final state. The required frequencies are
taken from the input stream in their usual position (see below).
♢ MaxBands=state: Set the highest class state to consider. The default is 3 for Initial and 7 otherwise.
♢ MaxStates=n: Maximum number of initial vibrational states actually considered in the calculations. Only
valid with Initial. Note that this value is not the number of configurations printed by Gaussian. The
default is 50.
♢ ExcState=state: Excited electronic state actually treated in the Gaussian output file. Only used if the data
source for the excited state is a Gaussian output file.

DataAdd=DeltaE=value: Difference in energy between the electronic states (in Hartrees). By default, it is
calculated from the data sources used for the initial and final states.

DataMod=Duschinsky=params: Duschinsky matrix to use in the calculation, By default, the true Duschinsky
matrix is used. Note that the definition of the Duschinsky matrix depends on the model used to describe the
transition. Other options are:
♢ Identity: Use the identity matrix as the Duschinsky matrix.
♢ Diagonal: Swap the columns of the correct Duschinsky matrix to be as diagonal as possible and replace it
by the identity matrix. If this cannot be done because the matrix is not diagonal enough, an error occurs.

Superpose=params: Specifty the superposition procedure.

♢ Reorient: Reorient molecules to maximize overlap between the two structures. This is the default.
♢ NoReorient: Do not try to superpose the structures.
♢ Rotation=n: Rotation algorithm used for the superposition:
• 0: Alternate usage. First quaternions, then rotation angles. This is the default.
• 1: Use the program default (be aware that this may change between Gaussian versions).
• 2: Use quaternions only.
• 3: Use rotation angles only.
5.32 Freq 149

♢ RotNIter=xxxyyy: Maximum number of iterations for each superposition algorithm, where xxx is the number
of iterations for the algorithm based on quaternions, and yyy is the number of iterations for the angle-
based algorithm. The default parameter is 030100 or 30 for quaternions and 100 for rotation angles.

Output Selection

Print=params: This item controls the information included in the output.

♢ Spectra=params: Spectra to be included (the non-default items are not valid in the time-dependent frame-
work nor for Resonance Raman):
• Final: Print only the final spectrum. This is the default.
• All: Print the maximum number of class-specific spectra.
• ClassI: Print one spectrum for each class of the initial state.
• ClassF: Print one spectrum for each class of the final state.
♢ Matrix=list: Matrices to be displayed: J, K, A, B, C, D, E. The string is composed of the matrices of interest,
e.g., JK. A, B, C, D and E are the Sharp and Rosenstock matrices, J is the Duschinsky matrix, and K is
the shift vector.
♢ HuangRhys: Print Huang-Rhys factors [459].
♢ AssignThresh=n: Include data (assignment, energy, intensity) of the transitions, which contribute at least to
100n% to the total intensity of the spectrum obtained for each initial vibrational state. The default is 0.01
(1%).
♢ TDAutoCorr=n: Print n points of the time-dependent autocorrelation function. The default is 0 (output
disabled).
♢ Tensors: Print the transition tensors instead of the invariants. Only available for Resonance Raman.
♢ Conver: Print convergence data. Only available for Resonance Raman.
♢ Color=params: Specify RGB standard for color output:
• sRGB: Use the sRGB standard (white reference: D65, gamma correction based on the IEC 61966-
2-1 standard). This is the default.
• None: Do not print the color in an RGB format.
• CIE: Use the CIE RGB standard (white reference: D65, no gamma correction).
• HDTV: Use the HDTV RGB standard (white reference: D65, gamma correction based on the ITU-
R BT.709-3 standard).

Spectrum=params: Control spectrum layout.

♢ Lower=value: Energy of the lower bound of the spectrum (in cm−1 ). For absorption, the default is -1000
cm−1 . For emission, the default is -8000 cm−1 . The bound is defined with respect to the 0-0 transition.
♢ Upper=value: Energy of the upper bound of the spectrum (in cm−1 ). For absorption, the default is +8000
cm−1 . For emission, the default is +1000 cm−1 . The bound is defined with respect to the 0-0 transition.
♢ AbsBound: Deactivate the default behavior of Gaussian to define the lower and upper bounds of the spectrum
with respect to the 0-0 transition.
♢ Grain=value: Energy difference between two adjacent points for the discretization of the spectrum (in cm−1 ).
The default is 8cm−1 .
♢ Broadening=params: Discribution function used to compute the band-shape:
150 Chapter 5. List of Gaussian Keywords

• Gaussian: Use normal distribution functions to simulate the inhomogeneous broadening. This is
the default.
• Lorentzian: Use Cauchy distribution functions to simulate the homogeneous broadening.
• Stick: Do not simulate the band broadening. Print the bands as sticks.
♢ HWHM=value: Half-width at half-maximum of the distribution function used for the convolution (in cm−1 ).
The default is 135 cm−1 .

Reduced-Dimensionality Schemes

RedDim=params: Activates and sets a reduced-dimensionality scheme.

♢ Block: Use the correct Duschinsky matrix to find the projection of a list of modes given in the input stream
on the other state to reduce consistently the dimension of the problem. By default, the state of reference
is the lower one.
♢ ClearLowFreq=n: Remove all normal modes with a frequency below n cm−1 in absolute value. If this
parameter is specified but n is omitted, it defaults to 50.
♢ ClearImFreq: Remove at most one normal mode per state with an imaginary frequency. If there is one mode
with an imaginary frequency in each state, Gaussian checks that they are uncoupled to other modes and
project themselves on each other in the electronic transition.
♢ BlockThresh=value: Threshold for the block(s) construction (between 0 and 1). A high value ensures that
the selected modes are uncoupled from the remaining ones. The default is 0.9.
♢ BlockTol=n: Specifies the maximum ratio allowed between the final number of selected modes and the
initial set: if more than n × #modes chosen by the user are selected, Gaussian stops the calculations. The
default is 1.6.

Freq=ReadFCHT Additional Input Ordering

The potential input sections for the various Freq=ReadFCHT additional input items should follow the key-
word list section in the following order. Blank lines separate input sections, but each section and its terminating
blank line should be included only when the corresponding item is specified.

Freq=ReadFCHT input keywords

blank line
filename for the Chk or LogFile parameters to Input=Source
filename for the Chk or LogFile params. to Final=Source (OPA, OPE, ECD, CPL) or Intermediate=Source (RR)
blank line
initial state frequency list: Initial=Freq=Input and/or Final=Freq=Scale
blank line
final/intermediate state frequency list: the Freq=Input option to Final (OPA, OPE, ECD, CPL) or Intermediate (RR)
and/or Initial=Freq=Scale
blank line
transition dipole moment data for TransProp=DipA or TransProp=EDip
blank line
transition dipole moment data for TransProp=DipB or TransProp=MDip
blank line
list of modes for RedDim=Block
blank line
incident energies for ResonanceRaman=OmegaList
5.32 Freq 151

blank line

Examples
The following input file illustrates the use of additional input for FC analyses.
Example 1. The following calculation performs a Franck-Condon frequency analysis for phenoxyl:

%Chk=phenoxyls0.chk
# Freq=(FC,ReadFC,ReadFCHT) Geom=Check · · ·

Phenoxyl Frank-Condon analysis

0 2

Final=Source=Chk ReadFCHT input: specify source for final state.

Print=(Spectra=All,Matrix=JK) Output all spectra, the Duschinsky matrix and the shift vector.

phenoxyls1.chk Checkpoint file for the final state.

terminal blank line

Example 2. The following job predicts the ECD spectrum (selected by the item in the additional input section).
Note that the second checkpoint file for the final section is specified in the subsequent input section. It is read
even though there is no explicit item in the additional input section since Final=Source=Chk is the default for
emission spectra.

%Chk=initial
# Freq=(FCHT,ReadFC,ReadFCHT) Geom=AllCheck · · ·

Transition=Absorption ReadFCHT input.

Spectroscopy=CD Select spectrum to predict: ECD.

final.chk Checkpoint file for the final state.

terminal blank line

Example 3. The following job performs the analysis at 500 K, using the time-dependent framework.

%Chk=temp500init
# Freq=(FC,ReadFC,ReadFCHT,SaveNM) Geom=AllCheck · · ·

Temperature=Value=500.0

temp500final.chk
terminal blank line

Example 4. The following job computes the resonance Raman spectrum:

%Chk=S0_freq
# Freq=(FC,ReadFC,ReadFCHT) Geom=Check · · ·

RR spectrum
152 Chapter 5. List of Gaussian Keywords

0 1

Spectroscopy=RR ReadFCHT input: select spectrum to predict.

TransProp=EDip=Input
RR=OmegaList
TD=(2NSTEP=12,2NSTEPWIN=12,Time=1.0d-12,GauHWHM=100)
Print=(Tensors,Matrix=JK)

S2_freq.chk Checkpoint file for final state.

1.000D0 1.000D0 0.00D0 Transition dipole for TransProp=EDip.

55000 55500 57000 List of incident energies for RR=OmegaList.

terminal blank line

Example 5. The final job step below computes the vibrational envelope of a photoionization spectrum:

%chk=neutral Calculation on the neutral form (initial state).

# B3LYP/6-31+G(d,p) Freq=SaveNM

neutral form

0 1
molecule specification

--Link1--
%chk=cation Calculation on the cation (final state).
# B3LYP/6-31+G(d,p) Freq=SaveNM

cation

1 2
molecule specification

--Link1--
%oldchk=neutral Data for the neutral form.
%chk=fc
# B3LYP/6-31+G(d,p) Freq=(FC,ReadFCHT) Geom=Check

photoionization

0,1

Initial=Source=Calc Final=Source=Chk Retrieve final state from a checkpoint file.

Spectrum=(Lower=-500.,Upper=+5000.,Grain=1.,HWHM=50.) Parameters for computed spectrum.
Prescreening=(MaxC1=30.,MaxC2=20.) Parameters to select transitions.
Print=Matrix=JK Output Duschinsky matrix and shift vector.
 5.33 G09Defaults 153

cation.chk Checkpoint filename for final state.

terminal blank line

5.33 G09Defaults
This keyword restore the calculation defaults from Gaussian 09. It is equivalent to:
Integral=(FineGrid,Acc2E=10) Constants=2006 SCRF=G09Defaults

5.33.1 Related Keywords

Integral, Constants, SCRF

5.34 Gen and GenECP

A set of standard basis sets is stored internally in Gaussian (see the Basis Sets page); these basis sets
may be specified by including the appropriate keyword within the route section for the calculation. The Gen
keyword allows a user-specified basis set to be used in a Gaussian calculation. It is used in the place of a basis
set keyword or a density fitting basis set keyword. In this case, the basis set description must be provided as
input (in a separate basis set input section).
Gen may be used in a completely analogous way to specify an alternate density fitting basis set (see the
examples).
The GenECP variation may be used to read in both basis functions and ECPs; it is equivalent to Gen
Pseudo=Read. It is designed for use in ONIOM calculations in which you want to use a general basis set with
ECPs within one ONIOM layer.

Option
NZCore=N
Specifies that the basis set is N-zeta in the core. The default is 1 (minimal) except for internally stored
multiple-zeta core basis sets.
The GFPrint keyword may be used to include the gaussian function table within the output file. The
GFInput keyword may be used to have the table printed in a form that is suitable for input to Gen. The
ExtraBasis keyword may be used to make additions to standard basis sets. Similarly, the ExtraDensityBasis
keyword may be used to make additions to standard density fitting basis sets.
A brief general overview of basis functions is provided as the final subsection of this discussion.

5.34.1 Input
External basis sets are read into Gaussian by specifying Gen (for general basis) in the route section. The
keywords 5D, 6D, 7F, and 10F are used to specify use of Cartesian or pure d and f (and higher) functions; the
defaults are 5D and 7F. All d-shells in a calculation must have the same number of functions. Similarly, f- and
higher shells must either be all Cartesian or all pure.
Defining a shell. External basis input is handled by the routine GenBas in Link 301. The basic unit of
information that it reads from the basis set input section is the shell definition block. A shell definition block,
together with the global specification of pure vs. Cartesian functions, contains all necessary information to
define a shell of functions. It consists of a shell descriptor line, and one or more primitive gaussian lines:
154 Chapter 5. List of Gaussian Keywords

IType NGauss Sc Shell descriptor line: shell type, # primitive gaussians, and scale factor.
α1 d1 µ Primitive gaussian specification: exponent and contraction coefficient.
α2 d2 µ
···
αN dN µ There are a total of NGauss primitive gaussian lines.

IType defines the shell type and shell constraint and may be S, P, D, SP, F, G, · · · , for an s-shell, p-shell, d-
shell, sp-shell, f-shell, g-shell, and so on. NGauss specifies the number of primitive gaussian shells (the degree
of contraction) for the shell being defined. The shell scale factor is given by Sc (i.e., all primitive exponents are
scaled by Sc2 ).
The subsequent NGauss primitive gaussian lines define the exponents αk and contraction coefficients, dk µ .
Each line provides the exponent for one primitive, followed by its contraction coefficient (or s and p coefficients
for an sp-shell).
A second format also exists to specify a shell as a least-squares gaussian expansion of a Slater orbital. This
is requested by a shell descriptor line of the form STO, IOrb, NGauss, Sc. IOrb is one of 1S, 2S, 2P, 2SP, 3S,
3P, 3SP, 3D, 4SP, and specifies which expansion is requested. Note that 2SP requests the best least-squares
fit simultaneously to S and P slater orbitals and is not equivalent to separately specifying the best S and the
best P expansions. NGauss is the same as above. Gaussian expansions of Slater functions having from 1 to 6
primitives are available. Sc is the scale factor and hence the exponent of the slater function being expanded. No
primitive gaussian lines are required after a shell descriptor line requesting an STO expansion.

Defining the basis for an atom or atom type. One customarily places at least one, and often several,
shells on any given nuclear center (“atom”), via a center definition block. A center definition block consists
of a center identifier line and one shell definition block for each shell desired on the center(s) specified. It is
terminated by a line with either asterisks or plus signs in columns 1 through 4:

c1 c2 · · · 0 Center identifier line: specifies applicability for these shells.

IType NGauss Sc First shell definition block.
α2 d2 µ
···
αN dN µ
··· Additional shell definition blocks.
IType NGauss Sc Final shell definition block.
α2 d2 µ
···
αN dN µ
**** Separator: terminates the center definition block.

The center identifier line specifies a list of centers on which to place the basis functions in the center
definition block, terminated by a 0. It can contain one or more integers, which are used to indicate the corre-
sponding atom(s) in the molecule specification; more commonly, it contains a list of atomic symbols to refer
to all atoms of a specific type. Center numbers and atomic symbols may be freely intermixed within a single
 5.34 Gen and GenECP 155

center identifier line.

To help detect input mistakes, if a center definition block specifies an atom that is not present in the
molecule, the run is aborted. If the center is preceded by a minus sign (e.g. -H), the basis set information is
simply skipped if no atom of that type is present in the molecule specification (the terminal zero may also be
omitted in this case). The latter syntax is intended for creating basis set include files that specify a standard
basis set for many atoms; once built, it can be included in its entirety in the input stream when the basis set is
desired, via the include () function (as described earlier in this chapter).
A center or atom type may be specified in more than one center definition block. For example, in the
Gaussian 09 basis set directory – $g09root/g09/basis on UNIX systems – there is one file which specifies 6-
31G as a general basis set (631.gbs) and another file containing d exponents which would be included as well
to specify 6-31G* (631s.gbs). Every atom from H through Cl is specified in both files, and in practice both
of them would be included (most often along with additional basis set specifications for those atoms in the
molecule for which the 6-31G basis set is not available).

Basis set transformation option to the Integral keyword. Several options to the Integral keyword
control whether/how generalized contraction basis sets are transformed to reduce the number of primitives.
Int=BasisTransform=N says to transform generalized contraction basis sets to reduce the number of primitives,
neglecting primitives with coefficients of 10−N or less. This is the default, with N=4. Int=ExactBasisTransform
says to transform generalized contraction basis sets to reduce the number of primitives, but using only trans-
formations which are exact (do not change the computed energy). Finally, Int=NoBasisTransform says not to
transform generalized contraction basis sets to reduce the number of primitives.

Drawing on Pre-Defined Basis Sets in Gen Input. Gaussian adds flexibility to general basis set input
by allowing them to include pre-defined basis sets within them. Within a center definition block for an atom
type (or types), an entire shell definition block may be replaced by a line containing the standard keyword for
a pre-defined basis set. In this case, all of the functions within the specified basis set corresponding to the
specified atom type(s) will be used for all such atoms within the molecule.
The SDD, SHF, SDF, MHF, MDF, MWB forms may be used to specify Stuttgart/Dresden basis sets/po-
tentials within general basis set input. Note that the number of core electrons must be specified. The ECP
potential name def2 or the synonym QZV can be used in GenECP input to request the potentials which are used
with both the def2 and QZV basis sets.

5.34.2 Examples
Here is a portion of the Gen input corresponding to the 6-31+G(d) basis set:

H 0 Applies to all hydrogen atoms.

S 3 1.00
0.1873113696D+02 0.3349460434D-01
0.2825394365D+01 0.2347269535D+00
0.6401216923D+00 0.8137573262D+00
S 1 1.00
0.1612777588D+00 0.1000000000D+01
****
156 Chapter 5. List of Gaussian Keywords

C 0 Applies to all carbons.

S 6 1.00 6-31G functions.
0.3047524880D+04 0.1834737130D-02
0.4573695180D+03 0.1403732280D-01
0.1039486850D+03 0.6884262220D-01
0.2921015530D+02 0.2321844430D+00
0.9286662960D+01 0.4679413480D+00
0.3163926960D+01 0.3623119850D+00
SP 3 1.00
0.7868272350D+01 -0.1193324200D+00 0.6899906660D-01
0.1881288540D+01 -0.1608541520D+00 0.3164239610D+00
0.5442492580D+00 0.1143456440D+01 0.7443082910D+00
SP 1 1.00
0.1687144782D+00 0.1000000000D+01 0.1000000000D+01
D 1 1.00 Polarization function.
0.8000000000D+00 0.1000000000D+01
****
C 0 Applies to all carbons.
SP 1 1.00 Diffuse function.
0.4380000000D-01 0.1000000000D+01 0.1000000000D+01
****

The following Gen input uses the 6-31G(d,p) basis set for the carbon and hydrogen atoms and the 6-31G‡
basis set for the fluorine atoms in the molecule and places an extra function only on center number 1 (which
happens to be the first carbon atom in the molecule specification for 1,1-difluoroethylene):

C H 0
6-31G(d,p)
****
F 0
6-31G(d’,p’)
****
1 0 Place a diffuse function on just one carbon atom.
SP 1 1.00
0.4380000000D-01 0.1000000000D+01 0.1000000000D+01
****

The following job uses the Gaussian include file mechanism to specify the basis functions for chromium:

# Becke3LYP/Gen Opt Test

HF/6-31G(*) Opt of Cr(CO)6

molecule specification
5.34 Gen and GenECP 157

C O 0
6-31G(d)
****
@/home/gwtrucks/basis/chrome.gbs/N

Note that .gbs is the conventional extension for basis set files (for gaussian basis set).
The following example uses general basis set input to specify both the basis set and the density fitting
basis set.

# RBLYP/GEN/GEN 6D

HCl: reading in 6-31g* AO basis and DGA1 fitting set.

6D is specified because the default for general basis
input is 5D but the 6-31g* basis is defined to use 6D

0,1
cl
h,1,1.29

! here are the 6-31g* basis sets for Cl and H

cl 0
S 6 1.00
0.2518010000D+05 0.1832959848D-02
0.3780350000D+04 0.1403419883D-01
0.8604740000D+03 0.6909739426D-01
0.2421450000D+03 0.2374519803D+00
0.7733490000D+02 0.4830339599D+00
0.2624700000D+02 0.3398559718D+00
SP 6 1.00
0.4917650000D+03 -0.2297391417D-02 0.3989400879D-02
0.1169840000D+03 -0.3071371894D-01 0.3031770668D-01
0.3741530000D+02 -0.1125280694D+00 0.1298800286D+00
0.1378340000D+02 0.4501632776D-01 0.3279510723D+00
0.5452150000D+01 0.5893533634D+00 0.4535271000D+00
0.2225880000D+01 0.4652062868D+00 0.2521540556D+00
SP 3 1.00
0.3186490000D+01 -0.2518280280D+00 -0.1429931472D-01
0.1144270000D+01 0.6158925141D-01 0.3235723331D+00
0.4203770000D+00 0.1060184328D+01 0.7435077653D+00
SP 1 1.00
0.1426570000D+00 0.1000000000D+01 0.1000000000D+01
D 1 1.00
0.7500000000D+00 0.1000000000D+01
****
h 0
S 3 1.00
 158 Chapter 5. List of Gaussian Keywords

0.1873113696D+02 0.3349460434D-01
0.2825394365D+01 0.2347269535D+00
0.6401216923D+00 0.8137573261D+00
S 1 1.00
0.1612777588D+00 0.1000000000D+01
****

! here are the DGA1 fitting sets for Cl and H

cl 0
S 1 1.00
0.2048000000D+05 0.1000000000D+01
S 1 1.00
0.4096000000D+04 0.1000000000D+01
S 1 1.00
0.1024000000D+04 0.1000000000D+01
S 1 1.00
0.2560000000D+03 0.1000000000D+01
S 1 1.00
0.6400000000D+02 0.1000000000D+01
SPD 1 1.00
0.2000000000D+02 0.1000000000D+01 0.1000000000D+01 0.1000000000D+01
SPD 1 1.00
0.4000000000D+01 0.1000000000D+01 0.1000000000D+01 0.1000000000D+01
SPD 1 1.00
0.1000000000D+01 0.1000000000D+01 0.1000000000D+01 0.1000000000D+01
SPD 1 1.00
0.25000D+00 0.10000D+01 0.10000D+01 0.10000D+01 0.0D+01 0.10000D+01
****
h 0
S 1 1.00
0.4500000000D+02 0.1000000000D+01
S 1 1.00
0.7500000000D+01 0.1000000000D+01
S 1 1.00
0.1500000000D+01 0.1000000000D+01
S 1 1.00
0.3000000000D+00 0.1000000000D+01
****

If you wanted to specify the density fitting basis set with general basis set input, then you would use a
route section like this one (substituting the appropriate basis set for your problem):
# RBLYP/6-31G(d,p)/Gen 6D

5.34.3 Related Keywords

ExtraBasis, ExtraDensityBasis, GFInput, GFPrint, Integral, Pseudo

 5.35 GenChk 159

5.34.4 Basis Function Overview

A single basis function is composed of one or more primitive gaussian functions. For example, an s-type
basis function φµ (r) is:
N
φµ (r) = ∑ diµ e−αiµ f µ r
2 2

i=1

S-Type Basis Function

N is the number of primitive functions composing the basis function, and it is called the degree-of-
contraction of the basis function. The coefficients diµ are called contraction coefficients. The quantities αiµ are
the exponents, and f is the scale factor for the basis function. The maximum degree-of-contraction permitted
in Gaussian is 100.
A shell is a set of basis functions φµ with shared exponents. Gaussian supports shells of arbitrary angular
momentum: s, p, d, f, g, h, and so on. An s-shell contains a single s-type basis function. A p-shell contains
the three basis functions pX , pY , and pZ . An sp-shell contains four basis functions with common gaussian
exponents: one s-type function and the three p-functions pX , pY , and pZ .
A d-shell may be defined to contain either the six second-order functions:
(dX 2 , dY 2 , dZ 2 , dXY , dXZ , dY Z )
or the five so-called “pure d” basis functions:
(dz2 −r2 , dx2 −r2 , dxy , dxz , dyz )
Likewise, an f-shell may contain either the 10 third-order gaussians or the 7 “pure f” functions. Higher-
order shells function similarly. Note that the contraction coefficients in a shell must be the same for all functions
of a given angular momentum, but that s and p contraction coefficients can be different in an sp-shell. A scale
factor is also defined for each shell. It is used to scale all the exponents of primitives in the shell. The program
has the ability to convert between the two types of functions [114].
Consider the series of basis sets STO-3G, 6-31G, and 6-311G(d) for the carbon atom. With the STO-3G
basis, there are two shells on a carbon atom. One is an s-shell composed of 3 primitive gaussian functions
(which are least-squares fit to a Slater 1s orbital). The other sp-shell is a least-squares fit of 3 gaussians to
Slater 2s and 2p orbitals with the constraint that the s and p functions have equal exponents. These expansions
are the same for all atoms. Only the scale factors for each shell differ from atom to atom. For carbon atoms,
the 1s- and 2sp-shells have scale factors of 5.67 and 1.72, respectively. The 6-31G basis on a first row atom
has three shells. One shell is a contraction of six primitive s-type gaussians. The second shell is a combination
of three primitive sp-shells. The third shell consists of a single sp-function. These functions were optimized
for the atom. Scale factors of 1.00, 1.00, and 1.04, respectively, for each shell for carbon were then determined
by molecular calculations. As its name implies, the 6-311G(d) basis has 5 shells: an s-shell with 6 primitives,
3 sp-shells with 3, 1, and 1 primitives, and an uncontracted d-shell. All shells are unscaled (have unit scale
factor).

5.35 GenChk
This keyword is found in the second and later automatically generated job steps for compound calculation
like Opt Freq. It serves to ensure that all basis set, ECP, and fitting set information (as applicable) is read
from the checkpoint file while retaining the keywords for internally stored components (regardless of whether
 160 Chapter 5. List of Gaussian Keywords

they were modified in the route) so that they can be reported in the output and archive entries for these later
calculations. This keyword serves no purpose within route sections created by users.

5.35.1 Example
The following output from the second job step of an Opt Freq calculation illustrates the GenChk keyword:

Link1: Proceeding to internal job step number 2.

-------------------------------------------------------------
#N Geom=AllCheck Guess=Read SCRF=Check GenChk RHF/STO-3G Freq
-------------------------------------------------------------

5.36 Geom
The Geom keyword specifies the source of the molecule specification input, options related to coordinate
definitions, and geometry-related output. By default, it is read from the input stream, as described previously.
Geom may be used to specify an alternate input source. It also controls what geometry-related information is
printed and use of internal consistency checks on the Z-matrix. The Geom keyword is not meaningful without
at least one item selection option.
Gaussian 16 supports generalized internal coordinates (GIC), a facility which allows arbitrary redundant
internal coordinates to be defined and used for optimization constraints and other purposes [460]. There are sev-
eral GIC-related options to Geom, and the GIC Info subsection describes using GICs as well as their limitations
in the present implementation.

5.36.1 Options
Geometry Retrieval Options
Checkpoint
Take the molecule specification (including variables) from the checkpoint file. Only the charge and
multiplicity are read from the input stream. For example, Geom=Checkpoint may be used by a later job
step to retrieve the geometry optimized during an earlier job step from the checkpoint file. Checkpoint
may be combined with the ModRedundant option or with the AddGIC option if you want to retrieve
and alter the molecule specification in a checkpoint file using internal coordinate-style modifications.
Note that Geom=(Checkpoint,ModRedundant,GIC) is equivalent to Geom=(Checkpoint,AddGIC). The
Geom=(Checkpoint,GIC) option (i.e., without ModRedundant) will not use the GICs from the checkpoint
file, but instead, it will build a new set of GICs automatically based on the current molecular specification
(e.g., Cartesian coordinates) from the checkpoint file. The Geom=(Checkpoint,ReadAllGIC) option will
not use the GICs from the checkpoint file, but instead, it will read a new set of GICs from the input file
and calculate their values based on the current molecular specification (e.g., Cartesian coordinates) from
the checkpoint file. Note that Geom=(Checkpoint,GIC) is equivalent to Geom=Checkpoint Opt=GIC,
and Geom=(Checkpoint,ReadAllGIC) is equivalent to Geom=Checkpoint Opt=ReadAllGIC.
AllCheck
Take the molecule specification (including variables), the charge and multiplicity, and the title section
from the checkpoint file. Thus, only the route section and any input required by keywords within it need
5.36 Geom 161

be specified when using this option. This option is not valid with Modify but may be combined with
ModRedundant, GIC, or AddGIC in the same way as the Checkpoint option.
Step=N
This option retrieves the structure produced by the N th step of a failed or partial geometry optimization
(it is not valid for a successful optimization). Step=Original recovers the initial starting geometry. This
option is used for restarting geometry optimization from intermediate points. It must be combined with
one of Checkpoint, AllCheck, or Modify. Note that not all steps are always present in the checkpoint file;
a Hessian updated message in the log file means that the corresponding step is available in the checkpoint
file. NGeom=N retrieves the N th geometry from an optimization checkpoint file using the same record
of points used for display in GaussView, where N=1 corresponds to the input molecule specification.
Geom=Step=M is automatically converted to Geom=NGeom=M+1 if the previous optimization used
redundant internal coordinates.
Modify
Note that this option refers to modification specifications for geometry optimizations using Z-matrix
coordinates only. In general, it is deprecated in favor of ModRedundant. It should not be used with
GICs. Use Geom=(Checkpoint,AddGIC) instead of Geom=Modify if you want to modify the generalized
internal coordinates.
This option specifies that the geometry is to be taken from the checkpoint file and that modifications will
be made to it. A total of two input sections will be read: the first contains the charge and multiplicity,
and the second contains alterations to the retrieved geometry.
Modification specifications for geometry optimizations using Z-matrix coordinates have the following
form:
variable [new-value] [A|F|D]
where variable is the name of a variable in the molecule specification, new-value is an optional new value
to be assigned to it, and the final item is a one-letter code indicating whether the variable is to be active
(i.e., optimized) or frozen; the code letter D requests numerical differentiation be performed with respect
to that variable and activates the variable automatically. If the code letter is omitted, then the variable’s
status remains the same as it was in the original molecule specification.

Geometry Specification & Modification Options

ModRedundant
Except for any case when it is combined with the GIC option (see below), the ModRedundant option
will add, delete, or modify redundant internal coordinate definitions (including scan and constraint infor-
mation) before performing the calculation. This option requires a separate input section following the
geometry specification. AddRedundant is synonymous with ModRedundant.
This option may be used for job types other than optimizations. It may also be combined with NGeom,
Check or AllCheck to retrieve and modify an internal coordinate definition from a checkpoint file.
When used with Check, or NGeom, two input sections will be read: the first contains the charge and multi-
plicity, and the second contains alterations to the retrieved internal coordinate definition. When combined
with the AllCheck option, only the internal coordinate definition modifications input is needed.
Lines in a ModRedundant input section use the following syntax:
[Type] N1 [N2 [N3 [N4]]] [A | F]
162 Chapter 5. List of Gaussian Keywords

[Type] N1 [N2 [N3 [N4]]] B

[Type] N1 [N2 [N3 [N4]]] K | R
[Type] N1 [N2 [N3 [N4]]] D
[Type] N1 [N2 [N3 [N4]]] H diag-elem
[Type] N1 [N2 [N3 [N4]]] S nsteps stepsize
N1, N2, N3, and N4 are atom numbers or wildcards (discussed below). Atom numbering begins at 1, and
any dummy atoms are not counted.
The atom numbers are followed by a one-character code letter indicating the coordinate modification
to be performed; the action code is sometimes followed by additional required parameters as indicated
above. If no action code is included, the default action is to add the specified coordinate. These are the
available action codes:

A Activate the coordinate for optimization if it has been frozen.

F Freeze the coordinate in the optimization.
B Add the coordinate and build all related coordinates.
K Remove the coordinate and kill all related coordinates containing this coordinate.
R Remove the coordinate from the definition list (but not the related coordinates).
D Calculate numerical second derivatives for the row and column of the initial Hessian for
this coordinate.
H Change the diagonal element for this coordinate in the initial Hessian to diag-elem.
S Perform a relaxed potential energy surface scan. Increment the coordinate by stepsize a
total of nsteps times, performing an optimization from each resulting starting geometry.

An asterisk (*) in the place of an atom number indicates a wildcard. Here are some examples of wildcard
use:

* All atoms specified by Cartesian coordinates.

** All defined bonds.
3* All defined bonds with atom 3.
*** All defined valence angles.
*4* All defined valence angles around atom 4.
**** All defined dihedral angles.
*34* All defined dihedral angles around the bond connecting atoms 3 and 4.

By default, the coordinate type is determined from the number of atoms specified: Cartesian coordi-
nates for 1 atom, bond stretch for 2 atoms, valence angle for 3 atoms, and dihedral angle for 4 atoms.
Optionally, type can be used to designate these and additional coordinate types:

X Cartesian coordinates.
B Bond length.
A Valence angle.
D Dihedral angle.
5.36 Geom 163

L Linear bend specified by three atoms (if N4 is -1) or by four atoms, where the fourth
atom is used to determine the 2 orthogonal directions of the linear bend.

See the examples under the Opt keyword for illustrations of the use of ModRedundant.
NewDefinition
Generate a new set of redundant internal coordinates, replacing any that were in the checkpoint file. This
option should not be used with GICs; use Geom=(Checkpoint,GIC) instead.
SkipAll
Do not generate any internal coordinates automatically. In the case of redundant internal coordinates
based on the old algorithm available in Gaussian 09, all of the required coordinates must be explicitly
specified in the ModRedundant input section. In the case of GIC-type internal coordinates based on the
new GIC algorithm, you should use Geom=ReadAllGIC instead of this option.
SkipAng
Generates bonds but omits angles and dihedrals.
SkipDihedral
Suppresses the generation of dihedrals.
SkipHBond
Skips generation of hydrogen-bond coordinates.
KeepConstants
KeepConstants retains and NoKeepConstants discards information about frozen variables. The default
is to retain them in symbolic form for the Berny algorithm and to discard them for older optimization
algorithms (which don’t understand them anyway).
NewRedundant
Rebuilds the redundant internal coordinates from the current Cartesian coordinates. If used with Geom=Modify,
the new modifications are appended to any earlier Opt=ModRedundant input before the coordinate sys-
tem is updated. This option should not be used with GICs; use GIC or AddGIC instead (as appropriate).
Redundant
Build an automatic set of redundant internal coordinates such as bonds, angles, and dihedrals from the
current Cartesian coordinates or Z-Matrix values, using the old algorithm available in Gaussian 09.

Specifying Connectivity
Connectivity
Specify explicit atom bonding data via an additional input section (blank line-terminated) following the
geometry specification and any modification to it. This option requires one line of input per atom, ordered
the same as in the molecule specification, using the following syntax:
N1 Order1 [N2 Order2 · · · ]
where the ’N’s are atoms to which the current atom is bonded, and the ’Order’s are the bond order of the
corresponding bond. For example, this input specifies that the current atom is bonded to atoms 4 and 5,
with bond orders of 1.0 and 2.0 respectively:
8 4 1.0 5 2.0
A bond order of 0.1 indicates a bond which should be used in generating internal coordinates but which
should not affect atom types or connectivity for molecular mechanics.
164 Chapter 5. List of Gaussian Keywords

This input section is terminated by a blank line.

ModConnectivity
Modify the connectivity of the atoms in the molecule specification (or retrieved from the checkpoint
file). This option requires an additional input section (blank line-terminated) following the geometry
specification and any modification to it. Connectivity modifications use the following syntax:
M N1 Order1 [N2 Order2 · · · ]
where M is the atom number, the ’N’s are atoms to which that atom is bonded, and the ’Order’s are
the bond order of the corresponding bond. A bond order of -1.0 removes a bond. For example, this
input specifies that atom 8 is bonded to atoms 4 and 5, with bond orders of 1.0 and 2.0 respectively, and
removes any bond to atom 9:
8 4 1.0 5 2.0 9 -1
This input section is terminated by a blank line.
ZMConnectivity
Read connectivity using the atom numbering specified in the Z-matrix (including dummy atoms). Bond
orders involving dummy atoms are discarded.
IHarmonic=n
Add harmonic constraints to the initial structure with force constant n/1000000 Hartree/Bohr2 . Initial-
Harmonic is a synonym for this option.
ChkHarmonic=n
Add harmonic constraints to the initial structure saved on the checkpoint file with force constant n/1000000
Hartree/Bohr2 . CHarmonic is a synonym for this option.
ReadHarmonic=n
Add harmonic constraints to an additional structure read in the input stream (in the input orientation),
with force constant n/1000000 Hartree/Bohr2 . RHarmonic is a synonym for this option.
ReadOptimize
Read an input section modifying which atoms are to be optimized. The atom list is specified in a separate
input section (terminated by a blank line). By default, the atom list contains all atoms in the molecule,
unless any atoms are designated as frozen within the molecule specification, in which case the initial
atom list excludes them. If the structure is being read in from the checkpoint file, then the list of atoms
to be optimized matches that in the checkpoint file. ReadOpt and RdOpt are synonyms for this option.
ReadFreeze and RdFreeze are deprecated synonyms.
The input section uses the following format:
atoms=list [notatoms=list]
where each list is a comma- or space-separated list of atom numbers, atom number ranges, and/or atom
types. Keywords are applied in succession. Here are some examples:

atoms=3-6,17 notatoms=5 Adds atoms 3,4,6,17 to atom list. Removes 5 if present.

atoms=3 C 18-30 notatoms=H Adds all C & non-H among atoms 3, 18-30.
atoms=C N notatoms=5 Adds all C and N atoms except atom 5.
atoms=1-5 notatoms=H atoms=8-10 Adds atoms 8-10 and non-hydrogens among atoms 1-5,

Bare integers without a keyword are interpreted as atom numbers:

5.36 Geom 165

1,3,5 7 Adds atoms 1, 3, 5 and 7.

For ONIOM optimizations only, block and notblock can be similarly used to include/not include rigid
blocks defined in ONIOM molecule specifications. If there are contradictions between atoms specified as
atoms and within blocks – e.g., an atom is included within a block but excluded by atom type – Gaussian
09 generates an error.
You can start from an empty atom list by placing noatoms as the first item in the input section. For
example, the following input optimizes all non-hydrogen atoms within atoms 1-100 and freezes all other
atoms in the molecule:
noatoms atoms=1-100 notatoms=H
Atoms can also be specified by ONIOM layer via the [not]layer keywords, which accept these values:
real for the real system, model for the model system in a 2-layer ONIOM, middle for the middle layer in
a 3-layer ONIOM, and small for the model layer of a 3-layer ONIOM. Atoms may be similarly includ-
ed/excluded by residue with residue and notresidue, which accept lists of residue names. Both keyword
pairs function as shorthand forms for atom lists.
Micro
Set up redundant internal coordinates for ONIOM(MO:MM) microiterations, even if this is not an opti-
mization.

Output-Related Options

Distance
This option requests printing of the atomic distance matrix (which is the default for molecules with fewer
than 50 atoms). NoDistance suppresses this output.
CAngle
This option requests printing of interatomic angles using distance cutoffs to determine “bonded atoms”.
The default is not to print (NoAngle). Angle requests printing of the interatomic angles for Opt=Z-matrix
(using the Z-matrix to determine which atoms are bonded). Only one of CAngle, Angle, and NoAngle
may be specified.
CDihedral
This option requests printing of dihedral angles using distance cutoffs to determine “connectivity”. The
default is not to print (NoDihedral). Dihedral specifies printing of dihedral angles for Opt=Z-matrix
(using connectivity information from the Z-matrix to decide which atoms are bonded). Only one of
CDihedral, Dihedral, and NoDihedral may be specified.
PrintInputOrient
This option includes the table giving the Cartesian coordinates in the input orientation within the output
file.
Print
This option turns on additional printing by the model builder facility.

Generalized Internal Coordinate (GIC)-Related Options

GIC
This option builds an automatic set of GIC-type internal coordinates instead of the default. The option
NoGIC builds the internal coordinates of [461] as in Gaussian 09, and it is the default. The GIC-type
 166 Chapter 5. List of Gaussian Keywords

coordinates generated by the GIC option are essentially the same as those generated by default.
AddGIC
This option adds, deletes, or modifies the GIC-type internal coordinate definitions generated automati-
cally or retrieved from the checkpoint file. This option requires a separate GIC input section following
the geometry specification. The syntax of the GIC input section is described in GIC Info tab. Note that
Geom=(ModRedundant,GIC) is equivalent to Geom=AddGIC.
DefaultGIC
Make GICs the default (for use in a Default.Route file).
DefaultNoGIC
Make Peng internal coordinates the default (for use in a Default.Route, but this is the default anyway).
GICOld
Build the default set of redundant internal coordinates of [461] as in Gaussian 09, and then convert the
coordinates into GIC-type internal coordinate definitions.
ReadAllGIC
Do not build any redundant internal coordinates by default. Instead, read the input stream for user-
provided GIC definitions and create the coordinates. This option requires a separate GIC input section
following the geometry specification. The syntax of the GIC input section is described in GIC Info.

Geometry Checking Options

Crowd
Crowd activates and NoCrowd turns off a check that aborts the job if atoms are closer than 0.5 Å. By
default, the check is performed for every read-in geometry. It is not performed by default for later points
of geometry optimizations, numerical frequencies, etc., when the geometry has been generated during
the job. NoTest skips the test entirely.
Independent
Independent activates and NoIndependent turns off a check on the linear independence of the variables
specified in a Z-matrix. This is done by default only if a full optimization is requested using the Berny
algorithm (Opt=Z-matrix).

Other Options
Huge
Changes various defaults for huge (>20K atom) systems. Currently, this sets Geom=NoTest and Symm=None.

5.36.2 Related Keywords

Guess=Read, Opt=ModRedundant

5.36.3 GIC Info

The options that do not mention GIC and can be used with the Geom keyword should work as described –
except for NewDefinition and NewRedundant. The latter should not be combined with any GIC-related option.
In the case of GICs, you should use Geom=(Checkpoint,GIC) instead of Geom=NewDefinition, Geom=GIC in-
stead of Geom=NewRedundant, and Geom=(Checkpoint,addGIC) instead of Geom=(Modify,NewRedundant).
This section discusses specifying generalized internal coordinates (GICs) in Gaussian input files. GICs
have many potential uses: defining additional coordinates whose values are reported during geometry opti-
5.36 Geom 167

mizations, freezing various structural parameters during the optimization of a molecular system, specifying
parameters over which to perform a scan, defining constraints for geometry optimizations based on structural
parameters or complex relationships between them, requesting calculation of parts of the Hessian, and other
purposes.
The GIC input section is separated from the earlier input by a blank line. It has one or more lines con-
taining coordinate definitions, expressions or standalone options. Here is a simple GIC input section for water
illustrating some of the possible features:

R(1,2) Define a bond length coordinate for atoms 1 and 2

Bond2=R[1,3] Define another bond length coordinate named Bond2
HOH(freeze)=A(2,1,3) Define an optimization constraint: a bond angle coordinate named HOH
(∠2-1-3)

For an optimization, these coordinates will result in the bond angle remaining fixed at its initial value and
the two bond distances being optimized.
The basic form of a coordinate is the following:
label(options)=expression
All of the components are optional. In the preceding examples, all components were present only in the
third line. The first line contained only a coordinate expression, while the second line also contained a label
without options. Note that options may also be placed following the expression:
HOH=A(2,1,3) Freeze
Labels are user-assigned identifiers for the coordinate. They are not case sensitive. Labels many contain
letters and number, but must begin with a letter. If no label is specified, a generic one will be assigned by the
program (e.g., R1, R2, A1, etc.). A parenthesized, comma-separated list of options can be included following
the label if desired. Note that square brackets or braces may be substituted for parentheses anywhere in a
coordinate definition.

Structural Parameters
Coordinates are defined by expressions. The simplest expressions simply identify a specific structural
parameter within the molecule, using the following constructs. Note that an asterisk may be used as a wildcard
for any atom number (see the examples).
R(i,j)
Define a bond coordinate between atoms i and j. B, Bond and Stretch are synonyms for R.
A(i,j,k)
Define a non-linear angle coordinate involving atoms i, j and k where the angle vertex is at atom j. Angle
and Bend are synonyms for A.
D(i,j,k,l)
Define a dihedral angle between the plane containing atoms i, j and k and the plane containing atoms j, k
and l. Dihedral and Torsion are synonyms for D.
L(i,j,k,l,M)
Define the linear bend coordinate involving atoms i, j and k where the angle vertex is at atom j. Linear
and LinearBend are synonyms for L.
A linear bend definition has two components, indicated by M values of -1 and -2 for the first and second
168 Chapter 5. List of Gaussian Keywords

components, respectively (no other values are permitted). A linear bend is specified by defining its two
orthogonal directions. These can be indicated in two ways:
♢ For a nonlinear molecule with more than 3 atoms, a fourth atom which does not form a linear angle
with i, j and k in any combination can be used. In this case, l can be set to its atom number. For
example, the following may be used to specify a linear bend involving atoms 1, 2 and 3 using atom
6 to determine the two orthogonal directions:
L(1,2,3,6,-1)
L(1,2,3,6,-2)
If l is set to -4, then the fourth atom will be determined automatically based on the molecular
geometry.
♢ The other method is to project the linear bend onto one of the coordinate system’s axial planes: the
values of -1, -2 and -3 for l specify the YZ, XZ and XY planes (respectively). The value 0 may also
be used to request that the appropriate plane be determined automatically:
L(1,2,3,0,-1)
L(1,2,3,0,-2)
X(i)
Define the x Cartesian coordinate for atom i. Cartesian(i,-1) and Cartesian(i,X) are synonyms, and Carte-
sian may be abbreviated as Cart.
Y(i)
Define the y Cartesian coordinate for atom i. Cartesian(i,-2) and Cartesian(i,Y) are synonyms, and Carte-
sian may be abbreviated as Cart.
Z(i)
Define the z Cartesian coordinate for atom i. Cartesian(i,-3) and Cartesian(i,Z) are synonyms, and Carte-
sian may be abbreviated as Cart.
XCntr(atom-list)
YCntr(atom-list)
ZCntr(atom-list)
Define x, y or z Cartesian coordinate for the geometric center (centroid) of a molecular fragment that
contains specified atoms. The atom list is a comma-separated list of atom numbers and/or ranges. For
example, XCntr(1,12-15,27) defines the x coordinate of the fragment containing atoms 1, 12, 13, 14, 15
and 27. If the atom list is omitted, it defaults to the entire molecule.
DotDiff(i,j,k,l)
Define the dot product (a · b) of the two Cartesian coordinate difference vectors a and b for atoms i, j, k
and l determined as a = (Xi − X j , Yi −Y j , Zi − Z j ) and b = (Xk − Xl , Yk −Yl , Zk − Zl ).

Compound Expressions

Complex expressions may be constructed by combining multiple items using one or more mathematical
operations. The argument(s) A and B can be the labels of a previously defined coordinate, a valid GIC expres-
sion or even constants (integer or floating-point). The operation names are not case sensitive. The following
operations are available:
♢ Square root: SQRT(A).
♢ Power of e: EXP(A) for eA .
5.36 Geom 169

♢ Trigonometric functions: SIN(A), COS(A), TAN(A).

♢ Inverse cosine: ARCCOS(A).
♢ Addition: A+B
♢ Subtraction: A-B
♢ Multiplication: A*B
♢ Division: A/B
♢ Exponentiation: A**n for An (n is an integer). The form A^n is also accepted.
Here are some simple examples which define symmetrized OH bonds in water:

R12(inactive)=B(1,2)
R13(inactive)=B(1,3)
RSym = (R12 + R13)/SQRT(2)
RASym = [Bond(1,2) - Bond(1,3)]/SQRT(2)

The first two coordinates are set as inactive since they are intermediates not intended to be used in the
optimization. Line 3 illustrates an expression using previously defined labels, while line 4 shows the use of
literal expressions with operators. Note that the argument to the square root function is the constant 2.

Options

A comma separated list of options can follow the coordinate label, enclosed in parentheses. Alternatively,
options may follow the expression, separated from it and from one another by spaces. All options are case
insensitive.
For the purposes of geometry optimizations, a coordinate can be designated as:
♢ Active: The coordinate is part of the list of internal coordinates used in the geometry optimzation. In contrast,
Inactive coordinates are not included in the set used for the geometry optimization. By default, active
coordinates are unfrozen: allowed to change value (see the next bullet).
♢ Frozen: A coordinate whose value is held constant during the course of a geometry optimization. The values
of active, unfrozen coordinates change during a geometry optimization. The frozen or unfrozen status of
inactive coordinates is irrelevant during an optimization.
In the descriptions that follow, coordinates that “already exist” refers to previously-defined coordinates
with the same label or the same value expression. Such coordinates may have been defined earlier in the input
stream or retrieved from the checkpoint file from a previous job.
Active
If the specified coordinate does not already exist, build a new coordinate defined by the given expression,
and flag it as active and unfrozen. If the coordinate was previously defined, then flag it as active and
unfrozen (whatever its previous status). It is the default. Activate, Add and Build are synonyms for
Active. May be abbreviated to A when specified following the expression.
Frozen
Build a coordinate defined by the expression if it does not exist, and flag the coordinate as active for
geometry optimizations and freeze it at the current value.
Freeze is a synonym for Frozen. May be abbreviated to F when specified following the expression.
Inactive
If the coordiante does not already exist, build a new coordinate defined by the expression and flag it
170 Chapter 5. List of Gaussian Keywords

inactive. If the coordinate with the given label or for the given expression has been already built and
flagged as active (frozen or unfrozen), then remove it from the geometry optimization by flagging it as
inactive. Remove is a synonym for Inactive. May be abbreviated to R when specified following the
expression.
Kill
Remove the coordinate from the list of internal coordinates used in geometry optimization along with
any dependent coordinates by flagging all of them as inactive. The dependent coordinates include any
coordinate that depends on the same atoms as the given coordinate. For example, R(1,5) Kill will result
in removing the coordinate R(1,5) – the internuclear distance between atoms 1 and 5 – as well as the
valence angles, dihedral angles and any other coordinate that depends on the Cartesian coordinates of
atoms 1 and 5 in combination with other atoms in the molecule. RemoveAll is a synonym for Kill. May
be abbreviated to K when specified following the expression.
PrintOnly
Include the initial value of the coordinate in the starting geometry in the Gaussian output file, and then
flag it as inactive.
Modify
A label must be included in the coordinate specification for this option. It replaces the old coordinate
with the specified label with the new expression, and flags the newly modified coordinate as active and
unfrozen.
Diff
Calculate numerical second derivatives for the row and column of the initial Hessian corresponding to
this coordinate. May be abbreviated to D when specified following the expression.
FC=x
Change the diagonal element for the given coordinate in the initial Hessian to x, a floating-point number
in atomic units. ForceConstant is a synonym for FC.
Value=x
Set the initial value for the given internal coordinate to x, a floating point value. The units for the value
are those of the Gaussian program, as defined by the Units keyword (Angstroms or degrees by default).
The current Cartesian coordinates will be adjusted to match this value as closely as possible. This option
should be used cautiously and sparingly. It is far easier and more reliable to set the initial molecular
structure as desired in a graphical environment like GaussView.
StepSize=x,NSteps=n
These options are used to specify a relaxed potential energy surface scan in which the coordinate is
incremented by x a total of n times, and a constrained optimization is perfromed from each resulting
starting geometry. x should be a positive floating-point number in atomic units, n should be an integer
>1. When these options follow the expression, the comma separating them should be replaced by a space.
Min=min,Max=max
This option is used in combination with Active, Freeze or Inactive. It adds, freezes or makes inactive
the coordinate when its value satisfies the condition min ≤ value ≤ max. min and max are floating-point
numbers in the units defined by the Units (Angstroms or degrees by default). If Min or Max is omitted,
the condition becomes value ≤ max or min ≥ min respectively. When these options follow the expression,
5.36 Geom 171

the comma should be replaced by a space.

action OnlyIf condition
action IfNot condition
These options provide conditional coordinate operations. They can only be placed following the expres-
sion defining the current coordinate. Action is one of Active, Freeze or Inactive. The condition is a label
or expression for another coordinate. The specified action will be performed for the current coordinate if
the coordinate referred to in condition is active for OnlyIf or inactive for IfNot. Note that the conditional
test applies only to the action specified preceding the option and not to other options that may be present
in the coordinate specification.

Standalone Options
The following options are independent of coordinate definitions and apply globally. They should be spec-
ified alone on their input line.
FreezeAll
Freeze all internal coordinate previously added as active.
UnFreezeAll
Unfreeze all internal coordinates previously added as active frozen.
RemoveAll
Remove/inactivate all internal coordinate previously added as active (frozen or unfrozen).
Atom i action
Apply the specified action to the Cartesian coordinates of atom i. If i is an asterisk, then the action
applies to all atoms. Action is one of Active, Freeze, UnFreeze, Remove (make inactive), RemoveAll and
XYZOnly. These options are as defined above; XYZOnly says to remove any internal coordinates that
depend on atom i but to add/retain the coordinates of that atom. The default action is Active.

Examples
The following example manipulates some automatically-generated coordinates, defines some new ones,
and then uses wildcards to remove coordinates related to specific atoms:

R(5,9) freeze Freeze bond distance R(5,9).

R(8,9) Add a new active coordinate R(8,9) with a default label.
Ang189 = A(1,8,9) Add a new active coordinate A(1,8,9) labeled Ang189.
R10(remove) Remove a coordinate labeled R10.
Dih6123(remove) = D(6,1,2,3) If D(6,1,2,3) exists, then remove the coordinate.
Dis79(freeze) = R(7,9) Freeze the coordinate R(7,9): if it is new, then label it
Dis79; if it already exists, retain the old label.
G1 = (R16+R19)*0.529177 Add a new coordinate labeled G1.
Ang189a(modify)=cos(g2)*57.29577951Change the definition of coordinate Ang189a.
R(11,*) remove Remove distances between atom 11 and any other atom.
D(*,1,17,*) remove Remove any dihedral built around the 1-17 bond.

Note that if a specified coordinate already exists, then an entry adding it will result in an error (e.g., lines
1-3 above).
172 Chapter 5. List of Gaussian Keywords

The following example first defines the centroids of two fragments. Then, it defines the interfragment
distance as an optimization coordinate:

Define the center of Fragment 1, but don’t include it in the optimization.

XC1(Inactive)=XCntr(1-10)
YC1(Inactive)=YCntr(1-10)
ZC1(Inactive)=ZCntr(1-10)
Define the center of Fragment 2, but don’t include it in the optimization.
XC2(Inactive)=XCntr(11-21)
YC2(Inactive)=YCntr(11-21)
ZC2(Inactive)=ZCntr(11-21)
Define the distance F1-F2 and include it in the optimization. Its value will be reported in Å:
F1F2=sqrt[(XC1-XC2)^2+(YC1-YC2)^2+(ZC1-ZC2)^2]*0.529177

The following example requests a relaxed PES scan over the same coordinate:
F1F2(NSteps=10,StepSize=0.2)
The following example removes an angle coordinate generated by default if ≥179.9o , substituting a linear
bend:

A(1,2,3) Remove Min=179.9 Remove angle coordinate if too large.

L(1,2,3,0,-1) Add IfNot A(1,2,3) Add linear bend only if the angle coordinate not active.
L(1,2,3,0,-2) Add IfNot A(1,2,3)

The following example removes an angle coordinate if it is ≤ the specified value, setting the corresponding
force constant is set to 0.2 au. The latter applies whenever it is needed: as the initial force constant and the
force constant to use should be variable be reactivated. The second line specifies the force constant for a bond
coordinate:
A(1,2,3) Remove Min=3.139847 ForceConstant=0.2
R(1,2) FC=0.5
The following example sets the force constants for various coordinates. It also inactivates bond angle
coordinates ≥ 179.8o :

R(1,*) FC=0.8
D(*,4,5,*) FC=0.4
A(*,1,*) FC=0.5
A(*,*,*) R Min=179.8

Limitations of GICs in the Current Implementation

In the current implementation, GICs can be successfully used for many purposes including optimization
constraints and PES scans. However, there are potential problems with active composite coordinates including
multiple dihedral angles. In general, coordinates comprised of combinations of bond distances and bond angles
should behave well. Simple dihedral angles are also welll supported. Complex expressions involving multiple
dihedral angles are acceptable for frozen coordinates and for PES scans. However, they should be avoided as
active optimization coordinates.
 5.37 GFInput 173

In a non-GIC optimization, or one using GICs with only regular dihedrals, then the program is careful
about the periodicity of these coordinates. For example, in deciding whether a step in the geometry is too big
and needs to be scaled back, it recognizes that a change in value from 1 degree to 359 degrees is really a change
of -2 degrees rather than 358 degrees. Similarly, in numerically differentiating the forces in order to update the
Hessian, displacements between geometries in internal coordinates are needed, and the periodicity is accounted
for. A problem can arise when a GIC is a combination of parts for which such periodicity is important, typically,
combinations of multiple dihedral angles. For example, consider these GICs:

D1 = D(1,2,3,4)
D2 = D(5,6,7,8)
V1 = D1 + 2*D2

D1 and D2 are dihedral angles, but they are intermediates and are not used as variables in the optimization.
Their periodicity is not currently recognized in the composite coordinate V1. Suppose they have values of 1 and
2 degrees at one geometry and 1 and 359 degress at the next. The change in the optimization variable V1 should
be 0 + 2*(-3) = -6 degrees, but it is actually 0 + 2*(357) = 714 degrees, which looks like an enormous change.
This will result in the optimization algorithm performing very poorly. V1 isn’t a simple periodic function; it is
necessary to apply periodicity to its component parts as it is computed, which is not done in the current GIC
implementation.

GIC Units in Gaussian Output

The values of the GICs defined as pure distances and angles (including valence angles, linear bends and
dihedral angles/torsions) are computed from the Cartesian coordinates in atomic units (Bohrs) and stored in-
ternally in Bohrs and radians. However, for the user’s convenience, they are expressed as usual in Angstroms
and degrees in the Gaussian output. In the case of a generic GIC (i.e., when the GIC is not a pure Cartesian
coordinate, bond distance or angle), the GIC value is computed as a function of Cartesian coordinates and bond
distances in Bohrs and angles in radians, combined with optional constants in user-defined units. Such generic
GIC values (labeled as GIC) are computed, stored and output in these same units: i.e., if the GIC is a combi-
nation of bonds or a combination of valence angles, then the arbitrary units become Bohrs for the bonds and
radians for the angles.

Use of ModRedundant Format Input

Modifications to the GICs can be read in using the ModRedundant format from the current internal coordi-
nate algorithm. However, the old format is only available with the GICs that include only pure bond distances,
bond angles or torsion angles. In addition, the old format and the new GIC format described above cannot be
mixed together in the same input section.

5.37 GFInput

The GFInput (for Gaussian Function Input) output generation keyword causes the current basis set to be
printed in a form suitable for use as general basis set input and can thus be used in adding to or modifying
standard basis sets. By default, both the basis set and any fitting set are printed.
 174 Chapter 5. List of Gaussian Keywords

5.37.1 Options
JNormalization
Print the density basis using Coulomb normalization. This is the default for the fitting set.
AONormalization
Print the density fitting basis set using AO (atomic overlap) normalization. The basis set is always printed
using AO normalization.
RawNormalization
Print the density fitting set basis unnormalized.

5.37.2 Related Keywords

Gen, GFPrint

5.38 GFPrint
This output generation keyword prints the current basis set and density fitting basis set in tabular form.
The variant GFOldPrint keyword prints the basis set information in the Gaussian format.

5.38.1 Related Keywords

Gen, GFInput

5.39 Gn Methods
These method keywords request the following methods for computing very accurate energies:
♢ Gaussian-1 (G1) [462, 463]
♢ Gaussian-2 (G2) [464]
♢ Gaussian-3 (G3) [465]
♢ Gaussian-4 (G4) [466]
♢ G2MP2 requests the modified version of G2 known as G2(MP2), which uses MP2 instead of MP4 for the
basis set extension corrections [467] and is nearly as accurate as the full G2 method at substantially
reduced computational cost.
♢ G3MP2 requests the similarly modified G3(MP2) method [468].
♢ The G3 variants using B3LYP structures and frequencies [469] are requested with the G3B3 and G3MP2B3
keywords.
♢ G4 and G4MP2 request the fourth-generation methods [466, 470].
All of these methods are complex energy computations involving several pre-defined calculations on the
specified molecular system. All of the distinct steps are performed automatically when one of these keywords
is specified, and the final computed energy value is displayed in the output. No basis set keyword should be
specified with these keywords.
Users should generally consider other high accuracy methods before selecting one of these. CBS-QB3 is
equally accurate and significantly faster, while W1U is more accurate (but slower).
Either of the Opt=Maxcyc=n, QCISD=Maxcyc=n, or CCSD=Maxcyc=n keywords may be used in con-
junction with any of the these keywords to specify the maximum number of optimization, QCISD, or CCSD
cycles, respectively.
 5.39 Gn Methods 175

5.39.1 Options
SP
Do only a single-point energy evaluation using the specified compound model chemistry. No zero-point
or thermal energies are included.
NoOpt
Perform the frequencies and single-point energy calculation for the specified model chemistry at the input
geometry. Freq=TProjected is implied. This option is not meaningful or accepted for methods such as
G1, which use different geometries for the frequencies and the single-point steps. StartFreq is a synonym
for NoOpt.
ReadIsotopes
This option allows you to specify alternatives to the default temperature, pressure, frequency scale factor
and/or isotopes – 298.15 K, 1 atmosphere, no scaling, and the most abundant isotopes (respectively). It is
useful when you want to rerun an analysis using different parameters from the data in a checkpoint file.
Be aware, however, that all of these can be specified in the route section (Temperature, Pressure and Scale
keywords) and molecule specification (the Iso parameter), as in this example:

#T Method/6-31G(d) JobType Temperature=300.0 · · ·

···

0 1
C(Iso=13)
···

ReadIsotopes input has the following format:

temp pressure [scale] Values must be real numbers.

isotope mass for atom 1
isotope mass for atom 2
···
isotope mass for atom n

Where temp, pressure, and scale are the desired temperature, pressure, and an optional scale factor for
frequency data when used for thermochemical analysis (the default is unscaled). The remaining lines hold
the isotope masses for the various atoms in the molecule, arranged in the same order as they appeared
in the molecule specification section. If integers are used to specify the atomic masses, the program will
automatically use the corresponding actual exact isotopic mass (e.g., 18 specifies 18 O, and Gaussian uses
the value 17.99916).
Restart
Resume a partially-completed calculation from its checkpoint file. When used in combination with Read-
Iso, this option allows for the rapid computation of the energy using different thermochemistry parame-
ters and/or isotope selections.
 176 Chapter 5. List of Gaussian Keywords

5.39.2 Examples
Calculation Summary Output. After all of the output for the component job steps, Gaussian prints a
table of results for these methods. Here is the output from a G2 calculation:

Temperature= 298.150000 Pressure= 1.000000

E(ZPE)= .020511 E(Thermal)= .023346
E(QCISD(T))= -76.276078 E(Empiric)= -.024560
DE(Plus)= -.010827 DE(2DF)= -.037385
G1(0 K)= -76.328339 G1 Energy= -76.325503
G1 Enthalpy= -76.324559 G1 Free Energy= -76.303182
E(Delta-G2)= -.008275 E(G2-Empiric)= .004560
G2(0 K)= -76.332054 G2 Energy= -76.329219
G2 Enthalpy= -76.328274 G2 Free Energy= -76.306897

The temperature and pressure appear first, followed by the various components used to compute the G2
energy. The output concludes with the G2 energy at 0 K and at the specified temperature (the latter includes
a full thermal correction rather than just the zero-point energy correction), and (in the final output line) the
G2 theory predictions for the enthalpy and Gibbs free energy (both computed using the thermal-corrected G2
energy). (Note that the same quantities predicted at the G1 level are also printed in this summary section.)
The energy labels thus have the following meanings (G2 is used as an example):

G2 (0 K) Zero-point-corrected electronic energy: E0 = Eelec + ZPE

G2 Energy Thermal-corrected energy: E = E0 + Etrans + Erot + Evib
G2 Enthalpy Enthalpy computed using the G2 predicted energy: H = E + RT
G2 Free Energy Gibbs Free Energy computed using the G2 predicted energy: G = H - TS

Rerunning the Calculation at a Different Temperature. The following two-step job illustrates the
method for running a second (very rapid) G2 calculation at a different temperature. This job computes the G2
energy at 298.15 K and then again at 300 K:

%Chk=formald
# G2 Test

G2 on formaldehyde

0 1
molecule specification

--Link1--
%Chk=formald
%NoSave
# G2(Restart,ReadIso) Geom=Check

300.0 1.0
 5.40 Guess 177

isotope specifications

5.40 Guess
The Guess keyword controls the initial guess for the Hartree-Fock wavefunction. This keyword is not
meaningful without an option. By default, a Harris guess is used.

5.40.1 Options
Algorithm-Related Options
Harris
Diagonalize the Harris functional [471] for the initial guess. This is the default for all HF and DFT
calculations.
Huckel
Requests that a Huckel guess be generated. This is the default for CNDO, INDO, MNDO, and MINDO3.
The Huckel guess should be considered for PM6 calculations involving many second-row atoms.
RdScale
Read in the scale factor on atomic hardnesses used in iterative extended Huckel. The default is 7.0 times
the QEq value.
OldHuckel
Use the old Huckel guess (pre-Gaussian 03) instead of CNDO or the updated Huckel.
INDO
Use the Gaussian 98 default guess: INDO for first-row systems, CNDO for second-row, and Huckel for
third-row and beyond.
AM1
Do an AM1 calculation for the initial guess (currently only works with sparse matrix code). Guess=(AM1,
Always) causes later steps in a geometry optimization to generate a new guess at each point and compare
the energies with the density from the old point and the new guess and take the best one.
Core
Requests that the core Hamiltonian be diagonalized to form the initial guess. This is the default for AM1,
PM3, PM3MM, PM6, and PDDG.
TightConvergence
Change the defaults to 10−10 convergence on SCF and 10−8 for CIS, TD and CC. CPHF convergence is
not changed.

Orbital-Related Options
Permute
Read in a permutation of orbitals in the initial guess. The numbers of the generated guess orbitals are
given in the order in which they should be used in the SCF. Ranges (e.g. 7–12) can be used, and all
orbitals not listed are put in after the listed orbitals in their original order. Separate permutation lists for
α and β orbitals must be specified (each list separated by a blank line) for open shell systems.
Alter
Indicates that the orbitals selected for occupation in the Hartree-Fock wavefunction should not be those
178 Chapter 5. List of Gaussian Keywords

of lowest energy. Normally, the occupied orbitals are selected as those with lowest eigenvalues for the
one-electron Hamiltonian used in the initial guess programs. The alteration sections consist of a set of
transpositions indicating that one of these occupied orbitals is to be replaced by one of the other (virtual)
orbitals. Each such transposition is on a separate line and has two integers N1 and N2 (free format,
separated by spaces or a comma as usual) indicating that orbital N1 is to be swapped with orbital N2 . The
list of orbital transpositions is terminated by the blank line at the end of the input section.
For UHF calculations, two such orbital alteration sections are required, the first specifying transpositions
of α orbitals and the second specifying transpositions of β orbitals. Both sections are always required.
Thus, even if only α transpositions are needed, the β section is required even though it is empty (and
vice-versa). The second blank line to indicate an empty β section must be included.
Mix
Requests that the HOMO and LUMO be mixed so as to destroy α − β and spatial symmetries. This is
useful in producing UHF wavefunctions for singlet states. Mixing orbitals is only done by default when
generating a complex initial guess. NoMix says to not mix orbitals.
DensityMix[=N]
Whether to mix occupied and virtual orbital contributions in forming the initial guess density. N defaults
to -3 (use Huckel eigenvalues to decide which orbitals to mix).
CopyChk
Copy the MOs and density unedited, unprojected and unchecked from the checkpoint file for the guess.
Useful when importing from matrix element files.
Biorthogonalize
For an unrestricted guess, biorthogonalize the α and β MOs to maximally pair electrons of opposite spin.
Done automatically when a UHF wavefunction is read-in as a guess for ROHF. This option is also useful
in the combination of Guess=(BiOrth,Read,Only,Save) to replace the canonical UHF orbitals with ones
which have alpha and beta orbitals matched up as much as possible for viewing in GaussView or other
visualization packages.
NaturalOrbitals
Include natural orbitals in the checkpoint file. This must be accomplished via a separate job step specify-
ing this option as well as Only and Save. See the discussion of the Population keyword for details.

Procedural Options

Only
Guess=Only functions as a calculation type keyword and requests that the calculation terminate once
the initial guess is computed and printed. Note that the amount of orbital information that is printed is
controlled by the Pop keyword. Guess=Only may not be used with the MOPAC-based semi-empirical
methods (INDO, CNDO, MNDO, MINDO3).
This option is useful in preliminary runs to check if configuration alteration is necessary. For example,
Guess=Only may be specified with CASSCF in order to obtain information on the number of CI config-
urations in the CAS active space (as well as the initial orbitals).
Guess=(Only,Read) may also be used to produce population and other post-calculation analyses from
the data in a checkpoint file. For example, these options alone will produce a population analysis using
the wavefunction in the checkpoint file. Guess(Only,Read) Prop will cause electrostatic properties to be
5.40 Guess 179

calculated using the wavefunction in the checkpoint file.

Always
Requests that a new initial guess be generated at each point of an optimization. By default, the SCF
results from the last point are used for the guess at the next point.
Fragment=N
Generate a guess built from fragment guesses or SCF solutions. The guess is saved on the checkpoint
file regardless of if it is used in the current calculation, allowing it to be used in subsequent ones. This
option is usually combined with Guess=Only to generate a guess from fragment guess orbitals (otherwise
a full SCF calculation is performed for each fragment). Assignment of atoms to fragments and fragment
charges and multiplicities are specified as described in Molecule Specifications, except that a negative
spin multiplicity means that the unpaired orbitals for the fragment are to become β spin orbitals in the
combined set.
Local
Requests that orbitals be localized using the Boys method [184]. Occupied and virtual orbitals are local-
ized separately, and the irreducible representations (after possible merging using LowSymm or NoSymm)
are not mixed. Localized orbital analysis of a converged SCF wavefunction may then be done using a
second job step, which includes Guess(Read,Local,Only) and Pop=Full in its route section.
Sparse
Perform a sparse SE calculation for the initial guess. This option may be useful for very, very large HF
or DFT calculations using the sparse matrix facility.
Extra
Do an extra, new initial guess when reading orbitals from the RWF (i.e., during geometry optimizations).
By default, this is done if the default Harris guess is allowed, no alteration of configuration was requested,
and the optimization did not take a small step as flagged by variable 4 in ILSW. Use NoExtra to disable
this feature.
Fock
Reuse Fock matrices rather than orbitals when reading from previous results from the read-write or
checkpoint files. This is the default for periodic boundary conditions calculations if Guess=Alter is not
specified. NoFock disables this behavior, and it is the default for non-PBC calculations.

Guess Reading/Saving Options

Read
Requests that the initial guess be read from the checkpoint file (Guess=Read is often specified along
with Geom=Checkpoint). This option may be combined with Alter, in which case the orbitals are read
from the checkpoint file, projected onto the current basis set, and then the specified alterations are made.
Checkpoint is a synonym for Read. The TCheck option says to attempt to read a guess from the check-
point file but to generate a new one if necessary.
Alpha
Use alpha orbitals for both alpha and beta guess during Guess=Read.
Translate
Translate requests that the coordinates of the atoms used to produce a guess, which is read in, be translated
to the current atomic coordinates. This is the default. It may fail in unusual cases, such as when a wave-
180 Chapter 5. List of Gaussian Keywords

function is used as a guess for a system with a different stoichiometry, in which case Guess=NoTranslate
should be specified.
Cards
Specifies that after the initial guess is generated, some or all of the orbitals will be replaced with ones
read from the input stream. This option can be used to read a complete initial guess from the input stream
by replacing every orbital. The replacement orbitals are placed in the input section following the guess
alteration commands, if any. For UHF, there are separate α and β replacement orbital input sections.
The replacement orbitals input section (the α replacement orbitals section for UHF) begins with a line
specifying the Fortran format with which to read the replacement orbital input, enclosed in parentheses.
For example: (4E20.8). The remainder of the section contains one or more instances of the following:

IVec Orbital to replace (0=end, -1=replace all orbitals in order).

(A(I,IVec),I=1,N) New orbital in the format specified in the first line.

The format for the line containing IVec is Fortran I5. The β orbital replacement section for UHF calcula-
tions differs only in that it omits the initial format specification line. See the examples section for sample
replacement orbital input.
Input
Read a line from the input file containing the name of a checkpoint file. Instead of a filename, you can
specify one of the following keywords:
♢ generate says to generate a guess as usual.
♢ read and chk say to retrieve data from the job’s checkpoint file. They are thus equivalent to Guess=Read,
and use the checkpoint file specified to %Chk or %OldChk as usual.
♢ none says to skip generating a guess at all.
♢ dummy generates a dummy guess that does not require any work.
See the examples section for information about using this option with ONIOM.
Restart
Start a new SCF calculation using the restart data saved on the checkpoint file from a job with a different
geometry and/or basis set. (The option name is a bit of a misnomer.)
Save
Save the generated initial guess back into the checkpoint file at the conclusion of a Guess=Only run. This
option is useful for saving localized orbitals.
Print
Print the initial guess.

Symmetry-Related Options
LowSymm
Requests that irreducible representations of the molecular point group be combined in the symmetry
information used in the N 3 steps in the SCF to allow lowered symmetry of the wavefunction. This
enables the orbitals (and possibly but not necessarily the total wavefunction) to have lower symmetry
than the full molecular point group. This option is available only for GVB calculations, where it is often
necessary for calculations on symmetric systems (see the discussion of the GVB keyword below for an
example using this option).
 5.40 Guess 181

The option expects a single line of input (in the format 16I2) giving the numbers of the irreducible
representations to combine, with the new groups separated by 0; the list itself must be terminated by a
9. The numbers correspond to the order in which the representations are listed by Link 301 in the output
file (see the examples subsection below).
Since this input section is always exactly one line long, it is not terminated by a blank line. Note that
irreducible representations are combined before orbital localization is done and that localized orbitals
retain whatever symmetry is kept. Guess=NoSymm removes all orbital symmetry constraints without
reading any input.
NoSymm
Requests that all orbital symmetry constraints be lifted. Synonymous with SCF=NoSymm and Symm=NoSCF.
ForceAbelianSymmetry
Force the initial guess orbitals to transform according to irreducible representations of the Abelian point
group. NoForceAbelianSymmetry is the default.

Valid Option Combinations

Only reasonable combinations are valid. For example Guess=(Always,Alter) and Guess=(Read,Alter)
work as expected (in the former case, alterations are read once and the same interchanges are applied at each
geometry). Conversely, Guess=(Always,Read) is contradictory and will lead to unpredictable results. Refer to
the input sections order table at the beginning of this chapter to determine the ordering of the input sections for
combinations of options like Guess=(Cards,Alter).

5.40.2 Restrictions
Guess=Only may not be used with the MOPAC-based semi-empirical methods: INDO, CNDO, MNDO,
and MINDO3.

5.40.3 Related Keywords

Geom, Pop

5.40.4 Examples
Transposing Two Orbitals with Guess=Alter
This example finds the UHF/STO-3G structure of the 2 A1 excited state of the amino radical. First, a
Guess=Only calculation is run to determine whether any alter (reordering) instructions are needed to obtain the
desired electronic state. The HF/STO-3G theoretical model is used by default:

# Guess=Only Test

Amino radical test of initial guess

0 2
n
h 1 nh
h 1 nh 2 hnh
182 Chapter 5. List of Gaussian Keywords

nh 1.03
hnh 120.0

Here is the orbital symmetry summary output from the job, which comes immediately before the popula-
tion analysis in the output:
Initial guess orbital symmetries:
Alpha Orbitals:
Occupied (A1) (A1) (B2) (A1) (B1)
Virtual (A1) (B2)
Beta Orbitals:
Occupied (A1) (A1) (B2) (A1)
Virtual (B1) (A1) (B2)
The electronic state of the initial guess is 2-B1.
Initial guess <Sx>= 0.0000 <Sy>= 0.0000 <Sz>= 0.5000 <S**2>= 0.7500 S= 0.5000

Since a doublet state is involved, α and β orbitals are given separately. From the orbital symmetries,
the electron configuration in the initial guess is a21 a21 b22 a21 b11 , yielding a 2 B1 wavefunction. This is indeed the
ground state of NH2 . The expectation value of S2 for the unrestricted initial guess is printed, in this case, that
corresponding to a pure doublet: 0.75.
Since we want to model the 2 A1 excited state of the amino radical, we will need to alter this initial or-
bital configuration: a β electron must be moved from orbital 4 to orbital 5 (the electron configuration is then
a21 a21 b22 b21 a11 ).
Guess=Alter may be used to accomplish this. Here is the input for the geometry optimization:

# UHF/6-31G(d) Opt Guess=Alter

Amino radical: HF/6-31G(d)

Structure of 2-A1 state

0 2
n
h 1 nh
h 1 nh 2 hnh
Variables:
nh 1.03
hnh 120.0
Blank line ends the molecule specification section.
Blank line ends the alpha section (empty in this case).
4 5 Transpose orbitals 4 and 5.
End of the beta alteration section.

Note that an extra blank line – line 14 – is necessary to indicate an empty α alteration section. The final
two lines then constitute the β alteration section.
The initial guess program prints a list of orbitals that were interchanged as a result of the Alter option:
Harris functional with IExCor= 205 diagonalized for initial guess.
5.40 Guess 183

···
No Alpha orbitals switched.
Pairs of Beta orbitals switched:
4 5
Initial guess orbital symmetries:
Alpha Orbitals:
Occupied (A1) (A1) (B2) (A1) (B1)
Virtual (A1) (B2) (B1) (A1) (B2) (A1) (B2) (A1) (A2) (A1)
(B1) (A1) (B2) (A1)
Beta Orbitals:
Occupied (A1) (A1) (B2) (B1)
Virtual (A1) (A1) (B2) (B1) (A1) (B2) (A1) (B2) (A1) (A2)
(A1) (B1) (A1) (B2) (A1)
The electronic state of the initial guess is 2-A1.
Initial guess <Sx>= 0.0000 <Sy>= 0.0000 <Sz>= 0.5000 <S**2>= 0.7500 S= 0.5000

The SCF calculation follows, and the energy and S2 eigenvalue for the UHF wavefunction are printed. The
S2 value which results if contamination of the wavefunction from the next possible spin multiplicity (quartets
for doublets, quintets for triplets, etc.) is removed is also printed:
SCF Done: E(UHF) = -55.4915172451 A.U. after 12 cycles
Convg = 0.2693D-08 -V/T = 2.0038
<Sx>= 0.0000 <Sy>= 0.0000 <Sz>= 0.5000 <S**2>= 0.7534 S= 0.5017
<L.S>= 0.000000000000E+00
Annihilation of the first spin contaminant:
S**2 before annihilation 0.7534, after 0.7500

Although this calculation does in fact converge correctly to 2 A1 state, it sometimes happens that the order
of orbital symmetries switches during the course of the SCF iterations. If the orbital symmetries of the final
wavefunction are different from those in the initial guess (whether or not you are using Guess=Alter), we
recommend using the direct minimization routine, specified with the SCF=QC or SCF=DM keywords, which
usually holds symmetry from one iteration to the next.

Reordering Orbitals with Guess=Permute

This option is often is the easiest way to perform a complex modification of the initial guess, as in this
example:

# CASSCF/6-31G(d,p) Opt Guess=Permute Pop=Reg

CAS job

0 1
molecule specification

1-60 65 63 64 66 68 67 61-62 69 Specify new orbital ordering.

Here, we have rearranged orbitals 61-68. Listing the final orbital (69) is not really necessary, but it helps
to make the input easier to understand for humans.
184 Chapter 5. List of Gaussian Keywords

Specifying Calculation-Specific Guesses for ONIOM with Guess=Input

The Guess=Input is useful for ONIOM jobs where the SCF is hard to converge for some of the sub-
calculations at the initial geometry. Convergence can be accomplished using a procedure like the following:
Step 1. Use ONIOM=OnlyInput to print out input files for the individual calculations.
Step 2. Converge the SCF for the problem step separately (for example, using Stable=Opt).
Step 3. After verifying that the correct state has been found, run an ONIOM calculation with Guess=Input to
retrieve the correct initial guesses for the individual states. In the ONIOM input file, you will then have
a line for the guess for each calculation (i.e., 3 lines for a 2-layer MO:MO), where each line can be a
checkpoint file name or read (for Guess=Read from the regular checkpoint file) or generate (generate a
new initial guess), as appropriate. For example, if only the high level calculation on the model system
was problematic, the input would be:

generate Low level calculation on the real system.

Blank line.
guess_for_high.chk High level calculation on the model system.
Blank line.
generate Low level calculation on the model system.

Reading in Orbitals with Guess=Cards

Some or all of the orbitals may be replaced, after the initial guess is generated, using Guess=Cards. Here
is some sample input for this option, which replaces orbitals 1 and 4 (note that the format for the third and
following lines is specified in line 1):

(3E20.8)
1
0.5809834509E+00 0.4612416518E+00 -0.6437319952E-04
0.1724432549E-02 0.1282235396E-14 0.5417658499E-13
0.1639966912E-02 -0.9146282229E-15 -0.6407549694E-13
-0.4538843604E-03 0.6038992958E-04 -0.1131035485E-03
0.6038992969E-04 -0.1131035471E-03
4
0.7700779642E-13 0.1240395916E-12 -0.3110890228E-12
-0.4479190461E-12 -0.1478805861E-13 0.5807753928E+00
0.6441113412E-12 -0.3119296374E-14 0.1554735923E+00
-0.1190754528E-11 0.2567325943E+00 0.1459733219E+00
-0.2567325943E+00 -0.1459733219E+00
0

An orbital number of zero ends the replacement orbital input.

Antiferromagnetic Coupling

Here is an example of a fragment guess job. The first step generates guesses for each one of the fragments
and then combines them together into a guess for the SCF on the full molecule. The second step reads in
that guess for a subsequent calculation. The charge and multiplicity line has the overall molecular charge and
multiplicity first, followed by those for each fragment.
5.40 Guess 185

This example is Fe2 S2 + 4 S-R ligands, where R is a phenyl group. It is a singlet with an overall charge
of -2. The guess does each bare sulfur as S(2−) closed-shell (fragments 2 and 4), the two irons as Fe(3+) sextets
antiferromagnetically coupled (fragments 1 and 3, with 1 being alpha-spin and 3 beta-spin), and each of the
S-R fragments (5-8) as closed-shell singlet anions.

Figure 5.1: Fragment Assignments

%chk=FragGuess
%mem=64mw
#P UBP86/6-311G(d) Guess=(Fragment=8,Only) Pop=None

Fe2S2 cluster with phenylthiolates.

Step 1: Generate fragment guess

-2,1 3,6 -2,1 3,-6 -2,1 -1,1 -1,1 -1,1 -1,1

H(Fragment=7) 23.5010 2.2873 8.5744
S(Fragment=2) 14.8495 1.1490 7.0431
Fe(Fragment=3) 17.0430 1.0091 7.0068
S(Fragment=4) 17.4565 -1.1490 7.0431
S(Fragment=5) 14.3762 -2.1581 8.7983
C(Fragment=5) 12.5993 -2.1848 8.6878
H(Fragment=5) 12.3743 -3.6513 10.1678
C(Fragment=5) 10.4994 -3.1122 9.4309
H(Fragment=5) 9.9929 -3.7579 10.0022
C(Fragment=5) 9.8049 -2.2791 8.5639
H(Fragment=5) 8.8050 -2.2873 8.5744
C(Fragment=5) 10.4833 -1.4146 7.6615
H(Fragment=5) 9.9730 -0.8525 7.0106
186 Chapter 5. List of Gaussian Keywords

S(Fragment=8) 14.3794 -1.8091 5.0446

C(Fragment=5) 11.9048 -1.3675 7.7057
H(Fragment=5) 12.4158 -0.7843 7.0743
C(Fragment=6) 17.2999 3.4265 4.6624
C(Fragment=6) 16.6376 4.1967 5.6090
H(Fragment=6) 16.5022 3.8494 6.5369
C(Fragment=6) 16.1530 5.4856 5.2463
H(Fragment=6) 15.6665 6.0472 5.9155
C(Fragment=6) 16.3468 5.9257 4.0431
H(Fragment=6) 16.0236 6.8408 3.8020
C(Fragment=6) 17.0091 5.1398 3.0522
H(Fragment=6) 17.1330 5.4944 2.1254
C(Fragment=6) 17.4775 3.8823 3.3884
H(Fragment=6) 17.9400 3.3149 2.7071
S(Fragment=7) 17.9298 2.1581 8.7983
C(Fragment=7) 19.7067 2.1848 8.6878
C(Fragment=7) 20.4174 3.0650 9.5194
H(Fragment=7) 19.9317 3.6513 10.1678
C(Fragment=7) 21.8066 3.1122 9.4309
H(Fragment=7) 22.3132 3.7579 10.0022
C(Fragment=7) 22.5011 2.2791 8.5639
C(Fragment=7) 21.8227 1.4146 7.6615
H(Fragment=7) 22.3330 0.8525 7.0106
C(Fragment=7) 20.4012 1.3675 7.7057
H(Fragment=7) 19.8902 0.7843 7.0743
C(Fragment=8) 15.0061 -3.4265 4.6624
Fe(Fragment=1) 15.2630 -1.0091 7.0068
C(Fragment=8) 15.6684 -4.1967 5.6090
H(Fragment=8) 15.8038 -3.8494 6.5369
C(Fragment=8) 16.1530 -5.4856 5.2463
H(Fragment=8) 16.6395 -6.0472 5.9155
C(Fragment=5) 11.8886 -3.0650 9.5194
C(Fragment=8) 15.9592 -5.9257 4.0431
H(Fragment=8) 16.2824 -6.8408 3.8020
C(Fragment=8) 15.2969 -5.1398 3.0522
H(Fragment=8) 15.1730 -5.4944 2.1254
C(Fragment=8) 14.8285 -3.8823 3.3884
H(Fragment=8) 14.3660 -3.3149 2.7071
S(Fragment=6) 17.9266 1.8091 5.0446

--Link1--
%chk=FragGuess
%mem=64mw
#P UBP86/6-311G*/Auto Guess=Read Geom=AllCheck · · ·
 5.41 GVB 187

5.41 GVB

This method keyword requests a perfect-pairing General Valence Bond (GVB-PP) calculation. GVB re-
quires one parameter: the number of perfect-pairing pairs to split; for example: GVB(4). This parameter may
also be specified with the NPair option. The natural orbitals for the GVB pairs are taken from occupied and
virtual orbitals of the initial guess determinant (described in the Input tab).

5.41.1 Input
Normally, most of the difficult input for a GVB-PP calculation involves specifying the initial guess (Link
401). This often includes alteration of orbitals to ensure the correct identification of high-spin, perfect-pairing,
and closed-shell orbitals and possible reduction of SCF symmetry to account for the localized orbitals which
usually represent the lowest energy solution for GVB-PP.
The GVB program reads the number of orbitals in each GVB pair (in format 40I2). The number of lines
read is fixed (and normally 1), so no terminating blank line is needed. For a molecule having spin multiplicity
S, N GVB pairs, and n1 , · · · , nN orbitals in each pair, orbitals from the initial guess are used in the following
manner by the GVB program:
♢ The S-1 highest occupied orbitals in the initial guess, which would have been singly occupied in an ROHF
calculation, become high-spin orbitals.
♢ The next lower N occupied orbitals, which would have been doubly occupied in an ROHF calculation,
become the first natural orbitals of the GVB pairs.
♢ Any remaining orbitals occupied in the guess stay closed-shell.
♢ The lowest n1 − 1 virtual orbitals become natural orbitals 2 through n1 of the first GVB pair, then the next
n2 − 1 orbitals are assigned to pair 2, and so on. The GVB-PP scheme does not allow an orbital to be
shared by more than one GVB pair.
♢ Any remaining (virtual) orbitals from the initial guess become virtual orbitals in the GVB calculation.
Generally Guess=Alter is required to ensure that guess-occupied orbitals, which will be used as first natural
orbitals, match up with the correct guess virtual orbitals that will become the corresponding higher natural
orbitals. Often it is helpful to start off with Guess=(Local,Only), examine the orbitals to determine alteration
requirements, then do Guess=(Local,Alter) and GVB(NPair=N,Freeze) to allow the higher natural orbitals to
become more appropriate. Finally, the full calculation can be run with Guess=Read and all orbitals optimized
in the GVB. If there is any confusion or concern with the orbitals breaking symmetry, the calculation should
be done with Symm=NoSCF and initially with Guess=Local. In fact, this approach is generally recommended
except for those very expert users.
If the number of orbitals in a pair is negative, the root of the CI to use for that pair and the pair’s initial
GVB coefficients are read in format (I2,5D15.8). This is useful if a 1 Σ or 1 ∆ state is being represented as a
GVB pair of the form x2 ± y2 .

5.41.2 Options
NPair
Gives the number of perfect-pairing pairs. GVB(N) is equivalent to GVB(NPair=N). NPair=0 is accept-
able and results in a closed-shell or spin-restricted SCF calculation.
InHam=N
 188 Chapter 5. List of Gaussian Keywords

Read in N Hamiltonians (Fock operators, sets of coupling coefficients). This option may be combined
with perfect-pairing pairs. Each Hamiltonian is read using the following syntax (format in parentheses):
NO # of orbitals in current Hamiltonian (I5)
Fj Occup. # (1.0=closed-shell) (D15.8)
(AJ(I), I =1,NHam) J coefficients (5D15.8)
(AK(I), I =1,NHam) K coefficients (5D15.8)
Combining several orbitals with the same AJ and AK coefficients into one “shell” is not currently sup-
ported, so NO is always 1. The ham506 utility can be used to generate averaged Hamiltonians for the
common case of spherical averaging in atomic calculations. The Hamiltonian coefficients are described
in Bobrowicz and Goddard [472]. A good introduction to the qualitative interpretation of GVB wave-
functions can be found in the review article by Goddard and Harding [473].
OSS
Do a two-electron, two-orthogonal-orbital open-shell singlet. This option may be combined with perfect-
pairing pairs. OpenShellSinglet is a synonym for OSS.
Freeze
Freeze closed-shell and open-shell orbitals and first natural orbitals of GVB pairs, allowing only 2nd and
higher orbitals to vary. This option is useful for starting off difficult wavefunctions.

5.41.3 Availability
Energies, analytic gradients, and numerical frequencies.

5.41.4 Examples
Here is a GVB(3/6) calculation performed on singlet methylene:

# GVB(3)/6-31G(d) Pop=Full
Guess=(Local,LowSym,Alter)

GVB(3) on CH2

molecule specification

1 4 0 2 3 9 Guess=LowSym input
2,3 Guess=Alter input

2 2 2 GVB input

Each of the 3 valence electron pairs is split into a GVB pair. A preliminary Guess=Only calculation was
performed to determine the localized orbitals and which alterations would be required.
The perfect pairing GVB method includes the effects of intra-pair correlation but not those of inter-pair
correlation. Consequently, GVB electrons pairs tend to be localized. In the case of singlet methylene, the
carbon lone pair is localized even at the Hartree-Fock level. The canonical Hartree-Fock orbitals for the C-H
bonds are delocalized into linear combinations (C-H1 + C-H2 ) and (C-H1 – C-H2 ) having A1 and B2 symmetry,
respectively. In order to allow the localization in the guess to produce separate bond pairs, these two irreducible
 5.42 HF 189

representations must be combined. Similarly, the GVB calculation itself must be told not to impose the full
molecular symmetry on the orbitals, which would force them to be delocalized. Combining the A1 and B2
representations and combining the A2 and B1 representations causes the calculation to impose only Cs symmetry
on the individual orbitals, allowing separate GVB pairs for each bond. Since the resulting pairs for each bond
will be equivalent, the resulting overall wavefunction and density will still have C2v symmetry.
The Guess=LowSymm keyword specifies that the irreducible representations of the molecular point group
will be combined in the symmetry information used in a GVB calculation. It takes a single line of input consist-
ing of giving the numbers of the irreducible representations to combine, where the numbers correspond to the
order in which the representations are listed in the output file (they appear just after the standard orientation).
For example, here is the output for a molecule with C2v symmetry:

There are 4 symmetry adapted basis functions of A1 symmetry.

There are 0 symmetry adapted basis functions of A2 symmetry.
There are 1 symmetry adapted basis functions of B1 symmetry.
There are 2 symmetry adapted basis functions of B2 symmetry.

Thus for C2v symmetry, the order is A1, A2, B1, B2, referred to in the Guess=LowSym input as 1 through
4, respectively. A zero separates groups of representations to be combined, and a nine ends the list. Thus, to
combine A1 with B2 and A2 with B1, thereby lowering the SCF symmetry to Cs , the appropriate input line is:
1 4 0 2 3 9
Since this information always requires exactly one line, no blank line terminates this section.
The order of orbitals generated after localization by the initial guess in the first job step was C-1s C-H1
C-H2 C-2s for the occupied orbitals and C-2p C-H1 * C-H2 * for the lowest virtual orbitals. Hence if no orbitals
are interchanged, the C-2s lone pair would be correctly paired with the unoccupied p-orbital, but then the next
lower occupied, C-H2 , would be paired with the next higher virtual, C-H1 *. So either the two bond occupied
orbitals or the two bond virtual orbitals must be exchanged to match up the orbitals properly.
Finally, the one line of input to the GVB code indicates that there are 2 natural orbitals in each of the 3
GVB pairs.

5.42 HF
This method keyword requests a Hartree-Fock calculation [474]. Unless explicitly specified, RHF is used
for singlets and UHF for higher multiplicities. In the latter case, separate α and α orbitals will be computed
[475, 476] ([477] for electron correlation methods starting from a UHF reference). RHF, ROHF or UHF can
also be specified explicitly.

5.42.1 Availability
Energies, analytic gradients, and analytic frequencies for RHF and UHF and numerical frequencies for
ROHF.

5.42.2 Examples
The Hartree-Fock energy appears in the output as follows:

SCF Done: E(RHF) = -74.9646569691 A.U. after 4 cycles

 190 Chapter 5. List of Gaussian Keywords

Conv = 0.48D-08 -V/T = 2.0038

For UHF jobs, the output also prints S2 and related values:

SCF Done: E(UHF) = -38.7068863059 A.U. after 11 cycles

Convg = 0.7647D-08 -V/T = 2.0031
<Sx>= 0.0000 <Sy>= 0.0000 <Sz>= 1.0000 <S**2>= 2.0142 S= 1.0047
<L.S>= 0.000000000000E+00
Annihilation of the first spin contaminant:
S**2 before annihilation 2.0142, after 2.0001

The second and third lines give the SCF convergence limit and the expectation value of S2 .

5.43 Huckel

This method keyword requests an extended Huckel calculation [478–482]. ExtendedHuckel is a synonym
for this keyword. No basis set keyword should be specified.

5.43.1 Options
Hoffmann
Requests an Extended Huckel calculation using the default parameter set from the Huckel group.
Muller
Requests an Extended Huckel calculation using parameters collected by Edgar Muller.
Guess
Requests an Extended Huckel calculation using the modified parameters used for Guess=Huckel [483–
485].

5.43.2 Availability
Energies, “analytic” gradients, and numerical frequencies.

5.43.3 Examples
The energy appears in the output file as follows (followed by the x, y, and z components of the dipole
moment):

Huckel eigenvalues -- -1.245 -0.637 -0.558 -0.544 -0.043 0.352

Energy= -5.968836513622 NIter= 0.
Dipole moment= 0.000000 0.000000 0.000000

The energy is as defined by this semi-empirical model. Note that energy differences computed from the
values in semi-empirical calculations are in Hartrees and may be compared directly with energy differences
computed from jobs using other methods.

5.43.4 Related Keywords

Guess=Huckel
 5.44 INDO 191

5.44 INDO

Requests a semi-empirical calculation using the INDO Hamiltonian [486]. No basis set keyword should
be specified.

5.44.1 Availability

Energies, “analytic” gradients, and numerical frequencies.

5.44.2 Examples

The INDO energy appears in the output file as follows:

SCF Done: E(UINDO) = -8.08016620373 A.U. after 11 cycles
The energy is as defined by the INDO model.

5.45 Integral

The Integral keyword modifies the method of computation and use of two-electron integrals and their
derivatives.

5.45.1 Options
Integration Grid Selection Option
Grid=grid-name
Specifies the integration grid to be used for numerical integrations. Note that it is very important to use
the same grid for all calculations where you intend to compare energies e.g., computing energy differ-
ences, heats of formation, and so on.
“Pruned” grids are grids that have been optimized to use the minimal number of points required to achieve
a given level of accuracy. Pruned grids are used by default when available, currently defined for H through
Kr. For example FineGrid is a pruned (75,302 grid), having 75 radial shells and 302 angular points per
shell, resulting in about 7000 points per atom. UltraFine requests a pruned (99,590) grid. It is recom-
mended for molecules containing lots of tetrahedral centers and for computing very low frequency modes
of systems. This grid is also useful for optimizations of larger molecules with many soft modes such as
methyl rotations, making such optimizations more reliable. SuperFineGrid is a more accurate grid than
UltraFine; SuperFineGrid is a pruned 175,974 for first-row atoms and 250,974 for atoms in the second
and later rows.
Other special values for this parameter are CoarseGrid, which requests a pruned version of the (35,110)
grid, and SG1Grid, a pruned version of (50,194). Note, however, that they are not recommended for
production calculations [487]. Pass0Grid requests the obsolete pruned (35,110) grid once intended for
pass 0 of a tight SCF calculation.
The default grid is UltraFine, and the default grid for the CPHF is SG1. If SG1 is selected as the integra-
tion grid, the Coarse grid is used for the CPHF. When a specific grid is specified to the Int=Grid=grid-
name option, then that grid is also used for the CPHF. Finally, be aware that SG1 is used in the CPHF
as the default integration grid for a few DFT jobs including Polar=OptRot, Freq=Anharmonic, and
Freq=NNROA.
192 Chapter 5. List of Gaussian Keywords

The parameter to this option is either a grid name keyword or a specific grid specification. If a key-
word is chosen, then the option name itself may be omitted (i.e., Integral(Grid=SuperFine) and Inte-
gral(SuperFine) are equivalent).
Specific grids may be selected by giving an integer value N as the argument to Grid. N may have one of
these forms:
♢ A large positive integer of the form mmmnnn, which requests a grid with mmm radial shells around
each atom, and nnn angular points in each shell. The total number of integration points per atom is
thus mmm*nnn. For example, to specify the (99,302) grid, use Int(Grid=99302). The valid numbers
of angular points are 38, 50 [488], 72 [489], 86, 110 [488], 146, 194, 302 [490], 434 [491], 590,
770, and 974 [492]. If a larger number of angular points is desired, a spherical product grid can be
used.
♢ A large negative integer of the form -mmmnnn, which requests mmm radial shells around each atom,
and a spherical product grid having nnn θ points and 2*nnn φ points in each shell. The total number
of integration points per atom is therefore 2*mmm*nnn2 . This form is used to specify the (96,32,64)
grid commonly cited in benchmark calculations: Int(Grid=-96032).
Note that any value for nnn is permitted; although, small values are silly (values of nnn < 15 produce
grids of similar size and inferior performance to the special angular grids requested by the second format
above). Large values are expensive. For example, a value of 200100 would use 2*200*100*100 or 4
million points per atom!

Algorithm Selection Options

SSWeights
Use the weighting scheme of Scuseria and Stratmann [493] for the numerical integration for DFT calcu-
lations. This is the default.
FMMNAtoms=N
Set the threshold size for turning on FMM by default to N. The default is 60 atoms. Molecules with
symmetry have higher crossover points, and the threshold is increased accordingly, to 120 atoms for the
C2 and Cs point groups and 240 atoms for higher symmetry.
Symm
NoSymmetry disables and Symm enables the use of symmetry in the evaluation and storage of integrals
(Symm is the default). Synonymous with the keywords Symm=[No]Int, which is the recommended
usage.
FoFCou
Use routine FoFCou even when it would not otherwise be used. NoFoFCou forbid uses of FoFCou.
LTrace
Trace Linda transactions. Primarily for debugging.
SplitDBFSP
Split density S=P shells into separate S and P shells. NoSplitDBFSP is the default.
ECPAcc=N
Set ECP accuracy parameter to N.
Acc2E=N
Set 2-electron integral accuracy to 10−N . The default is 10−12 .
 5.45 Integral 193

DigestCartesian
Transform integrals from Cartesian to Pure form before digesting them (contracting with density matrices
during direct calculations). The default is to decide the based on parameters such as how many density
matrices are being processed.
UnconAOBasis
Uncontract all the primitives in the AO basis. UncontractAOBasis is a synonym for this option.
UnconDBF
Uncontract all the primitives in the density fitting basis. UncontractDensityBasis is a synonym for this
option.
NoXCTest
Skip tests of numerical accuracy of XC quadrature.
ReadB
Read common /B/ from disk after the initial geometry, even if a standard basis was set up.

General Basis Set-Related Options

Raff, Raf1, Raf2, Raf3
Whether to write out regular or the Raffenetti integrals. Raff and Raff1 integrals write the Raffenetti1 in-
tegrals. Raff2 and Raff3 will write the 1 and 2/1,2 and 3 Raffenetti integral combinations (respectively).
Primarily useful with External or Output=MatrixElement. NoRaff suppresses writing the Raffenetti inte-
grals and writes out the regular integrals.
BasisTransform=N
Transform generalized contraction basis sets to reduce the number of primitives, neglecting primitives
with coefficients of 10−N or less. This is the default, with N=4.
ExactBasisTransform
Transform generalized contraction basis sets to reduce the number of primitives, but using only transfor-
mations which are exact. Only exact duplicate primitives are removed, and there will be no change in the
energy value.
NoBasisTransform
Do not transform generalized contraction basis sets to reduce the number of primitives.

5.45.2 Relativistic Calculations

DKH
Requests a Douglas-Kroll-Hess 2nd order scalar relativistic calculation [494–497] (see [498, 499] for
an overview). This method uses a Gaussian nuclear model [500]. DKH2 and DouglasKrollHess are
synonyms.
DKH0
Requests a Douglas-Kroll-Hess 0th order scalar relativistic calculation.
DKHSO
Requests a Douglas-Kroll-Hess 4th order relativistic calculation including spin-orbit terms (if doing GH-
F/GKS).
RESC
Requests a RESC scalar relativistic calculation.
 194 Chapter 5. List of Gaussian Keywords

NoDKH and NonRelativistic request a non-relativistic core Hamiltonian, which is the default.

5.45.3 Related Keyword

SCF

5.46 IOp
The IOp keyword allows the user to set internal options (variables in system common /IOp/) to specific
values. The syntax is:
IOp(overlaya /optiona = valuea [,overlayb /optionb = valueb , · · · ])
which sets option number optiona to the value valuea for every occurrence of overlay number overlaya (and so
on for other entries in the list). For example, the following sets the value of option 12 in overlay 1 to 5 and that
of option 44 in overlay 3 to 0: IOp(1/12=5,3/44=0)
IOp values explicitly set in the route section are not passed on to the second and subsequent automatically-
generated job steps; this applies to keyword combinations like Opt Freq and to inherently multi-step methods
such as G2 and the CBS methods. For example, if you want to specify an alternate grid for a DFT optimiza-
tion+frequency job, you must use an option to the Int=Grid keyword rather than an explicit IOp value.
The execution of each overlay of Gaussian 16 is controlled by numbered options. Each option may be
assigned an integer value, with 0 being the default. The value of an option is held unchanged throughout
execution of all of the links in one overlay. Thus the significance of a particular option applies to all the
component links in one pass through the overlay. Since setting internal options can have arbitrary effects on the
calculation, archiving is disabled by use of this keyword.
The full list of Gaussian 16 options is given in the Gaussian 16 IOps Reference.

5.47 IRC
This calculation type keyword requests that a reaction path be followed by integrating the intrinsic reaction
coordinate [501, 502]. The initial geometry (given in the molecule specification section) is that of the transition
state, and the path can be followed in one or both directions from that point. The forward direction is defined
as the direction the transition vector is pointing when the largest component of the transition vector (“phase”)
is positive; it can be defined explicitly using the Phase option. By default, both reaction path directions are
followed.
IRC calculations require initial force constants to proceed. You must provide these to the calculation in
some way. The usual method is to save the checkpoint file from the preceding frequency calculation (used
to verify that the optimized geometry to be used in the IRC calculation is in fact a transition state), and then
specify the RCFC option in the route section. Another possibility is to compute them at the beginning of the
IRC calculation (CalcFC). Note that one of RCFC and CalcFC must be specified (CalcAll is also available but
is not typically necessary with the HPC algorithm).
In Gaussian 16, most calculations use the HPC algorithm [502–504] by default (introduced in Gaussian
09). It is much more efficient than the one used in earlier program versions. ONIOM(MO:MM) calculations use
the Euler predictor-corrector integration algorithm. This same integrator is also used by default in calculations
using methods with gradients but without analytic second derivatives; such calculations should include the
GradientOnly option. Available algorithms are discussed in Availability.
 5.47 IRC 195

The default is to report only the energies and reaction coordinate at each point on the path; if geomet-
rical parameters along the path are desired, these should be defined as redundant internal coordinates via
Geom=ModRedundant or as input to the IRC code via IRC(Report=Read) (see Options for the latter’s input
format).
You can specify alternative isotopes for IRC jobs using the ReadIsotopes option (described in Options).

5.47.1 Options
Path Specification Options
Phase=(N1, N2 [,N3 [,N4]])
Defines the phase for the transition vector such that forward motion along the transition vector corre-
sponds to an increase in the specified internal coordinate, designated by up to four atom numbers. If two
atom numbers are given, the coordinate is a bond stretch between the two atoms; three atom numbers
specify an angle bend; and four atoms define a dihedral angle.
Forward
Follow the path only in the forward direction.
Reverse
Follow the path only in the reverse direction.
Downhill
Proceed downhill from the input geometry.
MaxPoints=N
Number of points along the reaction path to examine (in each direction if both are being considered). The
default is 10.
StepSize=N
Step size along the reaction path, in units of 0.01 Bohr. If N<0, then the step size is taken in units of 0.01
amu1/2 -Bohr. The default is 10.
ReadIsotopes
This option allows you to specify alternatives to the default temperature, pressure, frequency scale factor
and/or isotopes – 298.15 K, 1 atmosphere, no scaling, and the most abundant isotopes (respectively). It is
useful when you want to rerun an analysis using different parameters from the data in a checkpoint file.
Be aware, however, that all of these can be specified in the route section (Temperature, Pressure and Scale
keywords) and molecule specification (the Iso parameter), as in this example:

#T Method/6-31G(d) JobType Temperature=300.0 · · ·

···

0 1
C(Iso=13)
···

ReadIsotopes input has the following format:

temp pressure [scale] Values must be real numbers.

isotope mass for atom 1
196 Chapter 5. List of Gaussian Keywords

isotope mass for atom 2

···
isotope mass for atom n

Where temp, pressure, and scale are the desired temperature, pressure, and an optional scale factor for
frequency data when used for thermochemical analysis (the default is unscaled). The remaining lines hold
the isotope masses for the various atoms in the molecule, arranged in the same order as they appeared
in the molecule specification section. If integers are used to specify the atomic masses, the program will
automatically use the corresponding actual exact isotopic mass (e.g., 18 specifies 18 O, and Gaussian uses
the value 17.99916).

Algorithm Selection Options

HPC
Use the Hessian-based Predictor-Corrector integrator [502–504]: a very accurate algorithm that uses
the Hessian-based local quadratic approximation as the predictor component and a modified Bulrisch-
Stoer integrator for the corrector portion. This corrector integrator is done using a distance-weighted
interpolant surface [505] fitted to energies, gradients, and Hessians at the beginning and ending points
of the predictor step. This is the default for most calculations. Note that it is not practical for extremely
large molecular systems.
EulerPC
Use the first-order Euler integration for the predictor step along with the HPC corrector step. This is the
default for IRC=GradientOnly calculations. This is also the default algorithm for IRC calculations using
an ONIOM(MO:MM) method. It is a practical choice for such calculations on large molecules.
LQA
Use the local quadratic approximation [406, 409] for the predictor step.
DVV
Use the damped velocity verlet integrator [506].
Euler
Use only the first-order Euler integration predictor step for the IRC. This option is not recommended for
production use.
ReCalc=N
Compute the Hessian analytically every N predictor steps or every |N| corrector steps if N<0. Analytic sec-
ond derivatives can be requested intermittently during IRCs using IRC=(CalcFC,RecalcFC=(Predictor=N,
Corrector=M)), which computes second derivatives at the initial point and then at every N th predictor step
and every Mth corrector step. You must still specify RCFC or CalcFC to provide the initial Hessian. Up-
date is a synonym for ReCalc. Requires a method which has analytic second derivatives.
GradientOnly
Use an algorithm that does not require second derivatives. Note that you must specify this option explic-
itly for such methods (they are not automatically detected). Can be combined with EulerPC (the default),
HPC, Euler, or DVV.
5.47 IRC 197

Coordinate System Selection Options

MassWeighted
Follow the path in mass-weighted Cartesian coordinates. MW is a synonym for MassWeighted. This is
the default.
Cartesian
Follow the path in Cartesian coordinates without mass-weighting.

Options For Generating Initial Force Constants

RCFC
Specifies that the computed force constants in Cartesian coordinates from a frequency calculation are to
be read from the checkpoint file. ReadCartesianFC is a synonym for RCFC.
CalcFC
Specifies that the force constants be computed at the first point.

Procedure-Related Options
Restart
Restarts an IRC calculation that did not complete, or restarts an IRC calculation which did complete, but
for which additional points along the path are desired.
Report[=item]
Controls which geometric parameters are reported by an IRC. By default, no geometrical parameters are
reported. Report without a parameter includes all of the generated internal coordinates. The possible
values for item are:

Read Read a list of internal coordinates to report. These are specified as 1-4 atom num-
bers only (ModRedundant-style coordinate specifications are not supported).
Bonds Reports bonds from the internal coordinates (if present).
Angles Reports angles from the internal coordinates (if present).
Dihedrals Reports dihedrals from the internal coordinates (if present).
Cartesians Reports all Cartesian coordinates.

ReCorrect[=when]
Controls testing-and-recomputing for the correction step of HPC and EulerPC IRCs. ReCorrect (without
a parameter) and ReCorrect=Yes say to repeat the corrector step whenever the correction is greater than
the threshold (which can be decreased with the Tight and VTight options). The parameter can take on
the following values:

Never Do not repeat correction steps (i.e., suppress the threshold test).
Always Always recompute the corrector at least once regardless of the size of the initial
correction.
Test Test the quality of the corrector step and report the results, but do not take an ad-
ditional corrector step. The computed IRC path will be the same as with ReCor-
rect=Never.

The default is Yes for EulerPC and HPC, and Never for other integrators.
 198 Chapter 5. List of Gaussian Keywords

MaxCycle=N
Sets the maximum number of steps to N. The default is 20.
Tight
This option tightens the cutoffs on forces and step size that are used to determine convergence. For DFT
calculations, Int=UltraFine should be specified as well.
VeryTight
Extremely tight optimization convergence criteria. VTight is a synonym for VeryTight. For DFT calcula-
tions, Int=UltraFine should be specified as well.

Options For Compatibility with Gaussian 03

The GS2 option requests the IRC algorithm used in Gaussian 03 within the new IRC implementation.
Use the keyword Use=L115 in order to run the code that was the default in Gaussian 03 (recommended for
reproducing old results only).
GS2
Use the IRC algorithm that was the default in Gaussian 03 and earlier [507, 508]. The geometry is
optimized at each point along the reaction path such that the segment of the reaction path between any
two adjacent points is described by an arc of a circle and so that the gradients at the end points of the
arc are tangent to the path. By default, a GS2 IRC calculation steps 6 points in mass-weighted internal
coordinates in the forward direction and 6 points in the reverse direction, in steps of 0.1 amu1/2 Bohr
along the path.
CalcAll
Specifies that the force constants be computed at every point.

5.47.2 Availability
The default algorithms are available for HF, all DFT methods, CIS, TD, MP2, MP3, MP4(SDQ), CID,
CISD, CCD, CCSD, QCISD, BD, CASSCF, and all semi-empirical methods.

5.47.3 Related Keywords

Opt, Scan, IRCMax

5.47.4 Examples
When the IRC has completed, the program prints a table summarizing the results:

Reaction path calculation complete.

Energies reported relative to the TS energy of -91.564851

----------------------------------------------------------------------
Summary of reaction path following
----------------------------------------------------------------------
Energy Rx Coord
1 -0.00880 -0.54062
2 -0.00567 -0.43250
3 -0.00320 -0.32438
 5.48 IRCMax 199

4 -0.00142 -0.21626
5 -0.00035 -0.10815
6 0.00000 0.00000 transition state
7 -0.00034 0.10815
8 -0.00131 0.21627
9 -0.00285 0.32439
10 -0.00487 0.43252
11 -0.00725 0.54065
----------------------------------------------------------------------

The initial geometry (transition structure) appears in the middle of the table (in this case, as point 6). It
can be identified quickly by looking for reaction coordinate and energy values of 0.00000.

5.48 IRCMax
Performs an IRCMax calculation using the methods of Petersson and coworkers [509–517]. Taking a
transition structure as its input, this calculation type finds the maximum energy along a specified reaction path,
using the GS2 algorithm [507, 508] (see IRC=GS2 for details).
IRCMax requires two model chemistries as its options, separated by a colon: IRCMax(model2:model1):
e.g., IRCMax(B3LYP/6-31G(d,p):HF/6-31G(d,p))

5.48.1 Options
ZC-VTST Options
Zero
Include the zero-point energy in the IRCMax computation.

Path Selection Options

Forward
Follow the path only in the forward direction.
Reverse
Follow the path only in the reverse direction.
ReadVector
Read in the vector to follow. The format is Z-matrix (FFF(I), I=1,NVAR), read as (8F10.6).
MaxPoints=N
Number of points along the reaction path to examine (in each direction if both are being considered). The
default is 6.
StepSize=N
Step size along the reaction path, in units of 0.01 amu1/2 -Bohr. The default is 10.
MaxCyc=N
Sets the maximum number of steps in each geometry optimization. The default is 20.

Coordinate System Selection Options

MassWeighted
Follow the path in mass-weighted internal (Z-matrix) coordinates (which is equivalent to following the
200 Chapter 5. List of Gaussian Keywords

path in mass-weighted Cartesian coordinates). MW is a synonym for MassWeighted. This is the default.
Internal
Follow the path in internal (Z-matrix) coordinates without mass-weighting.
Cartesian
Follow the path in Cartesian coordinates without mass-weighting.

Convergence-Related Option
VeryTight
Tightens the convergence criteria used in the optimization at each point along the path. This option is
necessary if a very small step size along the path is requested.

Options For Generating Initial Force Constants

CalcFC
Specifies that the force constants be computed at the first point.
CalcAll
Specifies that the force constants be computed at every point. The projected vibrational frequencies for
motion are calculated for each optimized point on the path [453]. Note that these projected vibrational
frequencies are valid only for reaction paths computed in mass-weighted internal coordinates.

Specifying Alternate Isotopes

ReadIsotopes
This option allows you to specify alternatives to the default temperature, pressure, frequency scale factor
and/or isotopes – 298.15 K, 1 atmosphere, no scaling, and the most abundant isotopes (respectively). It is
useful when you want to rerun an analysis using different parameters from the data in a checkpoint file.
Be aware, however, that all of these can be specified in the route section (Temperature, Pressure and Scale
keywords) and molecule specification (the Iso parameter), as in this example:

#T Method/6-31G(d) JobType Temperature=300.0 · · ·

···

0 1
C(Iso=13)
···

ReadIsotopes input has the following format:

temp pressure [scale] Values must be real numbers.

isotope mass for atom 1
isotope mass for atom 2
···
isotope mass for atom n

Where temp, pressure, and scale are the desired temperature, pressure, and an optional scale factor for
frequency data when used for thermochemical analysis (the default is unscaled). The remaining lines hold
 5.49 LSDA 201

the isotope masses for the various atoms in the molecule, arranged in the same order as they appeared
in the molecule specification section. If integers are used to specify the atomic masses, the program will
automatically use the corresponding actual exact isotopic mass (e.g., 18 specifies 18 O, and Gaussian uses
the value 17.99916).

Restart Option
Restart
Restarts an IRCMax calculation which did not complete, or restarts an IRCMax calculation which did
complete, but for which additional points along the path are desired.

5.48.2 Availability
Analytic gradients are required for the IRC portion of the calculation (model1 above). Any non-compound
energy method and basis set may be used for model2.

5.48.3 Related Keywords

IRC, Opt, Freq

5.48.4 Examples
The following calculation will find the point on the HF/6-31G(d,p) reaction path where the B3LYP/6-
31G(d,p) energy is at its maximum:
# IRCMax(B3LYP/6-31G(d,p):HF/6-31G(d,p))
The Zero option will produce the data required for zero curvature variational transition state theory (ZC-
VTST) [509–512, 514, 517]. Consider the following route:
# IRCMax(MP2/6-311G(d):HF/6-31G(d),Zero,Stepsize=15,CalcAll)
This job will start from the HF/6-31G(d) TS and search along the HF/6-31G(d) IRC with a step size of 0.15
amu1/2 Bohr until the maximum of the MP2/6-311G(d) energy (including the HF/6-31G(d) ZPE) is bracketed.
The position along the HF/6-31G(d) IRC for this MP2/6-311G(d) TS will then be optimized. The output
includes all quantities required for the calculation of reaction rates using the ZC-VTST version of absolute rate
theory: TS moments of inertia, all real vibrational frequencies (HF/6-31G(d)), the imaginary frequency for
tunneling (fit to MP2/6-311G(d) + ZPE), and the total MP2/6-311G(d) + ZPE energy of the TS. Note if CalcAll
is not used then all these quantities (ZPE, frequencies, etc.) are only computed at the HF/6-31G(d) level and
the same quantities are used for all points in the IRCMax path.

5.49 LSDA
This method keyword requests a Local Spin Density Approximation calculation, using the Slater exchange
functional and the VWN correlation functional for the DFT calculation. It is equivalent to SVWN. Note that
LSDA is not uniquely defined in the literature. In fact, many differing but related methods are referred to using
this term. Other programs offering an LSDA method may use somewhat different functionals. For example,
some implement the functional specified by the SVWN5 keyword, while others use a correlation functional of
Perdew. While Gaussian offers this keyword for convenience, it is probably better practice to specify the exact
functional desired; see DFT Methods for full details on specifying and using Density Functional Methods in
Gaussian.
 202 Chapter 5. List of Gaussian Keywords

5.50 MaxDisk
The MaxDisk keyword specifies the amount of disk storage available for scratch data, in 8-byte words
(default). This value may also be followed by KB, MB, GB, TB, KW, MW, GW or TW (without intervening
spaces) to specify units of kilo-, mega-, giga- or tera-bytes or words. Normally, this is set for a site in the
Default.Route file.
Not all calculations can dynamically control their disk usage, so the effects of this keyword vary:
♢ SCF energy, gradient, and frequency calculations use a fixed amount of disk. This is quite small (only cubic
in the size of the system) and is not usually a limitation.
♢ MP2 energies and gradients obey MaxDisk, which must be at least 2ON2 .
♢ Analytic MP2 frequencies attempt to obey MaxDisk, but have minimum disk requirements.
♢ CI-Singles energies and gradients in the MO basis require about 4O2 N2 words of disk for a limited set of
transformed integrals. Additional scratch space is required during the transformation and this is limited
as specified by MaxDisk. This disk requirement can be eliminated entirely by performing a direct CI-
Singles calculation by using CIS=Direct.
♢ CID, CISD, CCD, BD, and QCISD energies also have a fixed storage requirement proportional to O2 N2 ,
with a large factor, but obey MaxDisk in avoiding larger storage requirements.
♢ CCSD, CCSD(T), QCISD(T), and BD(T) energies have fixed disk requirements proportional to ON3 which
cannot be limited by MaxDisk.
♢ CID, CISD, CCD, QCISD densities, and BD and CCSD densities and gradients have fixed disk requirements
of about N4 /2 for closed-shell and 3N4 /4 for open-shell.
♢ EOM-CCSD initially sets its space requirements to its minimum needs. If this amount is more than MaxDisk,
it obeys the latter at the expense of I/O and computation time.

5.51 MINDO3
The MINDO3 keyword requests a semi-empirical calculation using the MINDO3 Hamiltonian [518, 519]
method. No basis set keyword should be specified.

5.51.1 Availability
Energies, “analytic” gradients, and numerical frequencies. Restricted open-shell (RO) wavefunctions are
limited to optimizations using the Fletcher-Powell and pseudo-Newton-Raphson methods (the FP and EnOnly
options to Opt, respectively).

5.51.2 Examples
The MINDO3 energy appears in the output file as follows:
SCF Done: E(UMINDO3) = -8.08016620373 A.U. after 11 cycles
The energy is as defined by the MINDO3 model.

5.52 MNDO
The MNDO keyword requests a semi-empirical calculation using the MNDO Hamiltonian [519–527]
method. No basis set keyword should be specified.
 5.53 MM (Molecular Mechanics) Methods 203

5.52.1 Availability
Energies, “analytic” gradients, and numerical frequencies. Restricted open shell (RO) wavefunctions are
limited to optimizations using the Fletcher-Powell and pseudo-Newton-Raphson methods (FP and EnOnly,
respectively).

5.52.2 Examples
The MNDO energy appears in the output file as follows:
SCF Done: E(UMNDO) = -8.08016620373 A.U. after 11 cycles
The energy is as defined by the MNDO model.

5.53 MM (Molecular Mechanics) Methods

There are three Molecular Mechanics methods available in Gaussian. They were implemented for use
in ONIOM calculations, but they are also available as independent methods. No basis set keyword should be
specified with these keywords.
The following force fields are available:
♢ Amber: The Amber force field as described in [Cornell95]. The actual parameters (parm96.dat) have been
updated slightly since the publication of this paper. We use this current version from the Amber web site
(ambermd.org).
♢ Dreiding: The Dreiding force field as described in [Mayo90].
♢ UFF: The UFF force field as described in [Rappe92].

5.53.1 Availability
Analytic energies, gradients, and frequencies.

5.53.2 Atom Types & Charges

Molecular Mechanics Molecule Specifications
Molecular Mechanics calculations use atom types to determine the functions and parameters which make
up the force field. For a single element, such as carbon, there can be many different MM atom types. Which
one to use depends on aspects such as the hybridization, chemical environment, and so on.
Gaussian will attempt to assign atom types automatically for UFF and Dreiding calculations. However,
Amber calculations require that all atom types be explicitly specified within the molecule specification section,
as in these examples:

C-CT Specifies an SP3 aliphatic carbon atom, denoted by the Amber CT keyword.
C-CT-0.32 Specifies an SP3 aliphatic carbon atom with a partial charge of +0.32.
O-O-0.5 Specifies a carbonyl group oxygen atom (type O) with a partial charge of -0.5.

The atom type keyword is specified following the element symbol and a separating hyphen. Consult the
Amber paper [528] for definitions of atom types and their associated keywords.
As the second and third lines in the example illustrate, partial charges may also be specified, as the third
component of the atom description, preceded again by a hyphen separator. Partial atomic (point) charges are
used to compute the electrostatic interactions. Gaussian can assign these charges automatically using the QEq
 204 Chapter 5. List of Gaussian Keywords

formalism [529]. Request this by specifying the QEq option to the MM keyword: e.g., Dreiding=QEq. Note
that these charges depend on the geometry and are computed at the beginning of the calculation; however, they
are not updated during the course of an optimization or other process that changes the geometry.
Atom types and charges may also be provided for UFF and Dreiding calculations if desired. Be aware that
the automatic assignment of UFF and Dreiding atom types is only reliable for well-defined systems, and it is
often safer to specify them explicitly.
When using MM methods, and especially when you are modifying force field terms or defining new
ones (as discussed below), it is often necessary to specify the connectivity between atoms explicitly, using
Geom=Connectivity. Note that GaussView includes this input section automatically when it constructs input
files.

Charge Assignment-Related Options

Unless set in the molecule specification input, no charges are assigned to atoms by default when using any
molecular mechanics force field. Options are available to estimate charges at the initial point using the QEq
algorithm [529], under control of the following options, for any of the mechanics keywords:
QEq
Assign charges to all atoms using the QEq method [529]. OldQEq requests an older version which was
default in G09 Rev. C [530].
UnTyped
Assign QEq charges only to those atoms for which the user did not specify a particular type in the input.
UnCharged
Assign QEq charges only for atoms which have MM charge zero (i.e., all atoms which were untyped
or which were given a type but not a charge in the input), constraining the other atoms to retain their
specified charges.

5.53.3 Options
Parameter Precedence Options
Terminology: Gaussian contains built-in parameter sets for the built-in force fields listed above; these are
referred to as hard-wired parameters. Soft parameters are ones specified by the user in the input stream for
the current job (or a previous job when reading parameters from the checkpoint file). By default, when no
relevant option is given, the hard-wired parameters are the only ones used. This topic is discussed in detail in
Specifications tab.
HardFirst
Read additional parameters from the input stream, with hard-wired parameters having priority over the
read-in, soft ones. Hence, read-in parameters are used only if there is no corresponding hard-wired value.
Note that wildcard matches within the hard-wired parameter set take precedence over soft parameters,
even when the latter contains an exact match for the same item. Use SoftFirst if you want to override
hard-wired parameter matches.
SoftFirst
Read additional parameters from the input stream, with soft (read-in) parameters having priority over the
hard-wired values.
SoftOnly
5.53 MM (Molecular Mechanics) Methods 205

Read parameters from the input stream and use only them, ignoring hard-wired parameters.

Handling Multiple Parameter Specification Matches

Since parameters can be specified using wildcards (see the Specifying Force Fields tab), it is possible
for more than one parameter specification to match a given structure. The default is to abort if there are any
ambiguities in the force field. The following options specify other ways of dealing with multiple matches.
FirstEquiv
If there are equivalent matches for a required parameter, use the first one found.
LastEquiv
If there are equivalent matches for a required parameter, use the last one found.

Reading MM Parameters from the Checkpoint File

By default, when the geometry is read-in from the checkpoint file with Geom=Check or Geom=AllCheck,
any non-standard (soft) parameters present in the checkpoint file are also retrieved. These read-in parameters
are used with higher priority than corresponding hard-wired parameters, unless HardFirst is also specified. The
following options can be used to modify this default behavior.
ChkParameters
Read only the MM parameters from the checkpoint file. Any non-standard (soft) parameters present
in the checkpoint file are used with higher priority than corresponding hard-wired parameters, unless
HardFirst is also specified. Not valid with Geom=Check or Geom=AllCheck.
NewParameters
Ignore any parameters in the checkpoint file when reading the geometry.
Modify
Read additional parameter specifications and modifications after combining any soft parameters from the
checkpoint file and the hard-wired parameters (as controlled by the precedence options). This option
works analogously to Geom=Modify.

Printing MM Parameters
Print
By default, only the contributions to the energy are printed (i.e., from bond stretches, bends, electrostat-
ics, etc.) when #P is specified. The Print option will also print the energy contributions and the force
field parameters at the first geometry, and the energy contributions at later ones (since the parameters
don’t change). It will print two sets of parameters for ONIOM(MO:MM) since different parameters are
assigned for the model and real systems (i.e., since H may replace a C link atom).
Note that the parameters are printed for all atoms in the system, but not in a form suitable for input.
The internally stored parameters are already provided in the form of input files in the main Gaussian
directory (amber.prm, uff.prm, etc.), along with files for some force fields which are not stored internally
(amber98.prm and oplsaa.prm). Printing for all atoms in the current job is still useful because complex
rules are involved in deciding what parameters are actually applied to a given bond, dihedral, etc.

Switching Functions Options

VRange=N
Set the van der Waals cutoff to N Å. This is ROff if soft cutoffs are used, which is the default. N<0 for
 206 Chapter 5. List of Gaussian Keywords

hard cutoffs.
CRange=N
Set the Coulomb cutoff to N Å. Negative for hard cutoffs. The potential is (Qi Q j (1 − R2 /N 2 )2 )/R
CutRad=M
Use soft cutoffs with radius M (in Å), with either van der Waals or Coulomb if VRange or CRange was
set. Thus with N, M the soft cutoffs have ROn=N-M, ROff=N.
Switch=value
Switch=YK means use the York-Karplus function, which is the default. Switch=CHARMM means use
CHARMM-style switching for van der Waals. Switch=CHARMMSq means to use CHARMM-style
expression but with R2 instead of R for van der Waals switching. Switch=N means use switching function
number N.

5.53.4 MM Potential Functions

Gaussian offers a tremendous amount of flexibility to users that want to modify or otherwise customize
MM force fields. This section discusses the specifics of doing so, and it begins with some required background
information necessary for understanding the function and parameter input.
A basic MM potential function is usually of the form:
( )
2
∑ Kr (r − req ) + ∑ Kθ (θ − θeq ) +
2
E total = ∑ Vn
2 [1 + cos (nϕ − γ )] + ∑ Ai j
−
Bi j
+
qi q j
ε ri j
bonds angles dihedrals ri12j ri6j
i< j
stretch terms bend terms torsional terms non-bonded interactions
Molecular Mechanics Potential Function

As noted, the terms of the expansion are the stretch terms (bonds), bend terms (bond angles), torsional
terms (dihedral angles), and non-bonded interactions. The particular forms of the individual functions in this
equation are from the Amber force field, which uses simple harmonic functions for stretches and bends, a
cosine function for torsions, and the standard functions for electrostatic and van der Waals interactions. Other
force fields use different functions, and some include additional types of terms not included by Amber, such as
dipole interactions or stretch-bend couplings.
In order to evaluate the MM potential function, Gaussian needs to know which structures – stretches,
bends, and torsion – are present in the system, as well as the functions and parameters to be used for them. The
structures can be identified from the molecular connectivity. By default, Gaussian determines which atoms are
bonded and the corresponding bond orders (single, double, and so on). It does a good job when the input geom-
etry is reasonable and the bond orders (single, double, etc.) are all well defined. However, if the calculation is
started with a more approximate geometry, or if there are bonds whose orders are not easy to identify, it is safer
to specify the connectivity list explicitly in the input stream, using Geom=Connectivity.

Viewing the MM Functions

A useful way to begin consideration of this topic is to examine the output from a Gaussian MM job. Here
is the input file we used for an Amber calculation on methane:

#P Amber=Print Geom=Connectivity

Methane
5.53 MM (Molecular Mechanics) Methods 207

0 1
C-CT--0.4 -0.85 0.42 0.00
H-HC-0.1 -0.50 -0.57 0.00
H-HC-0.1 -0.50 0.93 0.87
H-HC-0.1 -0.50 0.93 -0.87
H-HC-0.1 -1.92 0.42 0.00

Note that the atoms types are CT for the carbon atom and HC for the hydrogen atoms. We have also
assigned partial charges to each atom.
Here is the portion of the output produced by Amber=Print in the job’s route section:

Atomic parameters: MM functions for single atoms.

Center VDW
1 1.9080 .1094000
2 1.4870 .0157000
3 1.4870 .0157000
4 1.4870 .0157000
5 1.4870 .0157000
Molecular mechanics terms: MM functions of 2 of more atoms.
NBDir 3 1 0 0 Non-bonded interactions master function.
HrmStr1 1-2 340.00 1.0900 Stretch terms.
HrmStr1 1-3 340.00 1.0900
HrmStr1 1-4 340.00 1.0900
HrmStr1 1-5 340.00 1.0900
HrmBnd1 2-1-3 35.00 109.50 Bend terms.
HrmBnd1 2-1-4 35.00 109.50
HrmBnd1 2-1-5 35.00 109.50
HrmBnd1 3-1-4 35.00 109.50
HrmBnd1 3-1-5 35.00 109.50
HrmBnd1 4-1-5 35.00 109.50
NBPair 2-1 3 1 0 0 -1.000 -1.000 Non-bonded interactions
NBPair 3-1 3 1 0 0 -1.000 -1.000 of close neighbors.
NBPair 3-2 3 1 0 0 -1.000 -1.000
NBPair 4-1 3 1 0 0 -1.000 -1.000
NBPair 4-2 3 1 0 0 -1.000 -1.000
NBPair 4-3 3 1 0 0 -1.000 -1.000
NBPair 5-1 3 1 0 0 -1.000 -1.000
NBPair 5-2 3 1 0 0 -1.000 -1.000
NBPair 5-3 3 1 0 0 -1.000 -1.000
NBPair 5-4 3 1 0 0 -1.000 -1.000

Atomic Parameters

Some MM functions depend only on the atom type of the atom in question. In our example, Amber in-
cludes the van der Waals interaction for each atom, and the resulting values are listed in the preceding output
under Atomic parameters. The center number corresponds to the atom position within the molecule specifica-
208 Chapter 5. List of Gaussian Keywords

tion. The DREIDING and UFF force fields contain only terms of this type.
Force Field Terms lists terms within the total potential that describe the interactions of multiple atoms. For
example, there are stretch terms involving each bonded pair of atoms (1-2, 1-3 and 1-4), computed via the func-
tion called HrmStr1, using a force constant value of 340 kcal/(mol-Å2 ) and an equilibrium bond length of 1.09
Å. These parameter values are determined from the atom types of centers 1 and 2: CT and HC (respectively).
The particular function and parameters are chosen as follows: from the connectivity, the program knows
that a bond exists between centers 1 and 2. The Amber force field calls for a stretch term between all bonded
pairs of atoms, and the various functions and parameters are stored in internal tables within the program. In the
simplest case, Gaussian uses the two atom types to look up functions and parameters to use. In this case, the
entry
HrmStr1 CT HC 340 1.09
is used since it corresponds to the two atom types in the C-H bond in methane. The force constant and equilib-
rium bond length specified in the entry are then used within the computation. When we look up this function in
the reference section below, we see that the actual term will be computed as ForceC ∗ (R − Req )2 where ForceC
is the force constant, Req is the equilibrium bond length and R is the bond length; in this case, this becomes
340.0*(R-1.09)2 .
The list of terms includes stretch terms for all bonded pairs of atoms and bend terms for all corresponding
bond angles.

Non-Bonded Interaction Terms

The remaining terms in the list are those corresponding to non-bonded interactions: contributions to the
potential arising from interactions between atoms which are not bonded. Before considering them specifically,
we need to look at how they are computed.
In general, the list of non-bonded terms is formed from all possible pairs of atoms, and thus the number
of terms scales quadratically with the number of atoms. However, interactions between atoms that are close
together, based on the number of bonds that separate them, are usually scaled down. Typically, one- and two-
bond separated interactions are scaled to zero (since these interactions are described by stretch and bend terms).
Similarly, three-bond separated interactions are scaled with a factor between zero and one, depending on the
force field. It is clear that for larger systems, the list of non-bonded terms can become very long. In most
MM programs, cutoffs are used the keep the list manageable. In Gaussian, we use a less common approach to
efficiently deal with the non-bonded interactions.
The total non-bonded energy in the system can be written as follows:

N j<i [ ]
E NB = ∑ ∑ svdWij E vdW
ij + sQ Q
E
ij ij
i j
N j<i [ ] N j<i [( ) ( ) ]
Q vdW E vdW + 1 − sQ E Q
= ∑ ∑ EivdW
j + E ij + ∑ ∑ 1 − sij ij ij ij
i j i j
all pairs “overcounted” pairs
Total Non-Bonded Energy Expression

Where E vdW and E Q are the van der Waals and electrostatic interactions between the two centers (respectively),
and the corresponding s values are the associated scaling factors.
The first equation is expressed in the usual form for the non-bonded interactions, and the second one is an
 5.53 MM (Molecular Mechanics) Methods 209

equivalent expression where all possible non-bonded interactions (regardless of distance) are evaluated without
scaling (first term) followed by subtraction of the overcounted pairs (second term).
This reformulation has significant computational advantages. The first term can be evaluated in an efficient
manner, using linear scaling and other techniques. In addition, most of the pairs in the second term give a zero
interaction (provided the system is not too small), because the scaling factor si j is 1 for most pairs. The program
simply keeps a list of those pairs that give non-zero interactions to compute the second term. The result is an
efficient algorithm that does not use cutoffs, and requires only a list whose length scales linearly with the size
of the system.
The functions NBDir and NBTerm are used when forming these two non-bonded interaction terms. As
the previous methane job output illustrates, a single NBDir function describes the complete set of interactions
between all pairs of atoms, i.e., the first term of the rewritten equation. The various NBTerm entries comprise
the second term in the equation. The final two parameters to these functions are the scale factors for van der
Waals and Coulomb interactions (respectively). In the methane example, both scale factors are 1 for all terms
since no atoms are separated by more than two bonds in methane, and the final non-bonded interaction is
accordingly 0.

5.53.5 Specifying Force Fields

Adding and Replacing Parameters
When hard-wired parameters are not available, either from incomplete tables or the introduction of new
atom types, they need to be specified in the input stream. Determining the appropriate parameters to use can be
challenging. They can often be found in the literature; otherwise they need to be derived from experimental or
accurate computational data (this topic is beyond the scope of our discussion here).
To specify new parameters, use the Amber=HardFirst keyword, and then add them to the input file in
a separate section. In this case, we define HrmBnd1 functions for the missing atom type sequences. The
2-methylpropene job then looks like:

# Amber=HardFirst

2-methylpropene

0 1
C-CM -2.53 0.19 0.00
molecule specification continues· · ·

HrmBnd1 CT CM CT 70.0 120.0

HrmBnd1 HA CM HA 40.0 120.0

The parameter values used in this example are a rough guess based on existing Amber parameters. The
HardFirst option indicates that the usual Amber hard-wired parameters tables are checked first for functions –
referred to as the hard parameters – and that functions defined in the input file are to be used only when no
match is present. With the SoftFirst option, one can replace parameters from the hard-wired set. Note that
the ordering specified by HardFirst and SoftFirst only matters when one or more functions is defined in both
parameter lists. Finally, the SoftOnly option indicates that the complete force field definition will be provided
210 Chapter 5. List of Gaussian Keywords

in the input file, ignoring the hard-wired set completely.

Specifying Missing Parameters

Consider the following molecule: 2-methylpropene. We’ve set up an Amber calculation for this system,
specifying the SP2 hybridized carbons as atom type CM, and the SP3 hybridized carbons as CT.

Figure 5.2: 2-MethylPropene

# Amber

2-methylpropene

0 1
C-CM -2.53 0.19 0.00
H-HA -2.00 -0.73 0.00
H-HA -3.60 0.19 0.00
C-CM -1.86 1.37 0.00
C-CT -2.63 2.70 0.00
H-HC -1.93 3.51 0.07
H-HC -3.24 2.76 -0.88
H-HC -3.24 2.76 0.85
C-CT -0.32 1.37 0.00
H-HC 0.03 1.87 -0.83
H-HC 0.03 1.87 0.81
H-HC 0.03 0.36 -0.00

When we run this job, the program terminates with the following error message:

Angle bend undefined between atoms 2 1 3

Angle bend undefined between atoms 5 4 9
MM function not complete

Atoms 2-1-3 correspond to types HA-CM-HA, and 5-4-9 correspond to CT-CM-CT. Even though the atom
types and the sequence are chemically reasonable, there are no entries for these bending terms in the hard-wired
5.53 MM (Molecular Mechanics) Methods 211

tables. The reason is that the Amber force field has been developed specifically for biochemical systems, in
which these particular sequences of atom types do not occur. Hence, the parameters have not been defined by
Amber. Note that Gaussian only checks if functions are found for all the stretches and bends; torsional and
other terms are simply left out of the total potential function if no entries exist in the tables.

Using External Parameter Files

It is possible to include MM function entries within an external file by replacing the entries within the
input file with the usual Gaussian include file mechanism: e.g., @oplsaa.prm. Parameter files for various force
fields are included within the main Gaussian directory (i.e., $g16root/g16). If you want to specify the entire
force field via an external file, use an input file like the following:

# UFF=SoftOnly

Read-in force field example

molecule specification

@$g16root/g16/oplsaa.prm

Note that the choice of a molecular mechanics keyword is arbitrary as the entire force field depends on the
read-in functions and parameters and not on any internal ones (in other words, specifying Amber would yield
the same result as UFF).

Wildcards within Function Specifications

Wildcards can be used in function specifications given in the input file. For example, this Amber bend
function specifies that all the bends with a central carbon atom of type CM will have the same parameter
values:
HrmBnd1 * CM * 70.0 120.0
One could also include a generic entry using wildcards as well as other more specific entries:
HrmBnd1 * CM * 70.0 120.0
HrmBnd1 HA CM HA 40.0 120.0
By default, the program uses the most specific entry that applies to a specific structure (here, a bond angle
centered on a CM carbon). Relative specificity is determined by the number of wildcards within an entry. If
there happen to be different entries that are equally specific, the program terminates with a multiple matching
entries error message. In such cases, you can direct the program to use either the first or last match with the
FirstEquiv or LastEquiv options, respectively. Be aware, however, that the multiple matching entries message
typically indicates some inconsistency in the soft parameter set which needs to be investigated and resolved.
Note that wildcards/entry specificity do not affect whether an entry from the hard-wired or soft set is used.
Thus, when SoftFirst is specified, an entry in the input file with three wildcards will be used even if there is an
entry containing the exact atom type sequence in question within the hard-wired set.

Substructures: Using Bond Orders and Other Structural Features to Select Parameters
Substructures provide a mechanism for using additional structural information like bond orders and bond
angle values to determine which parameters are used. Consider butadiene (illustrated below). The carbon atoms
212 Chapter 5. List of Gaussian Keywords

are all of type CM, but two bonds are formally double, and one is single. By default, Amber uses the same force
constant and equilibrium bond length for the stretching term for each defined atom type combination. However,
substructures can be used to assign different values for the different types of bonds.
Substructure numbers are appended to the function name, separated by a hyphen: e.g., HrmStr-1, HrmStr-
2, and so on. In this case, the numbers refer to the bond order (see substructure definitions below). Sometimes,
multiple substructure suffixes will be used (e.g., AmbTrs-1-2).
The butadiene calculations input file is shown below the molecular structure:

Figure 5.3: Butadiene Molecule

# Amber=SoftFirst Geom=Connectivity

Butadiene

0 1
C-CM -2.49 -0.07 0.00
H-HA -1.96 -1.00 0.00
H-HA -3.56 -0.07 0.00
C-CM -1.82 1.09 0.00
H-HA -2.35 2.02 0.00
C-CM -0.28 1.09 0.00
H-HA 0.24 0.16 0.00
C-CM 0.39 2.26 -0.00
H-HA -0.13 3.19 0.00
H-HA 1.46 2.26 -0.00

1 2 1.0 3 1.0 4 2.0

2
3
4 5 1.0 6 1.0
5
6 7 1.0 8 2.0
7
8 9 1.0 10 1.0
9
10
5.53 MM (Molecular Mechanics) Methods 213

HrmBnd1 HA CM HA 40.0 120.0 Parameters values for illustration purposes only!

HrmBnd1 CM CM CM 70.0 120.0
HrmStr1-1 CM CM 350.0 1.51 Substructures: bond order-specific stretch parameters.
HrmStr1-2 CM CM 500.0 1.37

This example specifies a larger force constant value and a smaller equilibrium bond length for double
bonds for use with the HrmStr1 function.
Note that the values used for the parameters in this example are only for illustration purposes only. In fact,
for a production calculation, we would also need to define torsional parameters that are specific for single or
double central bonds, using the same substructures mechanism.
Besides the bond order, other examples of substructures are whether the term lies in a cyclic structure,
how many hydrogen atoms are connected to it, and the like. Note that multiple substructure suffixes can be
used with many functions: e.g., HrmStr1-1-0-4.
Substructure slots have relatively consistent meanings in the contexts of different functions. The first
substructure suffix defines the bond order or angle range, the second specifies the number of atoms bonded to
the current atom, and the third describes the ring environment (if any). A 0 value in any substructure slot acts
are a wildcard/placeholder and means that the particular substructure is to be ignored for that entry. Unneeded
terminal substructures can be similarly set to 0 or be simply omitted.
The following substructure applies to functions that depend only on the atom type:

Third substructure: ring context (the first and second substructures must be 0):
-0-0-1 None of the following ring contexts apply
-0-0-3 Atom is in a 3-membered ring
-0-0-4 Atom is in a 4-membered ring
-0-0-5 Atom is in a 5-membered ring

The following substructures apply to functions related to bond stretches:

First substructure: bond order

-0 Ignore this substructure (substructure “wildcard”)
-1 Single bond: 0.00 ≤ bond order < 1.50
-2 Double bond: 1.50 ≤ bond order < 2.50
-3 Triple bond: bond order ≥ 2.50
Third substructure: ring context (if used, the second substructure must be 0):
-x-0-1 None of the following ring contexts apply
-x-0-3 Bond is in a 3-membered ring
-x-0-4 Bond is in a 4-membered ring
-x-0-5 Bond is in a 5-membered ring

The following substructures apply to functions for bond angles (angle values are in degrees):

First substructure: angle value range

-1 0o ≤ θ ≤ 45o
-2 45o < θ ≤ 135o
214 Chapter 5. List of Gaussian Keywords

-3 135o < θ ≤ 180o

Second substructure: numbers of bonded atoms
-x-0 Ignore this substructure (substructure “wildcard”)
-x-n n is the number of atoms bonded to the central atom
Third substructure: ring context
-x-y-0 Ignore this substructure (substructure “wildcard”)
-x-y-1 None of the following ring contexts apply
-x-y-3 Bend is in a 3-membered ring
-x-y-4 Bend is in a 4-membered ring
-x-y-5 Bend is in a 5-membered ring
Fourth substructure: number of bonded hydrogens
x-y-z-n There are n+1 hydrogen atoms bonded to the central atom (other than ones compris-
ing the bond angle itself)

The following substructures apply to functions involving dihedral angles.

First substructure: bond order

-0 Skip this substructure (substructure “wildcard”)
-1 Single central bond: 0.00 ≤ bond order < 1.50
-2 Double central bond: 1.50 ≤ bond order < 2.50
-3 Triple central bond: bond order ≥ 2.50
Second substructure: bond type of the central bond
-x-0 Skip this substructure (substructure “wildcard”)
-x-1 Resonance central bond (1.30 ≤ bond order ≤ 1.70)
-x-2 Amide central bond (priority over resonance)
-x-3 Other central bond type
Third substructure: ring context
-x-y-1 None of the following ring contexts apply
-x-y-4 Dihedral is in a 4-membered ring
-x-y-5 Dihedral is in a 5-membered ring

For example, HrmStr1-2-0-4 specifies that the HrmStr1 term applies only to a stretch that involves a
double bond that lies in a four-membered ring (compare to HrmStr1-2 which applies to all double bonds). A
substructure value of zero is similar to a wildcard: HrnStr1-0-0-4 specifies that the term applies to a stretch of
any bond order, but it must be in a four-membered ring.
Note that substructures are not always needed. Some functions explicitly include bond orders and similar
structural information within their definitions. For example, the HrmStr3 stretch term from the UFF force field
includes the bond order as its third parameter. This parameter can be passed to this function during a UFF
calculation for each bond by specifying -1.0 as the value, using a specification like the following in the input
file (and the appropriate option to the UFF keyword):
HrmStr3 * * -1.0 0.1332
5.53 MM (Molecular Mechanics) Methods 215

Defining New Atom Types

Gaussian understands the standard MM atom types from the Dreiding, UFF, and Amber force fields.
However, when a system is studied that these force fields are not parametrized for, none of the available atom
types may be suitable. In that case, one can define a new atom type simply by using a new atom type label
within the molecule specification. Naturally, since any new atom types will not exist in the hard-wired tables,
you will need to also define all required functions using them within the input file.

The Non-Bonded Interaction Master Function

As we’ve seen, specifying non-bonded interaction terms can be quite lengthy, requiring many NBTerm
terms. When non-bonded interactions are specified in the input (using one of the options to the MM keyword),
they can be specified using the NonBon function. This function uses a single entry to define the non-bonded
interaction, and it is expanded automatically by the program into the appropriate NBDir and NBTerm entries.
This function has the following general form:
NonBon V-Type C-Type V-Cutoff C-Cutoff VScale1 VScale2 VScale3 CScale1 CScale2 CScale3
V-Type and C-Type are integers indicating the kind of van der Waals and Coulomb interactions to be used
(respectively). The remaining terms are cutoff values and three scale factors for each of the two interaction
types; the latter are scale factors for atoms separated by 1, 2 and 3 or more bonds (respectively). When any
scale factor is <0, a scale factor of 1.0/|scale-factor| is used.
As an example, here is the function used for the standard Amber force field:
NonBon 3 1 0 0 0.0 0.0 0.5 0.0 0.0 -1.2
This function specifies the Amber arithmetic van der Waals interaction, 1/R Coulomb interaction, and no cut-
offs. Van der Waals interactions are scaled by 0.5 for atoms more than 2 bonds distant and are removed for
nearer pairs. Coulomb interactions are scaled by 1.0/1.2 for atoms more than 2 bonds distant and are also
removed for nearer pairs.

Global Parameters
In some cases, a parameter needed for the potential function is not related to a specific atom type at all.
One example is the dielectric constant. For such cases, we use global parameters: defined values which may be
used as parameters within potential functions. Any defined global parameters are listed in the MM force field
definition section of the output (requested with the Print option). Here is an example definition of the dielectric
constant:
Dielc 78.39
Global parameters also can be specified in vector or matrix format. The following extract from the MM2
force field definition illustrates the use of a matrix in functions which specify the shift of the hydrogen (i.e.,
interatomic distance scaling) when calculating van der Waals interactions:

VDWShf1 * 1 0.0 By default, use index value 1 with VDWShf2

VDWShf1 MM5 2 -1.0 Use index value 2 for atom type MM5
VDWShf1 MM36 3 -1.0 Use index value 3 for atom type MM36
VDWShf2 1 2 0.915 Scale factor: matrix element (1,2)
VDWShf2 1 3 0.915 Scale factor: matrix element (1,3)

We’ll consider these two functions in reverse order. VDWShf2 sets up a lower triangular matrix of scale
216 Chapter 5. List of Gaussian Keywords

factors for the interatomic distance. The elements (1,2) and (1,3) are both set to 0.915; the other elements –
(1,1), (2,2), (2,3) and (3,3) – are left as the default value, meaning that the distance is unscaled in the van der
Waals interaction computation. Note that this formulation is independent of atom type.
The VDWShf1 function defines which matrix elements to use for various atom types. The first entry
specifies the default index value as 1, and the remaining two entries specify index values 2 and 3 for atom types
MM5 and MM36. The third parameter to this function specifies the second center involved in the interaction.
In the first entry, the 0.0 value functions as a wildcard, while in the other two entries, the value of -1 tells the
program to enter the appropriate center automatically.
These functions result in only bonds involving an atom of type MM5 (H) or MM36 (D) and another of
a different type being shifted. When these functions are evaluated, interactions of type MM5-X use element
(1,2) and ones of type MM36-X use (1,3). Interactions involving other types use (1,1), while MM5-MM5,
MM5-MM36 and MM36-MM36 use (2,2), (2,3) and (3,3), respectively – all of which use unscaled interatomic
distances.
Using this mechanism, parameter specification is much clearer and compact. Without it, an entry for every
pair of atoms would have been needed to achieve the same goal.

Step-Down Tables
Wildcards provide a mechanism for specifying generic parameters/defaults that do not explicitly depend
on each of the atom types involved in a particular term. Step-down tables have the same purpose, but are
more sophisticated. Consider the following example, which is taken from the UFF force field. In these entries,
the UseTable and StepDown entries are not potential functions and do not contain parameters, but instead
describe the step-down mechanism that is used to process entries that do refer to potential functions and contain
parameters.
In the following example, the first set of UFFBnd3 lines define potential functions, while the UFFBnd2
lines and the second set of UFFBnd3 lines use the step-down mechanism:

UseTable UFFBnd2 #3 Specify step-down table used for specified functions

UseTable UFFBnd3 #3
StepDown UFFBnd2 0 1 0 Matching rules for specified functions
StepDown UFFBnd2 0 2 0
StepDown UFFBnd3 0 1 0
StepDown UFFBnd3 0 2 0
Table #3 C_R Trig Define alternate atoms types
Table #3 N_R Trig
Table #3 H_ Lin
Table #3 Li Lin
UFFBnd3 0 C_3 0 109.471 -1.0 -1.0 0.1332 Functions defined with
UFFBnd3 0 N_3 0 106.700 -1.0 -1.0 0.1332 explicit atom types
UFFBnd3 0 N_2 0 111.200 -1.0 -1.0 0.1332
UFFBnd3 0 O_3 0 104.510 -1.0 -1.0 0.1332
UFFBnd2-0-2 0 Lin 0 2 -1.0 -1.0 0.1332 Functions defined with step-
UFFBnd2-0-3 0 Trig 0 3 -1.0 -1.0 0.1332 down types & substructures
UFFBnd3-0-3 0 Lin 0 180.0 -1.0 -1.0 0.1332
UFFBnd3-0-4 0 Lin 0 180.0 -1.0 -1.0 0.1332
UFFBnd3-0-5 0 Lin 0 180.0 -1.0 -1.0 0.1332
 5.53 MM (Molecular Mechanics) Methods 217

UFFBnd3-0-6 0 Lin 0 180.0 -1.0 -1.0 0.1332

UFFBnd3-0-2 0 Trig 0 120.0 -1.0 -1.0 0.1332
UFFBnd3-0-4 0 Trig 0 120.0 -1.0 -1.0 0.1332
UFFBnd3-0-5 0 Trig 0 120.0 -1.0 -1.0 0.1332
UFFBnd3-0-6 0 Trig 0 120.0 -1.0 -1.0 0.1332

H_ and N_R are UFF atom types in the UFF force field. If there is a bond angle involving such atoms in
the molecule – H_-N_R-H_ – the program needs to determine the appropriate function and parameters to use.
First, it determines the appropriate step-down tables for the available bend function. In this example, table #3
is used for both available bend functions: UFFBnd2 and UFFBnd3.
The Table entries define alternate types for specified atom types. Typically, they map many specific atom
types to a more generic pseudo-type (e.g., Lin and Trig in the example). These alternate types allow wide-
ranging default values to be specified for function parameters, effectively enabling undefined parameters to be
automatically estimated.
The StepDown entries specify matching rules for selecting specific function entries. In this example, both
bend functions use the same two entries: 0 1 0 and 0 2 0. They specify that first the program should look for an
entry specifying the original atom type as the center atom (zero values function as wild cards). If no such entry
is present, then an entry specifying the first alternate atom type as the central atom should be used.
In the example, the program would look for bend functions specifying N_R as the central atom, but none
is defined. Next, it would look for functions with Trig as the type of the central atom. There are four such
functions: UFFBnd2-0-3 and UFFBnd3-0 with second substructures 2, 4 and 5. Which one is used will depend
on the number of atoms bonded to the central nitrogen atom.
Note that in practice, step-down tables can specify multiple alternates for the various atom types and also
include many more types mapped to each listed alternate.
When a step-down table is in use, then any wildcards within other function specifications are ignored. In
other words, of you choose to use a step-down table, then wildcards cannot be used anywhere else.

5.53.6 Force Field Terms

Preliminary Notes
♢ Units: Unless otherwise indicated, distances are in Angstroms, angles are in degrees, energies are in kcal/mol
and charges are in atomic units.
♢ In equations, R refers to distances and θ refers to angles. Numerical and variable subscripts refer to centers,
and “eq” refers to equilibrium: e.g., R12 and Ri j are the bond distances between atoms 1 and 2 and atoms
i and j (respectively), Ri is the bond radii for atom i, Req and θeq are the equilibrium bond length and bond
angle, and Req12 is the equilibrium bond length between atoms 1 and 2 (typically used in an angle term).
♢ Wildcards may be used in any function definition. They are indicated by a 0 or an asterisk.
♢ Function equivalencies to those found in standard force fields are indicated in parentheses following the
description.
VDW : van der Waals parameters, used for NBDir and NBTerm (See MMFF94 below for MMFF94-type van
der Waals parameters)
VDW Atom-type Radius Well-depth
VDW94 : MMFF94 type van der Waals parameters (used for NBDir and NBTerm)
VDW94 Atom-type Atomic-pol NE Scale1 Scale2 DFlag
218 Chapter 5. List of Gaussian Keywords

Atomic-pol Atomic polarizability (Angstrom3 ).

NE Slater-Kirkwood effective number of valence electrons (dimensionless).
Scale1 Scale factor (Angstrom1/4 ).
Scale2 Scale factor (dimensionless).
DFlag 1.0 for donor type atom, 2.0 for acceptor type, otherwise 0.0.

Buf94 : MMFF94 electrostatic buffering

Buf94 Atom-type Value
NonBon : Non-bonded interaction master function. This function will be expanded into pairs and a direct
function (NBDir and NBTerm) before evaluation of the MM energy.
NonBon V-Type C-Type, V-Cutoff C-Cutoff VScale1 VScale2 VScale3 CScale1 CScale2 CScale3
V-Type is the van der Waals type:

0 No van der Waals

1 Arithmetic (as for Dreiding)
2 Geometric (as for UFF)
3 Arithmetic (as for Amber)
4 MMFF94-type van der Waals
5 MM2-type van der Waals
6 OPLS-type van der Waals

C-Type is the Coulomb type:

0 No Coulomb
1 1/R
2 1/R2
3 1/R buffered (MMFF94)
10 Form dipole-dipole interactions without cutoffs

V-Cutoff and C-Cutoff are the van der Waals and Coulomb cutoffs (respectively):

0 No cutoff
>0 Hard cutoff
<0 Soft cutoff

Vscale1-3 are van der Waals scale factors for 1- to 3-bond separated pairs. CScale1-3 are Coulomb scale
factors for 1- to 3-bond separated pairs. If any scale factor < 0.0, then 1.0/|scale-factor| scaling is used
(e.g., a scale factor specified as -1.2 results in scaling of 1.0/1.2).
NBDir : Coulomb and van der Waals direct (evaluated for all atom pairs)
NBDir V-Type C-Type V-Cutoff C-Cutoff
V-Type, C-Type, V-Cutoff, and C-Cutoff as above.
NBTerm : Coulomb and van der Waals single term cutoffs
NBTerm Atom-type1 Atom-type2 V-Type C-Type V-Cutoff C-Cutoff V-Scale C-Scale
5.53 MM (Molecular Mechanics) Methods 219

V-Type, C-Type, V-Cutoff, C-Cutoff, V-Scale, and C-Scale as above.

AtRad : Atomic single bond radius
AtRad Atom-type Radius
EffChg : Effective charge (UFF)
EffChg Atom-type Charge
EleNeg : GMP Electronegativity (UFF)
EleNeg Atom-type Value
Table : Step down table
Table Original-atom-type Stepping-down-type(s)
HrmStr1 : Harmonic stretch I (Amber 1): ForceC ∗ (R − Req )2
HrmStr1 Atom-type1 Atom-type2 ForceC Req

ForceC Force constant

Req Equilibrium bond length

HrmStr2 : Harmonic stretch II (Dreiding 4a): ForceC ∗ [R − (Ri + R j − Delta)]2

HrmStr2 Atom-type1 Atom-type2 ForceC Delta

ForceC Force constant

Delta Delta

Ri and R j are atomic bond radii specified with AtRad.

HrmStr3 : Harmonic stretch III (UFF 1a): k ∗ (R − Ri j )2
Equilibrium bond length Ri j = (1 − PropC ∗ lnBO) ∗ (Ri + R j ) − Ren
Force constant k = 664.12 ∗ Zi ∗ Z j /(R3i j )
Electronegativity correction Ren = Ri ∗ R j ∗ [SQRT (Xi ) − SQRT (X j )]2 /(Xi ∗ Ri + X j ∗ R j )
HrmStr3 Atom-type1 Atom-type2 BO PropC

BO Bond order (if <0, it is determined on-the-fly)

PropC Proportionality constant

Ri and R j are atomic bond radii defined with AtRad. Xi and X j are GMP electronegativity values defined
with EleNeg. Zi and Z j are the effective atomic charges defined with EffChg.
MrsStr1 : Morse stretch I (Amber): DLim ∗ (e−a(R−Req ) − 1)2 where a = SQRT(ForceC/DLim)
MrsStr1 Atom-type1 Atom-type2 ForceC Req DLim

ForceC Force constant

Req Equilibrium bond length
DLim Dissociation limit

MrsStr2 : Morse stretch II (Dreiding 5a): DLim ∗ (e−a(Ri +R j −Delta) − 1)2 where a = SQRT(ForceC/DLim)
MrsStr2 Atom-type1 Atom-type2 ForceC Delta DLim

ForceC Force constant

Delta Delta
220 Chapter 5. List of Gaussian Keywords

DLim Dissociation limit

Ri and R j are atomic bond radii defined with AtRad.

MrsStr3 : Morse stretch III (UFF 1b): BO ∗ DLim ∗ (e−a(R−Ri j ) − 1)2 where a = SQRT(k/[BO*DLim])
Equilibrium bond length Ri j = (1 − PropC ∗ lnBO) ∗ (Ri + R j ) − Ren
Force constant k = 664.12 ∗ Zi ∗ Z j /(R3i j )
Electronegativity correction Ren = Ri ∗ R j ∗ [SQRT (Xi ) − SQRT (X j )]2 /(Xi ∗ Ri + X j ∗ R j )
MrsStr3 Atom-type1 Atom-type2 BO PropC DLim

BO Bond order (if <0, it is determined on-the-fly)

PropC Proportionality constant
DLim Dissociation limit

Ri and R j are atomic bond radii defined with AtRad. Xi and X j are GMP electronegativity values defined
with EleNeg. Zi and Z j are the effective atomic charges defined with EffChg.
QStr1 : Quartic stretch I (MMFF94 2): (Req /2) ∗ (R − ForceC)2 ∗ [1 +CStr ∗ (R − ForceC + (7/12) ∗CStr2 ∗
(R − ForceC)2 ]
QStr1 Atom-type1 Atom-type2 ForceC Req CStr

ForceC Force constant (md-Angstrom−1 )

Req Equilibrium bond length
CStr Cubic stretch constant (Angstrom−1 )

UFFVOx : Atomic torsional barrier for the oxygen column (UFF 16)
UFFVOx Atom-type Barrier
UFFsp3 : Atomic SP3 torsional barrier (UFF 16)
UFFVsp3 Atom-type Barrier
UFFVsp2 : Atomic SP2 torsional barrier (UFF 17)
UFFVsp2 Atom-type Barrier
HrmBnd1 : Harmonic bend (Amber 1): ForceC ∗ (θ − θeq )2
HrmBnd1 Atom-type1 Atom-type2 Atom-type3 ForceC θeq

ForceC Force constant (in kcal/(mol*rad2 ))

θeq Equilibrium angle

HrmBdn2 : Harmonic Bend (Dreiding 10a): [ForceC/ sin(θeq

2 )] ∗ (cos(θ ) − cos(θ ))2
eq

HrmBnd2 Atom-type1 Atom-type2 Atom-type3 ForceC θeq

ForceC Force constant

θeq Equilibrium angle

LinBnd1 : Dreiding Linear Bend (Dreiding 10c): ForceC ∗ (1 + cos(θ ))

LinBnd1 Atom-type1 Atom-type2 Atom-type3 ForceC

ForceC Force constant

5.53 MM (Molecular Mechanics) Methods 221

UFFBnd3 : UFF 3-term bend (UFF 11): k ∗ (C0 +C1 ∗ cos(θ )) +C2 ∗ cos(2θ ) where
C2 = 1/(4 ∗ sin(θeq
2 )),

C1 = −4 ∗C2 ∗ cos(θeq ) and

C0 = C2 ∗ (2 ∗ cos(θeq
2 ) + 1)

Force constant: k = 664.12 ∗ Zi ∗ Zk ∗ (3 ∗ Ri j ∗ R jk ∗ (1 − cos(θeq

2 )) − cos(θ ) ∗ R2 )/R5
eq ik ik
UFFBnd3 Atom-type1 Atom-type2 Atom-type3 θeq BO12 BO23 PropC

θeq Equilibrium angle

BO12 Bond order for Atom-type1 - Atom-type2 (when <0, it is determined on-
the-fly)
BO23 Bond order for Atom-type2 - Atom-type3 (when <0, it is determined on-
the-fly)
PropC Proportionality constant

Ri , R j and Rk are atomic bond radii defined with AtRad. Xi , X j and Xk are GMP electronegativity defined
with EleNeg. Zi , Z j and Zk are effective atomic charges defined with EffChg.
UFFBnd2 : UFF 2-term bend (UFF 10): [k/(Per2 )] ∗ [1 − cos(Per ∗ θ )]
Force constant: k = 664.12 ∗ Zi ∗ Zk ∗ (3 ∗ Ri j ∗ R jk ∗ (1 − cos(Per2 )) − cos(Per) ∗ R2ik )/R5ik
UFFBnd2 Atom-type1 Atom-type2 Atom-type3 Per BO12 BO23 PropC

Per Periodicity: 2 for linear, 3 for trigonal, 4 for square-planar.

BO12 Bond order for Atom-type1 - Atom-type2 (when <0, it is determined on-
the-fly)
BO23 Bond order for Atom-type2 - Atom-type3 (when <0, it is determined on-
the-fly)
PropC Proportionality constant

Ri , R j and Rk are atomic bond radii defined with AtRad. Xi , X j and Xk are GMP electronegativity defined
with EleNeg. Zi , Z j and Zk are effective atomic charges defined with EffChg.
ZeroBnd : Zero bend term: used in rare cases where a bend is zero. This term is needed for the program not
to protest about undefined angles.
ZeroBnd Atom-type1 Atom-type2 Atom-type3
CubBnd : Cubic bend (MMFF94 3): (ForceC/2) ∗ (1 +CBend ∗ (θ − θeq )) ∗ (θ − θeq )2
CubBnd Atom-type1 Atom-type2 Atom-type3 ForceC θeq CBend

ForceC Force constant (in md*Angstrom/rad2 )

θeq Equilibrium angle
CBend Cubic Bend constant (in deg−1 )

LinBnd2 : MMFF94 Linear Bend (MMFF94 4): ForceC ∗ (1 + cos(θ ))

LinBnd2 Atom-type1 Atom-type2 Atom-type3 ForceC

ForceC Force constant (md)

222 Chapter 5. List of Gaussian Keywords

AmbTrs : Amber torsion (Amber 1): ∑i=1,4 (Magi ∗ [1 + cos(i ∗ θ − POi )])/NPaths
AmbTrs Atom-type1 A-type2 A-type3 A-type4 PO1 PO2 PO3 PO4 Mag1 Mag2 Mag3 Mag4 NPaths

PO1 –PO4 Phase offsets

Mag1 –Mag4 V/2 magnitudes
NPaths Number of paths. When zero or less, determined on-the-fly.

DreiTrs : Dreiding torsion (Dreiding 13): V ∗ [1 − cos(Period ∗ (θ − PO))]/(2 ∗ NPaths)

DreiTrs Atom-type1 Atom-type2 Atom-type3 Atom-type4 V PO Period NPaths

V Barrier height
PO Phase offset
Period Periodicity
NPaths Number of paths. When zero or less, determined on-the-fly.

UFFTorC : UFF torsion with constant barrier height (UFF 15): [V /2] ∗ [1 − cos(Period ∗ PO) ∗ cos(V ∗
θ )]/NPaths
UFFTorC Atom-type1 Atom-type2 Atom-type3 Atom-type4 Period PO V NPaths

Period Periodicity
PO Phase offset
V Barrier height
NPaths Number of paths. When zero or less, determined on-the-fly.

UFFTorB : UFF torsion with bond order based barrier height (UFF 17): [V /2] ∗ [1 − cos(Period ∗ PO) ∗
cos(Period ∗ θ )]/NPaths where V = 5 ∗ SQRT (U j ∗Uk ) ∗ [1 + 4.18 ∗ Log(BO12 )]
UFFTorB Atom-type1 Atom-type2 Atom-type3 Atom-type4 Period PO BO12 NPaths

Period Periodicity
PO Phase offset
BO12 Bond order for Atom-type1 – Atom-type2 (when <0, it is determined on-
the-fly)
NPaths Number of paths. When zero or less, determined on-the-fly.

U j and Uk are atomic constants defined with UFFVsp2.

UFFTor1 : UFF torsion with atom type-based barrier height (UFF 16): [V /2] ∗ [1 − cos(Period ∗ PO) ∗
cos(Period ∗ θ )]/NPaths where V = SQRT (V j ∗Vk )
UFFTor1 Atom-type1 Atom-type2 Atom-type3 Atom-type4 Period PO NPaths

Period Periodicity
PO Phase offset
NPaths Number of paths. When zero or less, determined on-the-fly.

V j and Vk are atomic constants defined with UFFVsp3.

UFFTor2 : UFF torsion with atom type based barrier height (UFF 16) (differs from UFFTor1 in the atomic
5.53 MM (Molecular Mechanics) Methods 223

parameter that is used): [V /2] ∗ [1 − cos(Period ∗ PO) ∗ cos(Period ∗ θ )]/NPAths where V = SQRT (V j ∗
Vk )
UFFTor2 Atom-type1 Atom-type2 Atom-type3 Atom-type4 Period PO NPaths

Period Periodicity
PO Phase offset
NPaths Number of paths. When zero or less, determined on-the-fly.

V j and Vk are atomic constants defined with UFFVOx.

VDWDreiTRS : Dreiding special torsion for compatibility with Gaussian 98 code. During processing, it is
replaced with DreiTRS, with the following parameters:
♢ If there are three atoms bonded to the third center and the fourth center is H, it is removed.
♢ If there are three atoms bonded to the third center, and at least one of them is H, but the fourth center
is not H, then these values are used: V=4.0, PO=0.0, Period=3.0, and NPaths=-1.0.
♢ Otherwise, these values are used: V=1.0, PO=0.0, Period=6.0, and NPaths=-1.0.
OldTor Atom-type1 Atom-type2 Atom-type3 Atom-type4
ImpTrs : Improper torsion (Amber 1): Mag ∗ [1 + cos(Period ∗ (θ − PO))]
ImpTrs Atom-type1 Atom-type2 Atom-type3 Atom-type4 Mag PO Period

Mag V/2 Magnitude

PO Phase offset
Period Periodicity

Wilson : Three term Wilson angle (Dreiding 28c, UFF 19): ForceC ∗ (C1 +C2 ∗ cos(θ ) +C3 ∗ cos(2θ )) aver-
aged over all three Wilson angles θ
Wilson Atom-type1 Atom-type2 Atom-type3 Atom-type4 ForceC C1 C2 C3

ForceC Force constant

C1, C2, C3 Coefficients

HrmWil1 : Harmonic Wilson angle I (MMFF94 6): (ForceC/2) ∗ (θ 2 ) summed over all 3 Wilson angles θ
HrmWil1 Atom-type1 Atom-type2 Atom-type3 Atom-type4 ForceC

ForceC Force constant

MM2Wil : MM2 Wilson sixth order bend (MM2): ∑i=1,2,3 (ForceCi /2) ∗ (θi2 ) ∗ [1 + 6Bend ∗ (θi4 )]
MM2Wil Atom-type1 Atom-type2 Atom-type3 Atom-type4 ForceC1 ForceC2 ForceC3 6Bend

ForceC1 – ForceC3 Force constants

6Bend Sixth order bend constant (in deg−4 )

StrBnd : Stretch-bend (MMFF94 5): (ForceC1 ∗ (R12 − Req12 ) + ForceC2 ∗ (R23 − Req23 )) ∗ (θ − θeq )
StrBnd Atom-type1 Atom-type2 Atom-type3 ForceC1 ForceC2 Req12 Req23 θeq

ForceC1, ForceC2 Force constants

224 Chapter 5. List of Gaussian Keywords

Req12 , Req23 Equilibrium bond lengths (if <0, retrieved from the appropriate stretch
terms)
θeq Equilibrium angle

CubStr1 : Cubic Stretch 1 (MM2): (ForceC/2) ∗ (1 −CStr ∗ (R − Req )) ∗ (R − Req )2

CubStr1 Atom-type1 Atom-type2 ForceC Req CStr

ForceC Force constant

Req Equilibrium bond length
CStr Cubic stretch constant (Angstrom−1 )

SixBnd1 : Sixth order bend (MM2): (ForceC/2) ∗ (θ − θeq )2 (1 + 6Bend ∗ (θ − θeq )4 )

SixBnd1 Atom-type1 Atom-type2 Atom-type3 ForceC θeq 6Bend

ForceC Force constant

θeq Equilibrium angle
6Bend Sixth order bend constant (in deg−4 )

MM2Tors : MM2 Torsional (MM2): En1/2(1 + cos θ ) + En2/2(1 − cos 2θ ) + En3/2(1 + cos 3θ )
MM2Tors Atom-type1 Atom-type2 Atom-type3 Atom-type4 En1 En2 En3

En1 – En3 Energies

MM2VDW : Parameters for the MM2 van der Waals function (MM2)
MM2VDW Par1 Par1 Par3 Par4 Par5

Par1 – Par5 Parameters

VDWX : Matrix with van der Waals parameters (MM2). These values do not depend on atom types, and
can be used as alternatives for the atomic parameters, as needed in the MM2 force field (see discussion
above).
VDWX Index1 Index2 Radius Well-depth IsDef

IsDef Indicates whether the pair (1.0) has or (0.0) has not been defined.

VDWI : Atomic indices, used to refer to the matrix in VDWXM (MM2)

VDWI Atom-type Index
VDWShf2 : Matrix with parameters for atom shifting in the van der Waals calculation (MM2)
VDWShf2 Index1 Index2 Shift
VDWShf1 : Atomic indices into the matrix in VDWShf2 (MM2)
VDWShf1 Atom-type Index BondTo

BondTo Center bonded to (if -1.0, determined by program).

SixBndI : Sixth order bend (MM2): (ForceC/2) ∗ (θ − θeq )2 (1 + 6Bend ∗ (θ − θeq )4 )

5.53 MM (Molecular Mechanics) Methods 225

SixBndI Atom-type1 Atom-type2 Atom-type3 ForceC θeq 6Bend Flag

ForceC Force constant

θeq Equilibrium angle
6Bend Sixth order bend constant (in deg−4 )
Flag If ≥ 0.0, suppress projection onto plane even when the central atom is
trigonal.

This bend is projected onto the plane in case of a trigonal center. If the center is not trigonal, the regular
bend is calculated.
Dipole : Bond dipole
Dipole Atom-type1 Atom-type2 DMom DPos

DMom Dipole moment (in Debye)

DPos Position along the Atom1-Atom2 bond of the dipole

DielC : Dielectric constant. This allows the dielectric constant to be specified via the parameter file; the default
is 1.
DielC DielConst

DielConst Dielectric constant

QStr2 : Quartic stretch 2 (MM2/Tinker): (ForceC/2) ∗ (1 +CStr ∗ (R − Req ) + QStr ∗ (R − Req )2 )(R − Req )2
QStr2 Atom-type1 Atom-type2 ForceC Req CStr QStr

ForceC Force constant

Req Equilibrium bond length
CStr Cubic stretch constant (Angstrom−1 )
QStr Quartic stretch constant (Angstrom−2 )

CubStr2 : Cubic stretch 2 (for compatibility with old MMVB): (ForceC/2) ∗ (1 −CStr ∗ (R − Req ) ∗ (R − Req )2
CubStr2 Atom-type1 Atom-type2 ForceC Req CStr

ForceC Force constant

Req Equilibrium bond length
CStr Cubic stretch constant (Angstrom−1 ; set to 0 when R > 15 Å)

NBonds : Formal number of bonds, based on atom type for this center
NBonds Atom-type NumBnd

NumBnd Formal number of bonds

StrUnit : Units for the force constant in stretching functions

StrUnit Flag

Flag 0 means units of kcal/(mol*Angstrom2 ); 1 means units of md/Angstrom

 226 Chapter 5. List of Gaussian Keywords

BndUnit : Units for the force constant in bending functions

BndUnit Flag

Flag 0 means units of kcal/(mol*rad2 ); 1 means units of md*Angstrom/rad2

TorUnit : Units for the barrier in torsion functions

TorUnit Flag

Flag 0 means units of kcal/mol; 1 means units of md*Angstrom

OOPUnit : Units for the force constant in out-of-plane bending functions

OOPUnit Flag

Flag 0 means units of kcal/(mol*rad2 ); 1 means units of md*Angstrom/rad2

SBUnit : Units for the force constant in stretch-bend functions

SBUnit Flag

Flag 0 means units of kcal/(mol*Angstrom*rad); 1 means units of md/rad

StrFact : Factor for the stretching functions

StrFact Value
BndFact : Factor for the bending functions
BndFact Value
TorFact : Factor for the torsion functions
TorFact Value
OOPFact : Factor for the out-of-plane functions
OOPFact Value
SBFact : Factor for the stretch-bend functions
SBFact Value

5.54 MP Methods

The MPn method keywords request a Hartree-Fock calculation (by default, RHF for singlets, UHF for
higher multiplicities) followed by a Møller-Plesset correlation energy correction [531]:
♢ MP2: The Møller-Plesset expansion is truncated at second-order [532–536].
♢ MP3: Third-order MP theory correction [198, 537].
♢ MP4: Fourth-order MP theory correction [538], which defaults to full MP4 with single, double, triple and
quadruple substitutions [538, 539] (MP4(SDTQ)).
♢ MP4(DQ): Include only the space of double and quadruple substitutions in the MP expansion.
♢ MP4(SDQ): Include only single, double and quadruple substitutions.
♢ MP5: Fifth-order MP theory correction [134]. The MP5 code has been written for the open-shell case only,
and so specifying MP5 defaults to a UMP5 calculation. This method requires O3 V3 disk storage and
scales as O4 V4 in cpu time.
 5.54 MP Methods 227

Analytic gradients are available for MP2 [227, 532, 533, 540], MP3 and MP4(SDQ) [541, 542], and
analytic frequencies are available for MP2 [536]. ROMP2, ROMP3 and ROMP4 energies are also available
[543–545].

Double-Hybrid Methods
Gaussian 16 also includes some double hybrid methods that combine exact HF exchange with an MP2-like
correlation to a DFT calculation. These methods have the same computational cost as MP2 (rather than that of
DFT). Gaussian 16 includes:
♢ Grimme’s B2PLYP [546] and mPW2PLYP [547] methods; the empirical dispersion corrected variations are
specified by appending a D to the keyword name: e.g., B2PLYPD for B2PLYP with empirical dispersion
[548].
♢ B2PLYPD3 requests the B2PLYP method combined with Grimme’s D3BJ dispersion [324, 332].
♢ DSDPBEP86 [549], a dispersion-corrected double hybrid functional.
♢ The PBE0DH [550] and PBEQIDH [551] double-hybrid functionals.

5.54.1 Options
Frozen Core Options
FC
All frozen core options are available with this keyword; a frozen core calculation is the default. See the
discussion of the FC options for full information.

Algorithm Selection Options for MP2 and Double Hybrid Methods

The appropriate algorithm for MP2 will be selected automatically based on the settings of %Mem and
MaxDisk. Thus, the following options are almost never needed.
FullDirect
Forces the fully direct algorithm, which requires no external storage beyond that for the SCF. Requires
a minimum of 2OVN words of main memory (O=number of occupied orbitals, V=number of virtual
orbitals, N=number of basis functions). This is seldom a good choice, except for machines with very
large main memory and limited disk.
TWInCore
Whether to store amplitudes and products in memory during higher-order post-SCF calculations. The
default is to store these if possible, but to run off disk if memory is insufficient. TWInCore causes
the program to terminate if these can not be held in memory, while NoTWInCore prohibits in-memory
storage.
SemiDirect
Forces the semi-direct algorithm.
Direct
Requests some sort of direct algorithm. The choice between in-core, fully direct and semidirect is made
by the program based on memory and disk limits and the dimensions of the problem.
InCore
Forces the in-memory algorithm. This is very fast when it can be used, but requires N 4 /4 words of
memory. It is normally used in conjunction with SCF=InCore. NoInCore prevents the use of the in-core
algorithm.
 228 Chapter 5. List of Gaussian Keywords

5.54.2 Availability
MP2, B2PLYP methods, mPW2PLYP methods: Energies, analytic gradients, and analytic frequencies.
MP3, MP4(DQ) and MP4(SDQ): Energies, analytic gradients, and numerical frequencies.
MP4(SDTQ) and MP5: Analytic energies, numerical gradients, and numerical frequencies.
RO may be combined with MP2, MP3 and MP4 for energies only.

5.54.3 Related Keywords

HF, SCF, Transformation, MaxDisk

5.54.4 Examples
The MP2 energy appears in the output as follows, labeled as EUMP2:

E2= -.3906492545D-01 EUMP2= -.75003727493390D+02

Here is the output from an MP4(SDTQ) calculation:

Time for triples= .04 seconds.

MP4(T)= -.55601167D-04
E3= -.10847902D-01 EUMP3= -.75014575395D+02
E4(DQ)= -.32068082D-02 UMP4(DQ)= -.75017782203D+02
E4(SDQ)= -.33238377D-02 UMP4(SDQ)= -.75017899233D+02
E4(SDTQ)= -.33794389D-02 UMP4(SDTQ)= -.75017954834D+02

The energy labeled EUMP3 is the MP3 energy, and the various MP4-level corrections appear after it, with
the MP4(SDTQ) value coming in the final line.
The B2PLYP energy appears as follows in the output:

E2(B2PLYP) = -0.3262340664D-01 E(B2PLYP) = -0.39113226645200D+02

5.55 Name
This keyword specifies the username that is stored in the archive entry for the calculation. It takes the
desired username as its parameter (e.g., Name=RChavez). On UNIX systems, the default for the username is
the operating system-level login name of the user who runs the job.

5.55.1 Related Keywords

Test

5.56 NMR
This properties keyword predicts NMR shielding tensors and magnetic susceptibilities using the Hartree-
Fock method, all DFT methods and the MP2 method [552–555].
NMR shielding tensors may be computed with the Continuous Set of Gauge Transformations (CSGT)
method [555–557] and the Gauge-Independent Atomic Orbital (GIAO) method [215, 555, 558–560]. Magnetic
susceptibilities may also be computed with both GIAOs [561] and CGST. Gaussian also supports the IGAIM
 5.56 NMR 229

method [556, 557] (a slight variation on the CSGT method) and the Single Origin method, for both shielding
tensor and magnetic susceptibilities.
Structures used for NMR calculations should have been optimized at a good level of theory. Note that
CSGT calculations require large basis sets to achieve accurate results.
Spin-spin coupling constants may also be computed during an NMR job [562–566], via the SpinSpin
option.

5.56.1 Options
SpinSpin
Compute spin-spin coupling constants in addition to the usual NMR properties. Be aware that this calcu-
lation type has a computational cost of about twice that of computing vibrational frequencies alone. It is
available only for Hartree-Fock and DFT methods.
Mixed
Requests a two-step spin-spin coupling calculation [566]. This option causes two job steps to be run.
In the first, the basis set specified by the user is modified to be appropriate for the Fermi Contact term,
by uncontracting the basis and adding tight polarization functions for the core. In the second step, the
other three terms in the spin-spin coupling are calculated with the unmodified basis set specified in the
route section. The final results reported at the end of the second job step include the Fermi Contact
contribution from the first step. This significantly improves the accuracy of spin-spin coupling constants,
especially when done with typical valence-oriented basis sets such as 6-311G+(d,p), aug-CC-pVDZ or
aug-CC-pVTZ. This approach is also faster than computing all four terms using a modified basis set
incorporating tight polarization functions.
ReadAtoms
Calculate spin-spin coupling constants only for selected atoms. The atom list is specified in a separate
input section (terminated by a blank line). The list is initially empty.
The input section uses the following format:
atoms=list [notatoms=list]
where each list is a comma or space-separated list of atom numbers, atom number ranges and/or atom
types. Keywords are applied in succession. Here are some examples:

atoms=3-6,17 notatoms=5 Adds atoms 3, 4, 6 and 17 to the atom list. Re-

moves 5 if present.
atoms=3 C 18-30 notatoms=H Adds all C atoms and all non-H among atoms 3,
18-30.
atoms=C N notatoms=5 Adds all C and N atoms except atom 5.
atoms=1-5 notatoms=H atoms=8-10 Adds atoms 8-10 and non-hydrogens among
atoms 1-5.

Bare integers without a keyword are interpreted as atom numbers:

1,3,5 7 Adds atoms 1, 3, 5 and 7.

CSGT
 230 Chapter 5. List of Gaussian Keywords

Compute NMR properties using the CSGT method only. The data file for the ACID program can be
generated with NMR=CSGT IOp(10/93=1).
GIAO
Compute NMR properties using the GIAO method only. This is the default.
IGAIM
Use atomic centers as gauge origins.
SingleOrigin
Use a single gauge origin. This method is provided for comparison purposes but is not generally recom-
mended.
All
Compute properties with all three of the SingleOrigin, IGAIM, and CSGT methods.
PrintEigenvectors
Display the eigenvectors of the shielding tensor for each atom.
FCOnly
Compute only the Fermi contact spin-spin terms.
ReadFC
Read the Fermi contact spin-spin terms from the checkpoint file and then compute the other spin-spin
coupling terms.
Susceptibility
Compute the magnetic susceptibility as well as the shielding.

5.56.2 Availability
SCF, DFT and MP2 methods. NMR may be combined with SCRF. NMR and Freq can now both be on
the same route for HF and DFT.

5.56.3 Examples
Here is an example of the default output from NMR:

Magnetic properties (GIAO method)

Magnetic shielding (ppm):

1 C Isotropic = 57.7345 Anisotropy = 194.4092
XX= 48.4143 YX= .0000 ZX= .0000
XY= .0000 YY= -62.5514 ZY= .0000
XZ= .0000 YZ= .0000 ZZ= 187.3406
2 H Isotropic = 23.9397 Anisotropy = 5.2745
XX= 27.3287 YX= .0000 ZX= .0000
XY= .0000 YY= 24.0670 ZY= .0000
XZ= .0000 YZ= .0000 ZZ= 20.4233

For this molecular system, the values for all of the atoms of a given type are equal, so we have truncated
the output after the first two atoms.
The additional output from spin-spin coupling computations appears as follows:
 5.57 ONIOM 231

Total nuclear spin-spin coupling K (Hz):

1 2
1 0.000000D+00
2 0.147308D+02 0.000000D+00
Total nuclear spin-spin coupling J (Hz):
1 2
1 0.000000D+00
2 0.432614D+03 0.000000D+00

The various components of the coupling constants precede this section in the output file. It displays the
matrix of isotropic spin-spin coupling between pairs of atoms in lower triangular form. The K matrix gives the
values which are isotope-independent, and the J matrix gives the values taking the job’s specific isotopes into
account (whether explicitly specified or the default isotopes).

5.57 ONIOM
This keyword requests a two- or three-layer ONIOM [567]. See [568–571] for recent developments, and
[572–577] for earlier work. In this procedure, the molecular system being studied is divided into two or three
layers which are treated with different model chemistries. The results are then automatically combined into the
final predicted results. The layers are conventionally known as the Low, Medium and High layers. By default,
atoms are placed into the High layer (from a certain point of view, any conventional calculation can be viewed
as a one-layer ONIOM). Layer assignments are specified as part of the molecule specification (see below).
GaussView provides many graphical tools that simplify setting up ONIOM calculations.
For MO:MM and MO:MO:MM jobs, the ONIOM optimization procedure uses microiterations [578] and
an optional quadratic coupled algorithm is also available [568]. The latter (requested with Opt=QuadMacro)
takes into account the coupling between atoms in the model system and the atoms only in the MM layer in
order to produce more accurate steps than the regular microiterations algorithm [579].
MO:MM and MO:MO:MM calculations can take advantage of electronic embedding (ONIOM=EmbedCharge
option). Electronic embedding incorporates the partial charges of the MM region into the quantum mechanical
Hamiltonian. This technique provides a better description of the electrostatic interaction between the QM and
MM regions (as it is treated at the QM level) and allows the QM wavefunction to be polarized.
There are several relevant considerations for MO:MM and MO:MO:MM optimizations and IRCs (note
that none of this is relevant to ONIOM without MM):
♢ The default optimization algorithm uses the RFO algorithm for steps in internal coordinates that include just
the model system, along with linear microiterations to optimize the atoms that are only in the real system
(i.e., only treated with MM). For minima, the default algorithm is usually the best choice.
♢ For problem convergence cases, the main alternative is Opt=QuadMac, which does a quadratic step in the
coordinates of all the atoms. Such an optimization can use either an updated approximate Hessian for
the internal coordinates or an analytically computed Hessian (see the next bullet). It computes products
of the low-level (MM) Hessian with vectors as needed.
♢ If there are still convergence problems, then try Opt=(QuadMac,CalcFC) or Opt=(QuadMac,CalcAll).
♢ For transition structures, the QuadMac option helps to ensure that you move in the direction of a proper
transition structure, so Opt=(QuadMac,TS,CalcFC) is usually a good choice.
 232 Chapter 5. List of Gaussian Keywords

♢ For both minima and transition structures, it is usually more efficient to first optimize using mechanical
embedding and then perform a second optimization with electronic embedding starting from the resulting
structure (rather than trying to use electronic embedding from the beginning).
♢ For IRCs, first run a frequency calculation to confirm that you have a proper transition structure. You can
then begin the IRC using that job’s force constants via IRC=RCFC. For very large systems, include the
Freq=SaveNM option so that IRC=RCFC does not have to recompute normal modes. The default IRC
algorithm for MO:MM, IRC=EulerPC, is best for large systems. However, IRC=HPC may be preferable
for small to medium-sized cases.
See [580] for an example study employing ONIOM.
ONIOM calculations can also use an external program for the calculations for one or more levels of theory.
See the External keyword for details.

5.57.1 Required Input

The two or three desired model chemistries are specified as the options to the ONIOM keyword, in the
order High, Medium, Low (the final one may obviously be omitted). The distinct models are separated by
colons. For example, this route section specifies a three-layer ONIOM calculation, using UFF for the Low
layer, PM6 for the Medium layer, and HF for the High layer:
# ONIOM(HF/6-31G(d):PM6:UFF)
Atom layer assignment for ONIOM calculations is done as part of the molecule specification, via addi-
tional parameters on each line according to the following syntax:
atom [freeze-code] coordinate-spec layer [link-atom [bonded-to [scale-fac1 [scale-fac2 [scale-fac3]]]]]
where atom and coordinate-spec represent the normal molecule specification input for the atom. The freeze-
code indicates if/how the atom is to be frozen during a geometry optimization. If the value is omitted or 0, then
the atom’s coordinates will be optimized. If the value is -1, then the atom will be frozen. If any other negative
integer is specified, then the atom is treated as part of a rigid fragment during the optimization; all atoms with
the same negative value move together as a rigid block. Blocks can be frozen or activated with Opt=ReadOpt.
Layer is a keyword indicating the layer assignment for the atom, one of High, Medium, and Low. The
other optional parameters specify how the atoms located at a layer boundary are to be treated. You use link-
atom to specify the atom with which to replace the current atom (it can include atom type and partial charge and
other parameters). Link atoms are necessary when covalent bonding exists between atoms in different layers in
order to saturate the (otherwise) dangling bonds.
Note: All link atoms must be specified by the user. Gaussian 16 does not define them automatically or
provide any defaults. GaussView does this automatically, but users still need to consider this general concern
and follow the rules in [570].
The bonded-to parameter specifies which atom the current atom is to be bonded to during the higher-level
calculation portion. If it is omitted, Gaussian will attempt to identify it automatically.
In general, Gaussian 16 determines bond distances between atoms and their link atoms by scaling the
original bond distance (i.e., in the real system), using scaling factors which the program determines automati-
cally. However, you can also specify these scale factors explicitly. For a two-layer calculation, the scale factors
specify the link atom bond distance in the model system when calculated at the low and high levels (respec-
tively). For a three-layer ONIOM, up to three scale factors may be specified (in the order low, medium, high).
 5.57 ONIOM 233

All of these scale factors correspond to the g-factor parameter as defined in reference [567], extended to allow
separate values for each ONIOM calculation level.
For a two-layer ONIOM, if only one parameter is specified, then both scale factors will use that value. For
a three-layer ONIOM, if only one parameter is specified, then all three scale factors will use that value; if only
two parameters are specified, then the third scale factor will use the second value.
If a scale parameter is explicitly set to 0.0, then the program will determine the corresponding scale factor
in the normal way. Thus, if you want to change only the second scale factor (model system calculated at the
medium level), then you must explicitly set the first scale factor to 0.0. In this case, for a three-layer ONIOM,
the third scale factor will have the same value as the second parameter unless it is explicitly assigned a non-zero
value (i.e., in this second context, 0.0 has the same meaning as an omitted value).

5.57.2 Per-layer Charge and Spin Multiplicity

Multiple charge and spin multiplicity pairs may also be specified for ONIOM calculations. For two-layer
ONIOM jobs, the format for this input line is:
chrgreal−low spinreal−low [chrgmodel−high spinmodel−high [chrgmodel−low spinmodel−low [chrgreal−high spinreal−high ]]]
where the subscript indicates the calculation for which the values will be used. The fourth pair applies only to
ONIOM=SValue calculations. When only a single value pair is specified, all levels will use those values. If
two pairs of values are included, then the third pair defaults to the same values as in the second pair. If the final
pair is omitted for an S-value job, it defaults to the values for the real system at the low level.
Values and defaults for three-layer ONIOM calculations follow an analogous pattern (in the subscripts
below, the first character is one of: Real, Int=Intermediate system, and Mod=Model system, and the second
character is one of: H, M and L for the High, Medium and Low levels):
c RealL s RealL [c IntM s IntM [c IntL s IntL [c ModH s ModH [c ModM s ModM [c ModL s ModL]]]]]

For 3-layer ONIOM=SValue calculations, up to three additional pairs may be specified:

· · · c IntH s IntH [c RealM s RealM [c RealH s RealH]]
Defaults for missing charge/spin multiplicity pairs are taken from the next highest calculation level and/or
system size. Thus, when only a subset of the six or nine pairs are specified, the charge and spin multiplicity
items default according to the following scheme, where the number in each cell indicates which pair of values
applies for that calculation in the corresponding circumstances:

Charge & Spin Defaults

# Pairs Specified (SValue only)
Calculation 1 2 3 4 5 6 7 8 9
Real-Low 1 1 1 1 1 1 1 1 1
Int-Med 1 2 2 2 2 2 2 2 2
Int-Low 1 2 3 3 3 3 3 3 3
Model-High 1 2 2 4 4 4 4 4 4
Model-Med 1 2 2 4 5 5 5 5 5
Model-Low 1 2 2 4 5 6 6 6 6
Int-High 1 2 2 2 2 2 7 7 7
Real-Med 1 1 1 1 1 1 1 8 8
Real-High 1 1 1 1 1 1 1 8 9
 234 Chapter 5. List of Gaussian Keywords

5.57.3 Options

EmbedCharge
Use MM charges from the real system in the QM calculations on the model system(s). NoEmbedCharge
is the default.
MKUFF
MKUFF uses the Merz-Kollman-Singh approximate charges during geometry optimization microitera-
tions with electronic embedding but using UFF radii, which are defined for the full periodic table. This
is the default.
MK
Specifies that Merz-Kollman-Singh (see Population=MK) approximate charges be used during geometry
optimization microiterations with electronic embedding.
Mulliken
Specifies that Mulliken approximate charges be used during geometry optimization microiterations with
electronic embedding. (See Population default method.)
HLYGAt
Specifies the Hu, Lu, and Yang (see Population=HLYGAt) charge fitting method be used during geometry
optimization microiterations with electronic embedding, but using Gaussian’s standard atomic densities
instead of those of HLY.
ScaleCharge=ijklmn
Specifies scaling parameters for MM charges during electronic embedding in the QM calculations. The
integers are multiplied by 0.2 to obtain the actual scale factors. Atoms bonded to the inner layers use a
scale factor of 0.2n, those two bonds away use 0.2m, and so on. However, the values of i through n must
be monotonically decreasing, and the largest value among them is used for all parameters to its left. Thus,
555500, 123500 and 500 are all equivalent. The default value is 500 (i.e., 555500), turning off charges
within 2 bonds of the QM region and leaving the rest unscaled. ScaleCharge implies EmbedCharge.
SValue
Requests that the full square be done for testing, to produce substituent values (S-values) for the S-value
test [581]. Additional charge and spin multiplicity pair(s) may be specified for the additional calculations
(see below).
Compress
Compress operations and storage to active atoms during MO:MM mechanical embedding second deriva-
tive calculations; this is the default. NoCompress performs the calculation without compression. Blank
does the uncompressed calculation but then discards contributions from inactive atoms (which are cur-
rently non-zero only for nuclear moment perturbations: shielding and spin-spin coupling tensors). Full-
Matrix causes the full Hessian to be stored and used in mechanical embedding Opt=QuadMac, instead of
using the molecular mechanics Hessian for the real system in operator form. This is faster for medium-
sized systems but uses more disk space for large ones.
InputFiles
Prints out an input file for each intermediate calculation, to facilitate running these calculations separately.
OnlyInputFiles just generates the files without doing any calculations.
 5.57 ONIOM 235

5.57.4 Availability
Energies, gradients and frequencies. Note that if any of the specified models require numerical frequencies,
then numerical frequencies will be computed for all models, even when analytic frequencies are available.
ONIOM can also perform CIS and TD calculations for one or more layers. The Gen, GenECP and ChkBas
keywords may also be specified for relevant models. Density fitting sets may also be used when applicable,
and they are specified in the usual manner (see the examples). NMR calculations may be performed with the
ONIOM model.

5.57.5 Related Keywords

Geom=Connect, Molecular Mechanics keywords, Opt=QuadMacro, External

5.57.6 Examples

Molecule Specifications for ONIOM Jobs. Here is a simple ONIOM input file:
# ONIOM(B3LYP/6-31G(d,p):UFF) Opt

2-layer ONIOM optimization

0 1 0 1 0 1
F -1.041506214819 0.000000000000 -2.126109488809 M
F -2.033681935634 -1.142892069126 -0.412218766901 M
F -2.033681935634 1.142892069126 -0.412218766901 M
C -1.299038105677 0.000000000000 -0.750000000000 M H 4
C 0.000000000000 0.000000000000 0.000000000000 H
H 0.000000000000 0.000000000000 1.100000000000 H
O 1.125833024920 0.000000000000 -0.650000000000 H

The High layer consists of the final three atoms. The other atoms are placed into the Medium layer. A link
atom is defined for the first carbon atom.
Here is an input file for a two-layer ONIOM calculation using a DFT method for the high layer and Amber
for the low layer. The molecule specification includes atom types (which are optional with UFF but required
by Amber). Note that atom types are used for both the main atom specifications and the link atoms:
# ONIOM(B3LYP/6-31G(d):Amber) Geom=Connectivity

2 layer ONIOM job

0 1 0 1 0 1 Charge/spin for entire molecule (real system), model system-high level & model-low
C-CA--0.25 0 -4.703834 -1.841116 -0.779093 L
C-CA--0.25 0 -3.331033 -1.841116 -0.779093 L H-HA-0.1 3
C-CA--0.25 0 -2.609095 -0.615995 -0.779093 H
C-CA--0.25 0 -3.326965 0.607871 -0.778723 H
C-CA--0.25 0 -4.748381 0.578498 -0.778569 H
C-CA--0.25 0 -5.419886 -0.619477 -0.778859 L H-HC-0.1 5
H-HA-0.1 0 -0.640022 -1.540960 -0.779336 L
H-HA-0.1 0 -5.264565 -2.787462 -0.779173 L
236 Chapter 5. List of Gaussian Keywords

···

This input also illustrates the use of multiple charge and spin multiplicity values for ONIOM jobs.

A Complex ONIOM Route. Here is an example of a complex ONIOM route section:

# ONIOM(BLYP/6-31G(d)/Auto TD=(NStates=8):UFF)
This example uses density fitting for the DFT high layer time-dependent excited states calculation.

Freezing Atoms During ONIOM Optimizations. ONIOM optimizations can take advantage of the optional
second field within molecule specifications. This field defaults to 0 if omitted. If it is set to -1, then the
corresponding atom is frozen during geometry optimizations, e.g.:
C -1 0.0 0.0 0.0
H 0 0.0 0.0 0.9
···

For ONIOM jobs only, if the field is set to a negative value other than -1, it is treated as part of a rigid
fragment during the optimization: all atoms with the same value (< -1) move only as a rigid block.

Handling an SCF convergence issue limited to one layer. For cases where it is difficult to converge the
initial SCF or to get it to converge to the lowest solution, the following procedure is helpful. Here is the initial
ONIOM input file:
%Chk=mychk
# ONIOM(BLYP/3-21G:UFF) Opt Freq

input file continues · · ·

First, create an input file for the high-level model system calculation by running the job and adding the
OnlyInputFiles option to ONIOM, which prints input files for each of the 3 individual calculations:
# ONIOM(BLYP/3-21G:UFF)=OnlyInputFiles
Use the input file for the high-level model calculation to obtain a converged SCF for this system, being
sure to save its checkpoint file, called for example highmod.chk. Use whatever options are required to get SCF
convergence (e.g., Stable=Opt).
Next, run the ONIOM job using Guess=Input:
%Chk=mychk
# ONIOM(BLYP/3-21G:UFF) Opt Freq Guess=Input

ONIOM Opt Freq

molecule specification

highmod.chk Checkpoint file for Guess=Input

When this job computes the initial guess, it reads a line from the input file saying what to do: generate,
read or the name of another checkpoint file, the option used here.
The procedure is similar for an MO:MO calculation. However, in this case, there will be three initial
guesses performed (since all of the calculations are MO calculations), with one input line read for each guess
 5.58 Optimization 237

when you use Guess=Input. For example, if only the high level calculation on the model system needs to be
converged separately, then the input would look like this:

%chk=mychk
# ONIOM(BLYP/6-31+G*:HF/STO-3G) Opt Freq Guess=Input

2 Layer MO:MO ONIOM Opt Freq

molecule specification

generate Generate initial guess for the low level real system.

highmod.chk Read initial guess from this file for the high level model system.

generate Generate initial guess for the low level model system.

S-Value Test. Here is some output from the ONIOM=SValue option:

S-Values (between gridpoints) and energies:

high 4 -39.322207 7 -39.305712 9

-114.479426 -153.801632 -193.107344
med 2 -39.118688 5 -39.106289 8
-114.041481 -153.160170 -192.266459
low 1 -38.588420 3 -38.577651 6
-112.341899 -150.930320 -189.507971
model mid real

The integers are the gridpoints, and under each one is the energy value. Horizontally between the grid
points are the S-values. These are the S-values obtained with the absolute energies. However, be aware that
when applying the S-value test, relative energies and S-values need to be used (see reference [581]).

5.58 Optimization
This keyword requests that a geometry optimization be performed. The geometry will be adjusted until
a stationary point on the potential surface is found. Analytic gradients will be used if available. For the
Hartree-Fock, CIS, MP2, MP3, MP4(SDQ), CID, CISD, CCD, CCSD, QCISD, BD, CASSCF, and all DFT and
semi-empirical methods, the default algorithm for both minimizations (optimizations to a local minimum) and
optimizations to transition states and higher-order saddle points is the Berny algorithm using GEDIIS [582] in
redundant internal coordinates [461, 583–587] (corresponding to the Redundant option). An brief overview of
the Berny algorithm is provided in the final subsection of this discussion. The default algorithm for all methods
lacking analytic gradients is the eigenvalue-following algorithm (Opt=EF).
Gaussian includes the STQN method for locating transition structures. This method, implemented by H. B.
Schlegel and coworkers [461, 587], uses a quadratic synchronous transit approach to get closer to the quadratic
region of the transition state and then uses a quasi-Newton or eigenvector-following algorithm to complete the
optimization. Like the default algorithm for minimizations, it performs optimizations by default in redundant
 238 Chapter 5. List of Gaussian Keywords

internal coordinates. This method will converge efficiently when provided with an empirical estimate of the
Hessian and suitable starting structures.
This method is requested with the QST2 and QST3 options. QST2 requires two molecule specifications,
for the reactants and products, as its input, while QST3 requires three molecule specifications: the reactants, the
products, and an initial structure for the transition state, in that order. The order of the atoms must be identical
within all molecule specifications. See the examples for sample input for and output from this method.
Basic information as well as techniques and pitfalls related to geometry optimizations are discussed in
detail in chapter 3 of Exploring Chemistry with Electronic Structure Methods [152]. For a review article on
optimization and related subjects, see [502].
Gaussian 16 supports generalized internal coordinates (GIC), a facility which allows arbitrary redundant
internal coordinates to be defined and used for optimization constraints and other purposes [460]. There are
several GIC-related options to Opt, and the GIC Info subsection describes using GICs as well as their limitations
in the present implementation.

5.58.1 Set Opt. Goal

By default, optimizations search for a local minimum.
QST2
Search for a transition structure using the STQN method. This option requires the reactant and product
structures as input, specified in two consecutive groups of title and molecule specification sections. Note
that the atoms must be specified in the same order in the two structures. TS should not be specified with
QST2.
QST3
Search for a transition structure using the STQN method. This option requires the reactant, product, and
initial TS structures as input, specified in three consecutive groups of title and molecule specification
sections. Note that the atoms must be specified in the same order within the three structures. TS should
not be specified with QST3.
TS
Requests optimization to a transition state rather than a local minimum, using the Berny algorithm.
Saddle=N
Requests optimization to a saddle point of order N using the Berny algorithm.
Conical
Search for a conical intersection or avoided crossing using the state-averaged CASSCF method. Avoided
is a synonym for Conical. Note that CASSCF=SlaterDet is needed in order to locate a conical intersection
between a singlet state and a triplet state.

5.58.2 Options
Options to Modify the Initial Geometry
ModRedundant
Except for any case when it is combined with the GIC option (see below), the ModRedundant option
will add, delete, or modify redundant internal coordinate definitions (including scan and constraint infor-
mation) before performing the calculation. This option requires a separate input section following the
geometry specification; when used in conjunction with QST2 or QST3, a ModRedundant input section
5.58 Optimization 239

must follow each geometry specification. AddRedundant is synonymous with ModRedundant.

Lines in a ModRedundant input section use the following syntax:
[Type] N1 [N2 [N3 [N4]]] [A | F]
[Type] N1 [N2 [N3 [N4]]] B
[Type] N1 [N2 [N3 [N4]]] K | R
[Type] N1 [N2 [N3 [N4]]] D
[Type] N1 [N2 [N3 [N4]]] H diag-elem
[Type] N1 [N2 [N3 [N4]]] S nsteps stepsize
N1, N2, N3, and N4 are atom numbers or wildcards (discussed below). Atom numbering begins at 1, and
any dummy atoms are not counted.
The atom numbers are followed by a one-character code letter indicating the coordinate modification
to be performed; the action code is sometimes followed by additional required parameters as indicated
above. If no action code is included, the default action is to add the specified coordinate. These are the
available action codes:

A Activate the coordinate for optimization if it has been frozen.

F Freeze the coordinate in the optimization.
B Add the coordinate and build all related coordinates.
K Remove the coordinate and kill all related coordinates containing this coordinate.
R Remove the coordinate from the definition list (but not the related coordinates).
D Calculate numerical second derivatives for the row and column of the initial Hessian
for this coordinate.
H Change the diagonal element for this coordinate in the initial Hessian to diag-elem.
S Perform a relaxed potential energy surface scan. Increment the coordinate by step-
size a total of nsteps times, performing an optimization from each resulting starting
geometry.

An asterisk (*) in the place of an atom number indicates a wildcard. Here are some examples of wildcard
use:

* All atoms specified by Cartesian coordinates.

** All defined bonds.
3* All defined bonds with atom 3.
*** All defined valence angles.
*4* All defined valence angles around atom 4.
**** All defined dihedral angles.
*34* All defined dihedral angles around the bond connecting atoms 3 and 4.

By default, the coordinate type is determined from the number of atoms specified: Cartesian coordi-
nates for 1 atom, bond stretch for 2 atoms, valence angle for 3 atoms, and dihedral angle for 4 atoms.
Optionally, type can be used to designate these and additional coordinate types:

X Cartesian coordinates.
240 Chapter 5. List of Gaussian Keywords

B Bond length.
A Valence angle.
D Dihedral angle.
L Linear bend specified by three atoms (if N4 is -1) or by four atoms, where the fourth
atom is used to determine the 2 orthogonal directions of the linear bend.

See the examples for illustrations of the use of ModRedundant.

ReadOptimize
Read an input section modifying which atoms are to be optimized. The atom list is specified in a separate
input section (terminated by a blank line). By default, the atom list contains all atoms in the molecule,
unless any atoms are designated as frozen within the molecule specification, in which case the initial
atom list excludes them. If the structure is being read in from the checkpoint file, then the list of atoms
to be optimized matches that in the checkpoint file. ReadOpt and RdOpt are synonyms for this option.
ReadFreeze and RdFreeze are deprecated synonyms.
The input section uses the following format:
atoms=list [notatoms=list]
where each list is a comma or space-separated list of atom numbers, atom number ranges and/or atom
types. Keywords are applied in succession. Here are some examples:

atoms=3-6,17 notatoms=5 Adds atoms 3,4,6,17 to atom list. Removes 5 if present.

atoms=3 C 18-30 notatoms=H Adds all C & non-H among atoms 3, 18-30.
atoms=C N notatoms=5 Adds all C and N atoms except atom 5.
atoms=1-5 notatoms=H atoms=8-10 Adds atoms 8-10 and non-hydrogens among atoms 1-5.

Bare integers without a keyword are interpreted as atom numbers:

1,3,5 7 Adds atoms 1, 3, 5 and 7.

For ONIOM optimizations only, block and notblock can be similarly used to include/not include rigid
blocks defined in ONIOM molecule specifications. If there are contradictions between atoms specified as
atoms and within blocks – e.g., an atom is included within a block but excluded by atom type – Gaussian
16 generates an error.
You can start from an empty atom list by placing noatoms as the first item in the input section. For
example, the following input optimizes all non-hydrogen atoms within atoms 1-100 and freezes all other
atoms in the molecule:
noatoms atoms=1-100 notatoms=H
Atoms can also be specified by ONIOM layer via the [not]layer keywords, which accept these values:
real for the real system, model for the model system in a 2-layer ONIOM, middle for the middle layer in
a 3-layer ONIOM, and small for the model layer of a 3-layer ONIOM. Atoms may be similarly includ-
ed/excluded by residue with residue and notresidue, which accept lists of residue names. Both keyword
pairs function as shorthand forms for atom lists.
Separate sections are read for each geometry for transition state optimizations using QST2 or QST3. Be
aware that providing contradictory input – e.g., different frozen atoms for the reactants and products –
5.58 Optimization 241

will produce unpredictable results.

NoFreeze
Activates (unfreezes) all variables, in other words freeze nothing and optimize all atoms. This op-
tion is useful when reading in a structure from a checkpoint file that contains frozen atoms (i.e. with
Geom=Check). This option should not be used with GICs; use UnFreezeAll in the GIC input section
instead.

General Procedural Options

MaxCycles=N
Sets the maximum number of optimization steps to N. The default is the maximum of 20 and twice
the number of redundant internal coordinates in use (for the default procedure) or twice the number of
variables to be optimized (for other procedures).
MaxStep=N
Sets the maximum size for an optimization step (the initial trust radius) to 0.01N Bohr or radians. The
default value for N is 30.
Restart
Restarts a geometry optimization from the checkpoint file. In this case, the entire route section will
consist of the Opt keyword and the same options to it as specified for the original job (along with Restart).
No other input is needed (see the examples).
InitialHarmonic=N
Add harmonic constraints to the initial structure with force constant N/1000000 Hartree/Bohr2 . IHar-
monic is a synonym for this option.
ChkHarmonic=N
Add harmonic constraints to the initial structure saved on the chk file with force constant N/1000000
Hartree/Bohr2 . CHarmonic is a synonym for this option.
ReadHarmonic=N
Add harmonic constraints to a structure read in the input stream (in the input orientation), with force
constant N/1000000 Hartree/Bohr2 . RHarmonic is a synonym for this option.
MaxMicroiterations=N
Allow up to N microiterations. The default is based on NAtoms but is at least 5000. MaxMicro is a
synonym for this option.
NGoDown=N
Mix at most N Hessian eigenvectors having negative eigenvalues when trying to go downhill. Defaults
to 3. If N=-1, do regular RFO step only. NoDownHill is equivalent to NGoDown = -1.

Options Related to Initial Force Constants

Unless you specify otherwise, a Berny geometry optimization starts with an initial guess for the second
derivative matrix – also known as the Hessian – which is determined using connectivity derived from atomic
radii and a simple valence force field [461, 588]. The approximate matrix is improved at each point using the
computed first derivatives. This scheme usually works fine, but for some cases the initial guess may be so
poor that the optimization fails to start off properly or spends many early steps improving the Hessian without
nearing the optimized structure. In addition, for optimizations to transition states, some knowledge of the
242 Chapter 5. List of Gaussian Keywords

curvature around the saddle point is essential, and the default approximate Hessian must always be improved.
There are a variety of options which retrieve or compute improved force constants for a geometry opti-
mization. They are listed following this preliminary discussion.
There are two other approaches to providing the initial Hessian which are sometimes useful:
♢ Input new guesses: The default approximate matrix can be used, but with new guesses read in for some
or all of the diagonal elements of the Hessian. This is specified in the ModRedundant input or on the
variable definition lines in the Z-matrix. For example:
1 2 H 0.55
The letter H indicates that a diagonal force constant is being specified for this coordinate and that its
value is 0.55 Hartree/au2 .
♢ Compute some or all of the Hessian numerically: You can ask the optimization program to compute part of
the second derivative matrix numerically. In this case each specified variable will be stepped in only one
direction, not both up and down as would be required for an accurate determination of force constants.
The resulting second-derivatives are not as good as those determined by a frequency calculation but are
fine for starting an optimization. Of course, this requires that the program do an extra gradient calculation
for each specified variable. This procedure is requested by a flag (D) on the variable definition lines:
1 2 D
1 2 3 D
This input tells the program to do three points before taking the first optimization step: the usual first
point, a geometry with the bond between atoms 1 and 2 incremented slightly, and a geometry with the
angle between atoms 1, 2 and 3 incremented slightly. The program will estimate all force constants (on
and off diagonal) for bond(1,2) and angle(1,2,3) from the three points. This option is only available with
the Berny and EF algorithms.

The following options select methods for providing improved force constants:
ReadFC
Extract force constants from a checkpoint file. These will typically be the final approximate force con-
stants from an optimization at a lower level, or (much better) the force constants computed correctly by
a lower-level frequency calculation (the latter are greatly preferable to the former).
CalcFC
Specifies that the force constants be computed at the first point using the current method (available for
the HF, CIS, MP2, CASSCF, DFT, and semi-empirical methods only).
RCFC
Specifies that the computed force constants in Cartesian coordinates (as opposed to internal) from a
frequency calculation are to be read from the checkpoint file. Normally it is preferable to pick up the force
constants already converted to internal coordinates as described above (CalcFC). However, a frequency
calculation occasionally reveals that a molecule needs to distort to lower symmetry. In this case, the
computed force constants in terms of the old internal coordinates cannot be used, and instead Opt=RCFC
is used to read the Cartesian force constants and transform them. Note that Cartesian force constants
are only available on the checkpoint file after a frequency calculation. You cannot use this option after
an optimization dies because of a wrong number of negative eigenvalues in the approximate second
derivative matrix. In the latter case, you may want to start from the most recent geometry and compute
5.58 Optimization 243

some derivatives numerically (see below). ReadCartesianFC is a synonym for RCFC.

CalcHFFC
Specifies that the analytic HF force constants are to be computed at the first point. CalcHFFC is used
with MP2 optimizations, and it is equivalent to CalcFC for DFT methods, AM1, PM3, PM3MM, PM6
and PDDG.
CalcAll
Specifies that the force constants are to be computed at every point using the current method (available
for the HF,CIS, MP2, CASSCF, DFT, and semi-empirical methods only). Note that vibrational frequency
analysis is automatically done at the converged structure and the results of the calculation are archived as
a frequency job.
RecalcFC=N
Do analytic second derivatives at step 1 and every N th step thereafter during an optimization.
VCD
Calculate VCD intensities at each point of a Hartree-Fock or DFT Opt=CalcAll optimization.
NoRaman
Specifies that Raman intensities are not to be calculated at each point of a Hartree-Fock Opt=CalcAll job
(since it includes a frequency analysis using the results of the final point of the optimization). The Raman
intensities add 10-20% to the cost of each intermediate second derivative point. NoRaman is the default
for methods other than Hartree-Fock.
StarOnly
Specifies that the specified force constants are to be estimated numerically but that no optimization is to
be done. Note that this has nothing to do with computation of vibrational frequencies.
NewEstmFC
Estimate the force constants using a valence force field. This is the default.
EstmFC
Estimate the force constants using the old diagonal guesses. Only available for the Berny algorithm.
FCCards
Requests that read the energy (although value is not used), cartesian forces and force constants from the
input stream, as written out by Punch=Derivatives. The format for this input is:

Energy Format (D24.16)

Cartesian forces Lines of format (6F12.8)
Force constants Lines of format (6F12.8)

The force constants are in lower triangular form: ((F(J,I),J=1,I),I=1,3Natoms ), where 3Natoms is the num-
ber of Cartesian coordinates.

Convergence-Related Options
These options are available for the Berny algorithm only.
Tight
This option tightens the cutoffs on forces and step size that are used to determine convergence. An
optimization with Opt=Tight will take several more steps than with the default cutoffs. For molecular
systems with very small force constants (low frequency vibrational modes), this may be necessary to en-
244 Chapter 5. List of Gaussian Keywords

sure adequate convergence and reliability of frequencies computed in a subsequent job step. This option
can only be used with Berny optimizations. For DFT calculations, Int=UltraFine should be specified as
well.
VeryTight
Extremely tight optimization convergence criteria. VTight is a synonym for VeryTight. For DFT calcula-
tions, Int=UltraFine should be specified as well.
EigenTest
EigenTest requests and NoEigenTest suppresses testing the curvature in Berny optimizations. The test
is on by default only for transition states in internal (Z-matrix) or Cartesian coordinates, for which it is
recommended. Occasionally, transition state optimizations converge even if the test is not passed, but
NoEigenTest is only recommended for those with large computing budgets.
Expert
Relaxes various limits on maximum and minimum force constants and step sizes enforced by the Berny
program. This option can lead to faster convergence but is quite dangerous. It is used by experts in
cases where the forces and force constants are very different from typical molecules and Z-matrices, and
sometimes in conjunction with Opt=CalcFC or Opt=CalcAll. NoExpert enforces the default limits and is
the default.
Loose
Sets the optimization convergence criteria to a maximum step size of 0.01 au and an RMS force of
0.0017 au. These values are consistent with the Int(Grid=SG1) keyword, and may be appropriate for
initial optimizations of large molecules using DFT methods which are intended to be followed by a full
convergence optimization using the default (Fine) grid. It is not recommended for use by itself.

Algorithm-Related Options

GEDIIS
Use GEDIIS optimization algorithm. This is the default for minimizations when gradients are available.
RFO
Requests the Rational Function Optimization [589] step during Berny optimizations. It is the default
for transition state optimizations (Opt=TS). This was also the default algorithm for minimizations using
gradients in Gaussian 03.
EF
Requests an eigenvalue-following algorithm [589–591], which is useful only for methods without deriva-
tives (for which it is the default). Available for both minima and transition states. and EigenvalueFollow
are all synonyms for EF. When used with Opt=Z-Matrix, a maximum of 50 variables may be optimized.

ONIOM-Related Options

Micro
Use microiterations in ONIOM(MO:MM) optimizations. This is the default, with selection of L120 or
L103 for the microiterations depending on whether electronic embedding is on or off. NoMicro forbids
microiterations during ONIOM(MO:MM) optimizations. Mic120 says to use microiterations in L120
for ONIOM(MO:MM), even for mechanical embedding. This is the default for electronic embedding.
Mic103 says to perform microiterations in L103 for ONIOM(MO:MM). It is the default for mechanical
5.58 Optimization 245

embedding, and it cannot be used with electronic embedding.

QuadMacro
Controls whether the coupled, quadratic macro step is used during ONIOM(MO:MM) geometry opti-
mizations [579]. NoQuadMacro is the default.

Coordinate System Selection Options

Redundant
Build an automatic set of redundant internal coordinates such as bonds, angles, and dihedrals from the
current Cartesian coordinates or Z-Matrix values, using the old algorithm available in Gaussian 16. Per-
form the optimization using the Berny algorithm in these redundant internal coordinates. This is the
default for methods for which analytic gradients are available.
Z-matrix
Perform the optimization with the Berny algorithm using internal coordinates [592–594]. In this case,
the keyword FOpt rather than Opt requests that the program verify that a full optimization is being done
(i.e., that the variables including inactive variables are linearly independent and span the degrees of
freedom allowed by the molecular symmetry). The POpt form requests a partial optimization in internal
coordinates. It also suppresses the frequency analysis at the end of optimizations which include second
derivatives at every point (via the CalcAll option). See Constructing Z-Matrices for details and examples
of Z-matrix molecule specifications.
Cartesian
Requests that the optimization be performed in Cartesian coordinates, using the Berny algorithm. Note
that the initial structure may be input using any coordinate system. No partial optimization or freezing
of variables can be done with purely Cartesian optimizations; the mixed optimization format with all
atoms specified via Cartesian lines in the Z-matrix can be used along with Opt=Z-matrix if these features
are needed. When a Z-matrix without any variables is used for the molecule specification, and Opt=Z-
matrix is specified, then the optimization will actually be performed in Cartesian coordinates. Note that
a variety of other coordinate systems, such as distance matrix coordinates, can be constructed using the
ModRedundant option.

Generalized Internal Coordinate (GIC) Options

GIC
Build an automatic set of redundant internal coordinates using the new GIC algorithm. Perform the
optimization using the Berny algorithm in the GIC-type internal coordinates. Note that the coordinates
generated with this option can be the same bonds, angles, and dihedrals generated by the default algo-
rithm. However, these coordinates are internally stored and manipulated as the generalized ones (e.g.,
relevant analytical derivatives with respect to Cartesian coordinates displacements can be calculated au-
tomatically via an auto differentiation engine). The GICs are more flexible and, in principle, can be
any combination of standard mathematical functions. Note that Geom=Checkpoint Opt=GIC option is
equivalent to Geom=(Checkpoint,GIC).
AddGIC
Add, delete, or modify GIC-type internal coordinate definitions (including scan and constraint informa-
tion) before performing the calculation using the new GIC algorithm. This option requires a separate
246 Chapter 5. List of Gaussian Keywords

input section following the geometry specification. When used in conjunction with QST2 or QST3,
a GIC input section must follow each geometry specification. The syntax of the GIC input section is
described in GIC Info. Note that Opt=(ModRedundant,GIC) is equivalent to Opt=AddGIC. Note that
Geom=Checkpoint Opt=ReadAllGIC is equivalent to Geom=(Checkpoint, ReadAllGIC).
GICOld
Build an automatic set of redundant internal coordinates using the current default algorithm (as with the
option Redundant) and then convert the coordinates into the GICs and treat them as such. Perform the
optimization using the Berny algorithm in the GIC-type internal coordinates.
ReadAllGIC
Do not build any redundant internal coordinates by default. Instead, read the input stream for user-
provided GIC definitions and create the coordinates. Perform the optimization using the Berny algorithm
in the GIC-type internal coordinates. This option requires a separate GIC input section following the
geometry specification. When used in conjunction with QST2 or QST3, a GIC input section must follow
each geometry specification. The syntax of the GIC input section is described in the GIC Considerations
tab.

Rarely Used Options

Path=M
In combination with either the QST2 or the QST3 option, requests the simultaneous optimization of a
transition state and an M-point reaction path in redundant internal coordinates [595]. No coordinate may
be frozen during this type of calculation.
If QST2 is specified, the title and molecule specification sections for both reactant and product structures
are required as input as usual. The remaining M-2 points on the path are then generated by linear interpo-
lation between the reactant and product input structures. The highest energy structure becomes the initial
guess for the transition structure. Each point is optimized to lie in the reaction path and the highest point
is optimized toward the transition structure.
If QST3 is specified, a third set of title and molecule specification sections must be included in the input
as a guess for the transition state as usual. The remaining M-3 points on the path are generated by two
successive linear interpolations, first between the reactant and transition structure and then between the
transition structure and product. By default, the central point is optimized to the transition structure,
regardless of the ordering of the energies. In this case, M must be an odd number so that the points on
the path may be distributed evenly between the two sides of the transition structure.
In the output for a simultaneous optimization calculation, the predicted geometry for the optimized tran-
sition structure is followed by a list of all M converged reaction path structures.
The treatment of the input reactant and product structures is controlled by other options: OptReactant,
OptProduct, BiMolecular.
Note that the SCF wavefunction for structures in the reactant valley may be quite different from that of
structures in the product valley. Guess=Always can be used to prevent the wavefunction of a reactant-like
structure from being used as a guess for the wavefunction of a product-like structure.
OptReactant
Specifies that the input structure for the reactant in a path optimization calculation (Opt=Path) should be
optimized to a local minimum. This is the default. NoOptReactant retains the input structure as a point
5.58 Optimization 247

that is already on the reaction path (which generally means that it should have been previously optimized
to a minimum). OptReactant may not be combined with BiMolecular.
BiMolecular
Specifies that the reactants or products are bimolecular and that the input structure will be used as an
anchor point in an Opt=Path optimization. This anchor point will not appear as one of the M points on
the path. Instead, it will be used to control how far the reactant side spreads out from the transition state.
By default, this option is off.
OptProduct
Specifies that the input structure for the product in a path optimization calculation (Opt=Path) should be
optimized to a local minimum. This is the default. NoOptProduct retains the input structure as a point
that is already on the reaction path (which generally means that it should have been previously optimized
to a minimum). OptProduct may not be combined with BiMolecular.
Linear
Linear requests and NoLinear suppresses the linear search in Berny optimizations. The default is to use
the linear search whenever possible.
TrustUpdate
TrustUpdate requests and NoTrustUpdate suppresses dynamic update of the trust radius in Berny opti-
mizations. The default is to update for minima.
Newton
Use the Newton-Raphson step rather than the RFO step during Berny optimizations.
NRScale
NRScale requests that if the step size in the Newton-Raphson step in Berny optimizations exceeds the
maximum, then it is to be scaled back. NoNRScale causes a minimization on the surface of the sphere of
maximum step size [596]. Scaling is the default for transition state optimizations and minimizing on the
sphere is the default for minimizations.
Steep
Requests steepest descent instead of Newton-Raphson steps during Berny optimizations. This is only
compatible with Berny local minimum optimizations. It may be useful when starting far from the mini-
mum, but is unlikely to reach full convergence.
UpdateMethod=keyword
Specifies the Hessian update method. Keyword is one of: Powell, BFGS, PDBFGS, ND2Corr, OD2Corr,
D2CorrBFGS, Bofill, D2CMix and None.
HFError
Assume that numerical errors in the energy and forces are those appropriate for HF and post-SCF calcu-
lations (1.0D-07 and 1.0D-07, respectively). This is the default for optimizations using those methods
and also for semi-empirical methods.
FineGridError
Assume that numerical errors in the energy and forces are those appropriate for DFT calculations using
the default grid (1.0D-07 and 1.0D-06, respectively). This is the default for optimizations using a DFT
method and using the default grid (or specifying Int=FineGrid).
SG1Error
 248 Chapter 5. List of Gaussian Keywords

Assume that numerical errors in the energy and forces are those appropriate for DFT calculations using
the SG-1 grid (1.0D-07 and 1.0D-05, respectively). This is the default for optimizations using a DFT
method and Int(Grid=SG1Grid).

5.58.3 Availability
Analytic gradients are available for the HF, all DFT methods, CIS, MP2, MP3, MP4(SDQ), CID, CISD,
CCD, CCSD, QCISD, CASSCF, and all semi-empirical methods.
The Tight, VeryTight, Expert, Eigentest and EstmFC options are available for the Berny algorithm only.
Optimizations of large molecules which have many very low frequency vibrational modes with DFT will
often proceed more reliably when a larger DFT integration grid is requested (Int=UltraFine).

5.58.4 Related Keywords

IRC, IRCmax, Scan, Force, Frequency, Geom

5.58.5 Examples
Output from Optimization Jobs. The string GradGradGrad· · · delimits the output from the Berny
optimization procedures. On the first, initialization pass, the program prints a table giving the initial values of
the variables to be optimized. For optimizations in redundant internal coordinates, all coordinates in use are
displayed in the table (not merely those present in the molecule specification section):

GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
Berny optimization. The opt. algorithm is identified by the header format & this line.
Initialization pass.
----------------------------
! Initial Parameters !
! (Angstroms and Degrees) !
-------------------- ----------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------
! R1 R(2,1) 1. estimate D2E/DX2 !
! R2 R(3,1) 1. estimate D2E/DX2 !
! A1 A(2,1,3) 104.5 estimate D2E/DX2 !
--------------------------------------------------------------------

The manner in which the initial second derivative are provided is indicated under the heading Derivative Info.
In this case the second derivatives will be estimated.
Each subsequent step of the optimization is delimited by lines like these:

GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
Berny optimization.
Search for a local minimum.
Step number 4 out of a maximum of 20

Once the optimization completes, the final structure is displayed:

Optimization completed.
-- Stationary point found.
5.58 Optimization 249

----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------- --------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------
! R1 R(2,1) 0.9892 -DE/DX = 0.0002 !
! R2 R(3,1) 0.9892 -DE/DX = 0.0002 !
! A1 A(2,1,3) 100.004 -DE/DX = 0.0001 !
--------------------------------------------------------------------

The redundant internal coordinate definitions are given in the second column of the table. The numbers
in parentheses refer to the atoms within the molecule specification. For example, the variable R1, defined as
R(2,1), specifies the bond length between atoms 1 and 2. The energy for the optimized structure will be
found in the output from the final optimization step, which precedes this table in the output file.
Compound Jobs. Optimizations are commonly followed by frequency calculations at the optimized struc-
ture. To facilitate this procedure, the Opt keyword may be combined with Freq in the route section of an input
file, and this combination will automatically generate a two-step job.
It is also common to follow an optimization with a single point energy calculation at a higher level of
theory. The following route section automatically performs an HF/6-31G(d,p) optimization followed by an
MP4/6-31G(d,p) single point energy calculation:
# MP4/6-31G(d,p)//HF/6-31G(d,p) Test
Note that the Opt keyword is not required in this case. However, it may be included if setting any of its
options is desired.
Modifying Redundant Internal Coordinates. The following input file illustrates the method for modify-
ing redundant internal coordinates within an input file:

# HF/6-31G(d) Opt=ModRedun Test

Opt job

0,1
C1 0.000 0.000 0.000
C2 0.000 0.000 1.505
O3 1.047 0.000 -0.651
H4 -1.000 -0.006 -0.484
H5 -0.735 0.755 1.898
H6 -0.295 -1.024 1.866
O7 1.242 0.364 2.065
H8 1.938 -0.001 1.499

3 8 Adds hydrogen bond (but not angles or dihedrals).

2 1 3 Adds C-C-O angle.

This structure is acetaldehyde with an OH substituted for one of the hydrogens in the methyl group; the
first input line for ModRedundant creates a hydrogen bond between that hydrogen atom and the oxygen atom
250 Chapter 5. List of Gaussian Keywords

in the carbonyl group. Note that this adds only the bond between these two atoms The associated angles and
dihedral angles could be added as well using the B action code:
3 8 B
Displaying the Value of a Desired Coordinate. The second input line for ModRedundant specifies the C-
C=O bond angle, ensuring that its value will be displayed in the summary structure table for each optimization
step.
Using Wildcards in Redundant Internal Coordinates. A distance matrix coordinate system can be
activated using the following input:

* * B Define all bonds between pairs of atoms

* * * K Remove all other redundant internal coordinates

The following input defines partial distance matrix coordinates to connect only the closest layers of atoms:

* * B 1.1 Define all bonds between atoms within 1.1 Å

* * * K Remove all other redundant internal coordinates

The following input sets up an optimization in redundant internal coordinates in which atoms N1 through
Nn are frozen (such jobs may require the NoSymm keyword). Note that the lines containing the B action code
will generate Cartesian coordinates for all of the coordinates involving the specified atom since only one atom
number is specified:

N1 B Generate Cartesian coordinates involving atom N1

···
Nn B Generate Cartesian coordinates involving atom Nn
* F Freeze all Cartesian coordinates

The following input defines special “spherical” internal coordinates appropriate for molecules like C60 by
removing all dihedral angles from the redundant internal coordinates:

* * * * R Remove all dihedral angles

Additional examples are found in the section on relaxed PES scans below.
Performing Partial Optimizations. The following job illustrates the method for freezing variables during
an optimization:

# B3LYP/6-31G(d) Opt=ReadOpt

Partial optimization of Fe2S2

cluster with phenylthiolates.

-2,1
Fe 15.2630 -1.0091 7.0068
S 14.8495 1.1490 7.0431
Fe 17.0430 1.0091 7.0068
S 17.4565 -1.1490 7.0431
5.58 Optimization 251

S 14.3762 -2.1581 8.7983

C 12.5993 -2.1848 8.6878
···
C 14.8285 -3.8823 3.3884
H 14.3660 -3.3149 2.7071

noatoms atoms=1-4 ReadOpt input.

The central cluster (the first four atoms) will be optimized while the phenylthiolates are frozen.
Restarting an Optimization. A failed optimization may be restarted from its checkpoint file by simply
repeating the route section of the original job, adding the Restart option to the Opt keyword. For example, this
route section restarts a B3LYP/6-31G(d) Berny optimization to a second-order saddle point:
%Chk=saddle2
# Opt=(TS,Restart,MaxCyc=50) Test
The model chemistry and starting geometry are retrieved from the checkpoint file. Options specifying the
optimization type and procedure are required in the route section for the restart job (e.g., TS in the preceding
example). Some parameter-setting options can be omitted to use the same values are for the original job, or they
can be modified for the restarted job, such as MaxCycle in the example. Note that you must include CalcFC
to compute the Hessian at the first point of the restarted job. Second derivatives are computed only when this
option is present in the route section of the restarted job, regardless of whether it was specified for the original
job.
Reading a Structure from the Checkpoint File. Redundant internal coordinate structures may be re-
trieved from the checkpoint file with Geom=Checkpoint as usual. The read-in structure may be altered by spec-
ifying Geom=ModRedundant as well; modifications have a form identical to the input for Opt=ModRedundant:
[Type] N1 [N2 [N3 [N4]]] [Action [Params]] [[Min] Max]]
Locating a Transition Structure with the STQN Method. The QST2 option initiates a search for a tran-
sition structure connecting specific reactants and products. The input for this option has this general structure
(blank lines are omitted):

# HF/6-31G(d) Opt=QST2 # HF/6-31G(d) (Opt=QST2,ModRedun)

First title section First title section
Molecule specification for the reactants Molecule specification for the reactants
Second title section ModRedundant input for the reactants
Molecule specification for the products Second title section
Molecule specification for the products
ModRedundant input for the products (optional)

Note that each molecule specification is preceded by its own title section (and separating blank line). If the
ModRedundant option is specified, then each molecule specification is followed by any desired modifications
to the redundant internal coordinates.
Gaussian will automatically generate a starting structure for the transition structure midway between the
reactant and product structures, and then perform an optimization to a first-order saddle point.
The QST3 option allows you to specify a better initial structure for the transition state. It requires the
252 Chapter 5. List of Gaussian Keywords

two title and molecule specification sections for the reactants and products as for QST2 and also additional,
third title and molecule specification sections for the initial transition state geometry (along with the usual
blank line separators), as well as three corresponding modifications to the redundant internal coordinates if
the ModRedundant option is specified. The program will then locate the transition structure connecting the
reactants and products closest to the specified initial geometry.
The optimized structure found by QST2 or QST3 appears in the output in a format similar to that for other
types of geometry optimizations:

----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
--------------------- ----------------------
! Name Definition Value Reactant Product Derivative Info. !
---------------------------------------------------------------------
! R1 R(2,1) 1.0836 1.083 1.084 -DE/DX = 0. !
! R2 R(3,1) 1.4233 1.4047 1.4426 -DE/DX = -0. !
! R3 R(4,1) 1.4154 1.4347 1.3952 -DE/DX = -0. !
! R4 R(5,3) 1.3989 1.3989 1.3984 -DE/DX = 0. !
! R5 R(6,3) 1.1009 1.0985 1.0995 -DE/DX = 0. !
! ··· !
---------------------------------------------------------------------

In addition to listing the optimized values, the table includes those for the reactants and products.
Performing a Relaxed Potential Energy Surface Scan. The Opt=ModRedundant option may also be
used to perform a relaxed potential energy surface (PES) scan. Like the facility provided by Scan, a relaxed
PES scan steps over a rectangular grid on the PES involving selected internal coordinates. It differs from Scan
in that a constrained geometry optimization is performed at each point.
Relaxed PES scans are available only for the Berny algorithm. If any scanning variable breaks symmetry
during the calculation, then you must include NoSymm in the route section of the job, since it may fail with an
error.
Redundant internal coordinates specified with the Opt=ModRedundant option may be scanned using the
S code letter: N1 N2 [N3 [N4]] S steps step-size. For example, this input adds a bond between atoms 2 and 3,
specifying three scan steps of 0.05 Å each:
2 3 S 3 0.05
Wildcards in the ModRedundant input may also be useful in setting up relaxed PES scans. For example,
the following input is appropriate for a potential energy surface scan involving the N1-N2-N3-N4 dihedral
angle:
N1 N2 N3 N4 S 20 2.0 Specify a relaxed PES scan of 20 steps in 2o increments
Cartesian coordinates can also include scan specifications:
X atom S x-steps x-size y-steps y-size z-steps z-size
For example, the following ModRedundant input performs a relaxed potential energy surface scan. Start-
ing at the initial position of atom 1 and moving in five 0.2 Angstrom steps in the X direction and three 0.1
Angstrom steps in the Z direction:
X 1 S 5 0.2 0 0.0 3 0.1
5.58 Optimization 253

The Berny geometry optimization algorithm in Gaussian is based on an earlier program written by H. B.
Schlegel which implemented his published algorithm [592]. The program has been considerably enhanced since
this earlier version using techniques either taken from other algorithms or never published, and consequently it
is appropriate to summarize the current status of the Berny algorithm here.

At each step of a Berny optimization the following actions are taken:

♢ The Hessian is updated unless an analytic Hessian has been computed or it is the first step, in which case an
estimate of the Hessian is made. Normally the update is done using an iterated BFGS for minima and
an iterated Bofill for transition states in redundant internal coordinates, and using a modification of the
original Schlegel update procedure for optimizations in internal coordinates. By default, this is derived
from a valence force field [588], but upon request either a unit matrix or a diagonal Hessian can also be
generated as estimates.
♢ The trust radius (maximum allowed Newton-Raphson step) is updated if a minimum is sought, using the
method of Fletcher [597–599].
♢ Any components of the gradient vector corresponding to frozen variables are set to zero or projected out,
thereby eliminating their direct contribution to the next optimization step.
If a minimum is sought, perform a linear search between the latest point and the best previous point (the
previous point having lowest energy). If second derivatives are available at both points and a minimum is
sought, a quintic polynomial fit is attempted first; if it does not have a minimum in the acceptable range
(see below) or if second derivatives are not available, a constrained quartic fit is attempted. This fits a
quartic polynomial to the energy and first derivative (along the connecting line) at the two points with the
constraint that the second derivative of the polynomial just reach zero at its minimum, thereby ensuring
that the polynomial itself has exactly one minimum. If this fit fails or if the resulting step is unacceptable,
a simple cubic is fit is done.
Any quintic or quartic step is considered acceptable if the latest point is the best so far but if the newest
point is not the best, the linear search must return a point in between the most recent and the best step to
be acceptable. Cubic steps are never accepted unless they are in between the two points or no larger than
the previous step. Finally, if all fits fail and the most recent step is the best so far, no linear step is taken.
If all fits fail and the most recent step is not the best, the linear step is taken to the midpoint of the line
connecting the most recent and the best previous points.
♢ If the latest point is the best so far or if a transition state is sought, a quadratic step is determined using
the current (possibly approximate) second derivatives. If a linear search was done, the quadratic step
is taken from the point extrapolated using the linear search and uses forces at that point estimated by
interpolating between the forces at the two points used in the linear search. By default, this step uses the
Rational Function Optimization (RFO) approach [589, 591, 600, 601]. The RFO step behaves better than
the Newton-Raphson method used in earlier versions of Gaussian when the curvature at the current point
is not that desired. The old Newton-Raphson step is available as an option.
♢ Any components of the step vector resulting from the quadratic step corresponding to frozen variables are
set to zero or projected out.
♢ If the quadratic step exceeds the trust radius and a minimum is sought, the step is reduced in length to the
trust radius by searching for a minimum of the quadratic function on the sphere having the trust radius,
as discussed by Jørgensen [596]. If a transition state is sought or if NRScale was requested, the quadratic
254 Chapter 5. List of Gaussian Keywords

step is simply scaled down to the trust radius.

♢ Finally, convergence is tested against criteria for the maximum force component, root-mean square force,
maximum step component, and root-mean-square step. The step is the change between the most recent
point and the next to be computed (the sum of the linear and quadratic steps).

Examples of Using GICs

Basic GIC input. Here is an example of using the generalized internal coordinates defined by the user
from scratch for the geometry optimization of the water molecule.
# HF opt=readallgic

Title

0 1
O 0.0000 0.0000 0.0000
H 0.0000 0.0000 1.3112
H 1.0354 0.0000 -0.6225

R(1,2)
R(1,3)
HOH=A(2,1,3)

The atomic indexes 1, 2, and 3 refer to the oxygen atom, the first and the second hydrogen atom, respec-
tively. The first and the second expression define the O-H bonds, and the third one defines the H-O-H valence
angle (with the user-provided label “HOH”). An excerpt of the output with a table containing the initial values
of the GICs is shown below.
----------------------------
! Initial Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.3112 estimate D2E/DX2 !
! R2 R(1,3) 1.2081 estimate D2E/DX2 !
! HOH A(2,1,3) 121.015 estimate D2E/DX2 !
--------------------------------------------------------------------------------

Note that the labels “R1” and “R2” above were assigned by default. The coordinates R1=R(1,2) and
R2=R(1,3) are parsed as pure distances and given here in Angstroms, and the HOH=A(2,1,3) is a pure valence
angle in degrees.
# HF opt=readallgic

Title

0 1
O 0.0000 0.0000 0.0000
H 0.0000 0.0000 1.3112
H 1.0354 0.0000 -0.6225
5.58 Optimization 255

OHSym1=(R(1,2)+R(1,3))/sqrt(2)
OHSym2=(R(1,2)-R(1,3))/sqrt(2)
HOH=A(2,1,3)

The first and the second expression in the example above define the symmetrized O-H bonds, and the third
one is the H-O-H valence angle.
----------------------------
! Initial Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! OHSym1 GIC-1 3.3664 estimate D2E/DX2 !
! OHSym2 GIC-2 0.1377 estimate D2E/DX2 !
! HOH A(2,1,3) 121.015 estimate D2E/DX2 !
--------------------------------------------------------------------------------
NOTE: GIC-type coordinates are in arbitrary units.

The coordinates OHSym1 and OHSym2 are parsed as generic GICs and therefore given here in arbitrary
units. The units are actually Bohrs in this case because the 2−1/2 factor is taken as dimensionless and the values
of R(1,2) and R(1,3) are taken in Bohrs.

# HF opt=readallgic

Title

0 1
O
H 1 1.3
H 1 1.2 2 120.

R12=SQRT[{X(2)-X(1)}^2+{Y(2)-Y(1)}^2+{Z(2)-Z(1)}^2]
R13=SQRT[{X(3)-X(1)}^2+{Y(3)-Y(1)}^2+{Z(3)-Z(1)}^2]
A0(Inactive)=DotDiff(2,1,3,1)/{R12*R13}
A213=ArcCos(A0)

The GIC input section above defines two bond distances and one valence angle expressed via Cartesian
coordinates. The coordinate A0 is defined as the dot-product (DotDiff) of the vectors ⃗R12 and ⃗R13 divided by
the product of their lengths, and it is selected as “inactive” (i.e., excluded from the geometry optimization). An
excerpt of the output with a table containing the initial values of the GICs is shown below.
----------------------------
! Initial Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R12 GIC-1 2.4566 estimate D2E/DX2 !
! R13 GIC-2 2.2677 estimate D2E/DX2 !
 256 Chapter 5. List of Gaussian Keywords

! A213 GIC-3 2.0944 estimate D2E/DX2 !

--------------------------------------------------------------------------------
NOTE: GIC-type coordinates are in arbitrary units.

The values of R12, R13, and the dot-product are calculated using the Cartesian coordinates given in Bohrs.
The GIC arbitrary units are Bohrs (for R12 and R13) and radians (for A213).

5.58.6 GIC Info

The options that do not mention GIC and can be used with the Opt keyword should work as described –
except for NoFreeze, which should not be combined with any GIC-related option. In the latter case, use the
UnFreezeAll flag in the GIC input section.
This section discusses specifying generalized internal coordinates (GICs) in Gaussian input files. GICs
have many potential uses: defining additional coordinates whose values are reported during geometry opti-
mizations, freezing various structural parameters during the optimization of a molecular system, specifying
parameters over which to perform a scan, defining constraints for geometry optimizations based on structural
parameters or complex relationships between them, requesting calculation of parts of the Hessian, and other
purposes.
The GIC input section is separated from the earlier input by a blank line. It has one or more lines con-
taining coordinate definitions, expressions or standalone options. Here is a simple GIC input section for water
illustrating some of the possible features:

R(1,2) Define a bond length coordinate for atoms 1 and 2

Bond2=R[1,3] Define another bond length coordinate named Bond2
HOH(freeze)=A(2,1,3) Define an optimization constraint: a bond angle coordinate named HOH
(∠2-1-3)

For an optimization, these coordinates will result in the bond angle remaining fixed at its initial value and
the two bond distances being optimized.
The basic form of a coordinate is the following:
label(options)=expression
All of the components are optional. In the preceding examples, all components were present only in the
third line. The first line contained only a coordinate expression, while the second line also contained a label
without options. Note that options may also be placed following the expression:
HOH=A(2,1,3) Freeze
Labels are user-assigned identifiers for the coordinate. They are not case sensitive. Labels many contain
letters and number, but must begin with a letter. If no label is specified, a generic one will be assigned by the
program (e.g., R1, R2, A1, etc.). A parenthesized, comma-separated list of options can be included following
the label if desired. Note that square brackets or braces may be substituted for parentheses anywhere in a
coordinate definition.

Structural Parameters
Coordinates are defined by expressions. The simplest expressions simply identify a specific structural
parameter within the molecule, using the following constructs. Note that an asterisk may be used as a wildcard
for any atom number (see the examples).
5.58 Optimization 257

R(i,j)
Define a bond coordinate between atoms i and j. B, Bond and Stretch are synonyms for R.
A(i,j,k)
Define a non-linear angle coordinate involving atoms i, j and k where the angle vertex is at atom j. Angle
and Bend are synonyms for A.
D(i,j,k,l)
Define a dihedral angle between the plane containing atoms i, j and k and the plane containing atoms j, k
and l. Dihedral and Torsion are synonyms for D.
L(i,j,k,l,M)
Define the linear bend coordinate involving atoms i, j and k where the angle vertex is at atom j. Linear
and LinearBend are synonyms for L.
A linear bend definition has two components, indicated by M values of -1 and -2 for the first and second
components, respectively (no other values are permitted). A linear bend is specified by defining its two
orthogonal directions. These can be indicated in two ways:

♢ For a nonlinear molecule with more than 3 atoms, a fourth atom which does not form a linear angle
with i, j and k in any combination can be used. In this case, l can be set to its atom number. For
example, the following may be used to specify a linear bend involving atoms 1, 2 and 3 using atom
6 to determine the two orthogonal directions:
L(1,2,3,6,-1)
L(1,2,3,6,-2)
If l is set to -4, then the fourth atom will be determined automatically based on the molecular
geometry.
♢ The other method is to project the linear bend onto one of the coordinate system’s axial planes: the
values of -1, -2 and -3 for l specify the YZ, XZ and XY planes (respectively). The value 0 may also
be used to request that the appropriate plane be determined automatically:
L(1,2,3,0,-1)
L(1,2,3,0,-2)

X(i)
Define the x Cartesian coordinate for atom i. Cartesian(i,-1) and Cartesian(i,X) are synonyms, and Carte-
sian may be abbreviated as Cart.
Y(i)
Define the y Cartesian coordinate for atom i. Cartesian(i,-2) and Cartesian(i,Y) are synonyms, and Carte-
sian may be abbreviated as Cart.
Z(i)
Define the z Cartesian coordinate for atom i. Cartesian(i,-3) and Cartesian(i,Z) are synonyms, and Carte-
sian may be abbreviated as Cart.
XCntr(atom-list)
YCntr(atom-list)
ZCntr(atom-list)
Define x, y or z Cartesian coordinate for the geometric center (centroid) of a molecular fragment that
contains specified atoms. The atom list is a comma-separated list of atom numbers and/or ranges. For
258 Chapter 5. List of Gaussian Keywords

example, XCntr(1,12-15,27) defines the x coordinate of the fragment containing atoms 1, 12, 13, 14, 15
and 27. If the atom list is omitted, it defaults to the entire molecule.
DotDiff(i,j,k,l)
Define the dot product (a·b) of the two Cartesian coordinate difference vectors a and b for atoms i,j,k and
l determined as a = (Xi − X j ,Yi −Y j , Zi − Z j ) and b = (Xk − Xl ,Yk −Yl , Zk − Zl ).

Compound Expressions
Complex expressions may be constructed by combining multiple items using one or more mathematical
operations. The argument(s) A and B can be the labels of a previously defined coordinate, a valid GIC expres-
sion or even constants (integer or floating-point). The operation names are not case sensitive. The following
operations are available:
♢ Square root: SQRT(A).
♢ Power of e: EXP(A) for eA .
♢ Trigonometric functions: SIN(A), COS(A), TAN(A).
♢ Inverse cosine: ARCCOS(A).
♢ Addition: A+B
♢ Subtraction: A-B
♢ Multiplication: A*B
♢ Division: A/B
♢ Exponentiation: A**n for An (n is an integer). The form A^n is also accepted.
Here are some simple examples which define symmetrized OH bonds in water:

R12(inactive)=B(1,2)
R13(inactive)=B(1,3)
RSym = (R12 + R13)/SQRT(2)
RASym = [Bond(1,2) - Bond(1,3)]/SQRT(2)

The first two coordinates are set as inactive since they are intermediates not intended to be used in the
optimization. Line 3 illustrates an expression using previously defined labels, while line 4 shows the use of
literal expressions with operators. Note that the argument to the square root function is the constant 2.

Options
A comma separated list of options can follow the coordinate label, enclosed in parentheses. Alternatively,
options may follow the expression, separated from it and from one another by spaces. All options are case
insensitive.
For the purposes of geometry optimizations, a coordinate can be designated as:
♢ Active: The coordinate is part of the list of internal coordinates used in the geometry optimzation. In contrast,
Inactive coordinates are not included in the set used for the geometry optimization. By default, active
coordinates are unfrozen: allowed to change value (see the next bullet).
♢ Frozen: A coordinate whose value is held constant during the course of a geometry optimization. The values
of active, unfrozen coordinates change during a geometry optimization. The frozen or unfrozen status of
inactive coordinates is irrelevant during an optimization.
In the descriptions that follow, coordinates that “already exist” refers to previously-defined coordinates
with the same label or the same value expression. Such coordinates may have been defined earlier in the input
5.58 Optimization 259

stream or retrieved from the checkpoint file from a previous job.

Active
If the specified coordinate does not already exist, build a new coordinate defined by the given expression,
and flag it as active and unfrozen. If the coordinate was previously defined, then flag it as active and
unfrozen (whatever its previous status). It is the default. Activate, Add and Build are synonyms for
Active. May be abbreviated to A when specified following the expression.
Frozen
Build a coordinate defined by the expression if it does not exist, and flag the coordinate as active for
geometry optimizations and freeze it at the current value.
Freeze is a synonym for Frozen. May be abbreviated to F when specified following the expression.
Inactive
If the coordiante does not already exist, build a new coordinate defined by the expression and flag it
inactive. If the coordinate with the given label or for the given expression has been already built and
flagged as active (frozen or unfrozen), then remove it from the geometry optimization by flagging it as
inactive. Remove is a synonym for Inactive. May be abbreviated to R when specified following the
expression.
Kill
Remove the coordinate from the list of internal coordinates used in geometry optimization along with
any dependent coordinates by flagging all of them as inactive. The dependent coordinates include any
coordinate that depends on the same atoms as the given coordinate. For example, R(1,5) Kill will result
in removing the coordinate R(1,5) – the internuclear distance between atoms 1 and 5 – as well as the
valence angles, dihedral angles and any other coordinate that depends on the Cartesian coordinates of
atoms 1 and 5 in combination with other atoms in the molecule. RemoveAll is a synonym for Kill. May
be abbreviated to K when specified following the expression.
PrintOnly
Include the initial value of the coordinate in the starting geometry in the Gaussian output file, and then
flag it as inactive.
Modify
A label must be included in the coordinate specification for this option. It replaces the old coordinate
with the specified label with the new expression, and flags the newly modified coordinate as active and
unfrozen.
Diff
Calculate numerical second derivatives for the row and column of the initial Hessian corresponding to
this coordinate. May be abbreviated to D when specified following the expression.
FC=x
Change the diagonal element for the given coordinate in the initial Hessian to x, a floating-point number
in atomic units. ForceConstant is a synonym for FC.
Value=x
Set the initial value for the given internal coordinate to x, a floating point value. The units for the value
are those of the Gaussian program, as defined by the Units keyword (Angstroms or degrees by default).
The current Cartesian coordinates will be adjusted to match this value as closely as possible. This option
260 Chapter 5. List of Gaussian Keywords

should be used cautiously and sparingly. It is far easier and more reliable to set the initial molecular
structure as desired in a graphical environment like GaussView.
StepSize=x,NSteps=n
These options are used to specify a relaxed potential energy surface scan in which the coordinate is
incremented by x a total of n times, and a constrained optimization is perfromed from each resulting
starting geometry. x should be a positive floating-point number in atomic units, n should be an integer
>1. When these options follow the expression, the comma separating them should be replaced by a space.
Min=min,Max=max
This option is used in combination with Active, Freeze or Inactive. It adds, freezes or makes inactive
the coordinate when its value satisfies the condition min ≤ value ≤ max. min and max are floating-point
numbers in the units defined by the Units (Angstroms or degrees by default). If Min or Max is omitted,
the condition becomes value ≤ max or min ≥ min respectively. When these options follow the expression,
the comma should be replaced by a space.
action OnlyIf condition
action IfNot condition
These options provide conditional coordinate operations. They can only be placed following the expres-
sion defining the current coordinate. Action is one of Active, Freeze or Inactive. The condition is a label
or expression for another coordinate. The specified action will be performed for the current coordinate if
the coordinate referred to in condition is active for OnlyIf or inactive for IfNot. Note that the conditional
test applies only to the action specified preceding the option and not to other options that may be present
in the coordinate specification.

Standalone Options
The following options are independent of coordinate definitions and apply globally. They should be spec-
ified alone on their input line.
FreezeAll
Freeze all internal coordinate previously added as active.
UnFreezeAll
Unfreeze all internal coordinates previously added as active frozen.
RemoveAll
Remove/inactivate all internal coordinate previously added as active (frozen or unfrozen).
Atom i action
Apply the specified action to the Cartesian coordinates of atom i. If i is an asterisk, then the action
applies to all atoms. Action is one of Active, Freeze, UnFreeze, Remove (make inactive), RemoveAll and
XYZOnly. These options are as defined above; XYZOnly says to remove any internal coordinates that
depend on atom i but to add/retain the coordinates of that atom. The default action is Active.

Examples
The following example manipulates some automatically-generated coordinates, defines some new ones,
and then uses wildcards to remove coordinates related to specific atoms:

R(5,9) freeze Freeze bond distance R(5,9).

R(8,9) Add a new active coordinate R(8,9) with a default label.
5.58 Optimization 261

Ang189 = A(1,8,9) Add a new active coordinate A(1,8,9) labeled Ang189.

R10(remove) Remove a coordinate labeled R10.
Dih6123(remove) = D(6,1,2,3) If D(6,1,2,3) exists, then remove the coordinate.
Dis79(freeze) = R(7,9) Freeze the coordinate R(7,9): if it is new, then label it
Dis79; if it already exists, retain the old label.
G1 = (R16+R19)*0.529177 Add a new coordinate labeled G1.
Ang189a(modify)=cos(g2)*57.29577951Change the definition of coordinate Ang189a.
R(11,*) remove Remove distances between atom 11 and any other atom.
D(*,1,17,*) remove Remove any dihedral built around the 1-17 bond.

Note that if a specified coordinate already exists, then an entry adding it will result in an error (e.g., lines
1-3 above).
The following example first defines the centroids of two fragments. Then, it defines the interfragment
distance as an optimization coordinate:
Define the center of Fragment 1, but don’t include it in the optimization.
XC1(Inactive)=XCntr(1-10)
YC1(Inactive)=YCntr(1-10)
ZC1(Inactive)=ZCntr(1-10)
Define the center of Fragment 2, but don’t include it in the optimization.
XC2(Inactive)=XCntr(11-21)
YC2(Inactive)=YCntr(11-21)
ZC2(Inactive)=ZCntr(11-21)
Define the distance F1-F2 and include it in the optimization. Its value will be reported in Å:
F1F2=sqrt[(XC1-XC2)^2+(YC1-YC2)^2+(ZC1-ZC2)^2]*0.529177

The following example requests a relaxed PES scan over the same coordinate:
F1F2(NSteps=10,StepSize=0.2)
The following example removes an angle coordinate generated by default if ≥179.9o , substituting a linear
bend:

A(1,2,3) Remove Min=179.9 Remove angle coordinate if too large.

L(1,2,3,0,-1) Add IfNot A(1,2,3) Add linear bend only if the angle coordinate not active.
L(1,2,3,0,-2) Add IfNot A(1,2,3)

The following example removes an angle coordinate if it is ≤ the specified value, setting the corresponding
force constant is set to 0.2 au. The latter applies whenever it is needed: as the initial force constant and the
force constant to use should be variable be reactivated. The second line specifies the force constant for a bond
coordinate:
A(1,2,3) Remove Min=3.139847 ForceConstant=0.2
R(1,2) FC=0.5
The following example sets the force constants for various coordinates. It also inactivates bond angle
coordinates ≥ 179.8o :

R(1,*) FC=0.8
262 Chapter 5. List of Gaussian Keywords

D(*,4,5,*) FC=0.4
A(*,1,*) FC=0.5
A(*,*,*) R Min=179.8

Limitations of GICs in the Current Implementation

In the current implementation, GICs can be successfully used for many purposes including optimization
constraints and PES scans. However, there are potential problems with active composite coordinates including
multiple dihedral angles. In general, coordinates comprised of combinations of bond distances and bond angles
should behave well. Simple dihedral angles are also welll supported. Complex expressions involving multiple
dihedral angles are acceptable for frozen coordinates and for PES scans. However, they should be avoided as
active optimization coordinates.
In a non-GIC optimization, or one using GICs with only regular dihedrals, then the program is careful
about the periodicity of these coordinates. For example, in deciding whether a step in the geometry is too big
and needs to be scaled back, it recognizes that a change in value from 1 degree to 359 degrees is really a change
of -2 degrees rather than 358 degrees. Similarly, in numerically differentiating the forces in order to update the
Hessian, displacements between geometries in internal coordinates are needed, and the periodicity is accounted
for. A problem can arise when a GIC is a combination of parts for which such periodicity is important, typically,
combinations of multiple dihedral angles. For example, consider these GICs:

D1 = D(1,2,3,4)
D2 = D(5,6,7,8)
V1 = D1 + 2*D2

D1 and D2 are dihedral angles, but they are intermediates and are not used as variables in the optimization.
Their periodicity is not currently recognized in the composite coordinate V1. Suppose they have values of 1 and
2 degrees at one geometry and 1 and 359 degress at the next. The change in the optimization variable V1 should
be 0 + 2*(-3) = -6 degrees, but it is actually 0 + 2*(357) = 714 degrees, which looks like an enormous change.
This will result in the optimization algorithm performing very poorly. V1 isn’t a simple periodic function; it is
necessary to apply periodicity to its component parts as it is computed, which is not done in the current GIC
implementation.

GIC Units in Gaussian Output

The values of the GICs defined as pure distances and angles (including valence angles, linear bends and
dihedral angles/torsions) are computed from the Cartesian coordinates in atomic units (Bohrs) and stored in-
ternally in Bohrs and radians. However, for the user’s convenience, they are expressed as usual in Angstroms
and degrees in the Gaussian output. In the case of a generic GIC (i.e., when the GIC is not a pure Cartesian
coordinate, bond distance or angle), the GIC value is computed as a function of Cartesian coordinates and bond
distances in Bohrs and angles in radians, combined with optional constants in user-defined units. Such generic
GIC values (labeled as GIC) are computed, stored and output in these same units: i.e., if the GIC is a combi-
nation of bonds or a combination of valence angles, then the arbitrary units become Bohrs for the bonds and
radians for the angles.
 5.59 Output 263

Use of ModRedundant Format Input

Modifications to the GICs can be read in using the ModRedundant format from the current internal coordi-
nate algorithm. However, the old format is only available with the GICs that include only pure bond distances,
bond angles or torsion angles. In addition, the old format and the new GIC format described above cannot be
mixed together in the same input section.

5.59 Output
The Output keyword is most often used to create input file for various external programs. It can also write
Fortran unformatted files containing calculation results. Its options control the contents of the created file.

5.59.1 Options
WFN
Write a PROAIMS wavefunction (.wfn) file. The name for the created file is read from the input stream,
on a separate line. PSI is a synonym for WFN.
WFX
Write a wavefunction file used by the newer versions of AIMPAC (.wfx files). The name for the created
file is read from the input stream, on a separate line. WfnX is a synonym for WFX.
GIAOCx
Include GIAO Cx in .wfn or .wfx file.
CSGTCx
Include CSGT Cx in .wfn or .wfx file.
Pickett
Write g tensors and other tensors for hyperfine spectra [602–607] to the output file in the form of input
for Pickett’s program [608] (see spec.jpl.nasa.gov). The following tensors can be computed by
Gaussian [410, 413–415, 609, 610]:
♢ Nuclear electric quadrupole constants: all jobs
♢ Rotational constants: Freq=(VibRot[,Anharmonic])
♢ Quartic centrifugal distortion terms: Freq=(VCD,Anharmonic)
♢ Electronic spin rotation terms: NMR
♢ Nuclear spin rotation terms: NMR
♢ Dipolar hyperfine terms: all jobs
♢ Fermi contact terms: all jobs
SpinRotation
Synonym for NMR Output=Pickett. Includes all hyperfine tensors which can be computed without doing
a vibrational frequency calculation.
RotationalConstants
Synonym for Freq=VibRot Output=Pickett. Includes almost all hyperfine tensors which can be computed
while performing only a harmonic vibrational frequency calculation.
For HF and DFT, you can combine the two preceding options. Output=(RotatationalConstants, Spin-
Rotation) includes all the tensors computable with no more than second derivatives. It is equivalent to
Freq=(VCD,VibRot) Output=Pickett.
 264 Chapter 5. List of Gaussian Keywords

QuarticCentrifugal
Synonym for Freq=(VibRot,Anharm) Output=Pickett. Includes quartic rotation-vibration coupling, but
does not include spin-rotation tensors which must be computed separately.
ReadAtoms
Read a list of the atoms to include in the input for Pickett’s program (note that this program only accepts
tensors for eight nuclei). Atoms numbers are specified in free format, and this input section is blank-
terminated. By default, eight interesting atoms are selected automatically by the program.

Gaussian Interfacing-Related Options

MatrixElement
Requests that a text data file for interfacing to other programs be generated. RawMatrixElement requests
a binary matrix element file be generated. See Interfacing to Gaussian 16 for details.
I4Labels
When combined with the MatrixElement option, use Integer*4 values rather than the current Gaussian
integer size when writing the matrix element file.
MO2ElectronIntegrals
When combined with the MatrixElement option, include two-electron integrals over MOs when writing
the matrix element file. In order to include the two-electron integrals in the AO basis within the matrix
element file, combine this option with SCF=Conventional.
DerivativeDensities
When combined with the MatrixElement option, include derivative densities from CPHF when writing
the matrix element file.
GIAOInts
When combined with the MatrixElement option, include GIAO L/R**3 and d2H/dBdm one-electron
integral derivatives when writing the matrix element file.
Files
When combined with the MatrixElement option, include the contents of the specified internal Gaussian
file within the generated matrix element file. For example, the following option:
Output=(Matrix,Files=(123,(456,offset=1,integer=27)))
will cause the contents of internal file 123 (assumed by default to be real values) to be included in the
matrix element file (labeled as “File 123”). The second item in the file list specifies the 27 integers in
internal file 456 starting after the first (8-byte) word (labeled as “File 456 integers section 001”), as well
as any real values following the integers (labeled “File 456 reals section 002”).

5.59.2 Related Keywords

Punch, SCRF=COSMORS, Pop=MK(Antechamber), NMR=CSGT (ACID).

5.60 PBC
This keyword allows you to specify options for Periodic Boundary Conditions jobs. Note PBC is turned on
simply by including translation vectors in the input structure, and this keyword is used only to control how PBC
calculations are performed. If you do not need any of these options, you do not have to include the keyword to
perform a PBC calculation.
 5.60 PBC 265

5.60.1 Options
GammaOnly
Do just the Γ point (k=0) rather than full k-integration.
NKPoint=N
Do approximately N k-points.
CellRange=N
Go out N Bohr in each direction in setting up image cells.
NCellMin=N
Include at least N cells.
NCellMax=N
Include at most N cells in any part of the calculation.
NCellDFT=N
Include at least N cells in DFT XC quadrature. NCellXC is a synonym for this option.
NCellK=N
Include at least N cells in exact exchange. By default, if exact exchange is included, then this is twice the
number of cells used for overlap-related quantities and XC quadrature.

5.60.2 Availability
HF and DFT analytic energy and optimizations, and numerical frequencies (no IR intensities). Not valid
with SCRF or Charge. For periodic systems of any reasonable size, acceptable performance may only be
feasible by using a pure DFT functional in combination with density fitting.

5.60.3 Examples
Periodic systems are specified with a normal molecule specification for the unit cell. The only addi-
tional required input are one, two or three translation vectors appended to the molecule specification (with no
intervening blank line), indicating the replication direction(s). For example, the following input specifies a
one-dimensional PBC single point energy calculation for neoprene:

# PBEPBE/6-31g(d,p)/Auto SCF=Tight

neoprene, -CH2-CH=C(Cl)-CH2- optimized geometry

0 1
C,-1.9267226529,0.4060180273,0.0316702826
H,-2.3523143977,0.9206168644,0.9131400756
H,-1.8372739404,1.1548899113,-0.770750797
C,-0.5737182157,-0.1434584477,0.3762843235
H,-0.5015912465,-0.7653394047,1.2791284293
C,0.5790889876,0.0220081655,-0.3005160849
C,1.9237098673,-0.5258773194,0.0966261209
H,1.772234452,-1.2511397907,0.915962512
H,2.3627869487,-1.0792380182,-0.752511583
Cl,0.6209825739,0.9860944599,-1.7876398696
TV,4.8477468928,0.1714181332,0.5112729831
 266 Chapter 5. List of Gaussian Keywords

The final line specifies the translation vector. Note that it specifies TV as the atom symbol.
The following molecule specification could be used for a two-dimensional PBC calculation on a graphite
sheet:

0 1
C 0.000000 0.000000 0.000000
C 0.000000 1.429118 0.000000
TV 2.475315 0.000000 0.000000
TV -1.219952 2.133447 0.000000

Here is the molecule specification that could be used for a three-dimensional PBC calculation on gallium
arsenide:

0 1
Ga 0.000000 0.000000 0.000000
Ga 0.000000 2.825000 2.825000
Ga 2.825000 0.000000 2.825000
Ga 2.825000 2.825000 0.000000
As 1.412500 1.412500 1.412500
As 1.412500 4.237500 4.237500
As 4.237500 1.412500 4.237500
As 4.237500 4.237500 1.412500
TV 5.650000 0.000000 0.000000
TV 0.000000 5.650000 0.000000
TV 0.000000 0.000000 5.650000

5.61 Polar
This method keyword requests that the dipole electric field polarizabilities (and hyperpolarizabilities, if
possible) be computed. No geometry change or derivatives are implied, but this keyword may be combined in
the same job with numerical differentiation of forces by specifying both Freq and Polar in the route section. Freq
and Polar may not be combined for methods lacking analytic gradients (MP4(SDTQ), QCISD(T), CCSD(T),
and so on). Note that Polar is done by default when second derivatives are computed analytically.
The polarizability and hyperpolarizability are presented in the output in the standard orientation in lower
triangular and lower tetrahedral order, respectively: αxx , αxy , αyy , αxz , αyz , αzz and βxxx , βxxy , βxyy , βyyy , βxxz ,
βxyz , βyyz , βxzz , βyzz , βzzz .
Normally, polarizabilities and hyperpolarizabilities are computed using static frequencies. However,
frequency-dependent polarizabilities and hyperpolarizabilities [611–615] may be computed by including CPHF=RdFreq
in the route section and specifying the desired frequency in the input file.
Optical rotations [616–625] may also be predicted via the OptRot option [396, 626–633]. See [634–636]
for example applications.

Predicting ROA and Raman Spectra

Raman and ROA intensities can be calculated separately from calculation of the force constants and normal
modes, to facilitate using a larger basis for these properties as recommended in [401]. The options Polar=Raman
and Polar=ROA request that the force constants be picked up from the checkpoint file (i.e., from a previous Freq
 5.61 Polar 267

calculation) and new polarizability derivatives (and the other two tensor derivatives for ROA) be computed and
combined with the force constants in predicting intensities and spectra. Test job 931 provides an example of a
two-step ROA calculation. For these jobs, be aware that the energy reported in the log file archive entry and
in the final checkpoint file/formatted checkpoint file is the one computed in the frequency job – i.e., the value
read from the checkpoint file at the start of the job – and not the energy computed with the model chemistry of
the Raman/ROA calculation and reported in the final SCF Done output line.

5.61.1 Options

ROA
Compute dynamic analytic Raman optical activity intensities using GIAOs [401]. This procedure requires
one or more incident light frequencies to be supplied in the input to be used in the electromagnetic
perturbations (CPHF=RdFreq is the default with Freq=ROA). See the Examples for a sample input file.
This option is valid for Hartree-Fock and DFT methods.
Raman
Calculate Raman spectrum from force constants read-in from the checkpoint file.
OptRot
Perform optical rotation calculation. Use CPHF=RdFreq to specify the desired frequencies. Avail-
able for HF and DFT only. This option cannot be combined with NMR. Include IOp(10/46=7) in
the route section to include the dipole-quadrupole contribution to the dipole-magnetic dipole polariz-
ability in order to compute the full optical rotation tensor [399, 627]; the latter will be labeled as
Optical Rotation G’ tensor in the output. Note that doing so does not change the optical
rotation.
DCSHG
Do extra frequency-dependent CPHF for dc-SHG (direct current second harmonic generation) hyperpo-
larizabilities. This option implies CPHF=RdFreq as well.
Gamma
Equivalent to Polar=(DCSHG,Cubic) to do 2nd hyperpolarizabilities.
Analytic
Analytically compute the polarizability and the hyperpolarizability when analytic third derivatives are
available. This option is the default for method with analytic second derivatives: RHF and UHF, CASSCF,
CIS, MP2 and DFT methods. Note that the polarizability is always computed during analytic frequency
calculations.
WorkerPerturbations
During numerical frequencies using Linda parallelism, run separate displacements on each worker in-
stead of parallelizing each energy+derivative evaluation across the cluster. More efficient, but requires
specifying an extra worker on the master node. This is the default if at least 3 Linda workers were
specified. NoWorkerPerturbations suppresses this behavior.
FourPoint
Do four displacements instead of two for each degree of freedom during numerical frequencies, polariz-
abilities, or freq=anharm. This gives better accuracy and less sensitivity to step size at the cost of doing
twice as many calculations.
 268 Chapter 5. List of Gaussian Keywords

DoubleNumer
Computes hyperpolarizabilities in addition to polarizabilities for methods with analytic gradients (first
derivatives). Computes polarizabilities by double numerical differentiation of the energy for methods
without analytic derivatives. EnOnly is a synonym for DoubleNumer.
Cubic
Numerically differentiate analytic polarizabilities to produce hyperpolarizabilities. Applicable only to
methods having analytic frequencies but no analytic third derivatives.
Numerical
Computes the polarizability as a numerical derivative of the dipole moment (it is the analytic derivative
of the energy, of course, not the expectation value in the case of MP2 or CI energies). The default for
methods for which only analytic first derivative gradients are available.
Step=N
Specifies the step size in the electric field to be 0.0001N atomic units (applies to numerical differentia-
tion).
Restart
Restarts a numerical calculation from the checkpoint file. A failed Polar calculation may be restarted
from its checkpoint file by simply repeating the route section of the original job, adding the Restart
option to the Polar keyword. No other input is required.
Susceptibility
Compute magnetic susceptibility as well as other properties (see NMR). Available for HF and DFT only.
TwoPoint
When computing numerical derivatives, make two displacements in each coordinate. This is the default.
FourPoint will make four displacements but only works with Link 106 (Polar=Numer). Not valid with
Polar=DoubleNumer.
Dipole
Compute the dipole polarizabilities (the default).

5.61.2 Availability
The following table summarizes the options to Polar that are required to compute polarizabilities and
hyperpolarizabilities for the available methods.

Method Capabilities Polarizability Hyperpolarizability

Analytic 3rd derivatives (HF, most DFT) Polar (default=Analytic) Polar (default=Analytic)
Analytic frequencies (MP2, CIS, · · · ) Polar (default=Analytic) Polar=Cubic
Only analytic gradients (CCSD, BD, · · · ) Polar (default=Numeric) Polar=DoubleNumer
No analytic derivatives (CCSD(T), · · · ) Polar (default=DoubleNumer) N/A

Frequency-dependent polarizabilities and hyperpolarizabilities (i.e., Polar CPHF=RdFreq) are available

only for HF and DFT methods.

5.61.3 Related Keywords

Freq, CPHF=RdFreq
 5.61 Polar 269

5.61.4 Examples
Frequency-Dependent Properties. The following job will compute frequency-dependent polarizabilities
and hyperpolarizabilities using ω =0.1 Hartrees:

# Polar CPHF=RdFreq HF/6-31G(d)

Frequency-dependent calculation: w=0.1

molecule specification

0.1

Performing a frequency-dependent Polar calculation produces the results for the specified frequency fol-
lowing those for the static case within the output. For example, here are the polarizability values for a frequency-
dependent job (ω =0.1 Hartree):

SCF Polarizability for W= 0.000000:

1 2 3
1 0.482729D+01
2 0.000000D+00 0.112001D+02
3 0.000000D+00 0.000000D+00 0.165696D+02
Isotropic polarizability for W= 0.000000 10.87 Bohr**3.
SCF Polarizability for W= 0.100000:
1 2 3
1 0.491893D+01
2 0.000000D+00 0.115663D+02
3 0.000000D+00 0.000000D+00 0.171826D+02

Isotropic polarizability for W= 0.100000 11.22 Bohr**3.

A static polarizability calculation would include only the first section. Similar output follows for hyperpo-
larizabilities and additional properties.
Optical Rotations. Here is the key part of the output for optical rotation jobs (OptRot option). In this
case, we have performed a frequency-dependent calculation by including CPHF=RdFreq in the route section
and specified a frequency of 589.3 nm:

Dipole-magnetic dipole polarizability for W= 0.077318:

1 2 3
1 -0.428755D+01 -0.175571D+01 0.000000D+00
2 -0.552645D+01 0.987070D+01 0.000000D+00
3 0.000000D+00 0.000000D+00 -0.676292D+00
w= 0.077318 a.u., Optical Rotation Beta= -1.6356 au.
Molar Mass = 172.2694 grams/mole, [Alpha]( 5893.0 A) = -366.99 deg.

The specific rotation value is highlighted in the example output.

 270 Chapter 5. List of Gaussian Keywords

Recommended Model Chemistries for ROA. The following two-step job illustrates the recommended
models for predicting ROA spectra from [401]:

%chk=freq.chk
# APFD/6-311+g(2d,2p) Opt Freq · · ·

Freq + ROA: optimization+frequency

0 1
molecule specification

--Link1--
%Oldchk=freq.chk
%Chk=roa.chk
# APFD/spAug-cc-pVTZ Polar=ROA Guess=Read Geom=Check · · ·

Freq + ROA: ROA calculation with larger basis set

0 1

532nm

5.62 Population
This properties keyword controls printing of molecular orbitals and several types of population analysis
and atomic charge assignments. The default is to print just the total atomic charges and orbital energies, except
for Guess=Only jobs, for which the default is Pop=Full (see Options). Populations are done once for single-
point calculations and at the first and last points of geometry optimizations. Note that the Population keyword
requires an option.
The density that is used for the population analysis is controlled by the Density keyword. Note that only
one density and method of charge fitting can be used in a job step. If several combinations are of interest,
additional jobs steps can be added by specifying Guess=Only Density=Check, to avoid repeating any costly
calculations.
Population analysis results are given in the standard orientation.
Output controlled by the Population keyword includes:
♢ Molecular orbitals and orbital energies. By default, all orbitals are included, but the output can be limited to
a specific orbital range with the Orbitals option.
♢ Atomic charge distribution. The total charge per fragment is also reported if applicable.
♢ Multipole moments: dipole through hexadecapole.
APT charges are also computed by default during vibrational frequency calculations [637].

5.62.1 Options
5.62 Population 271

Options Controlling Output File Contents

None
No orbitals are printed, and no population analysis is done. This is the default for all calculations using
the ZIndo method.
Minimal
Total atomic charges and orbital energies are printed. This is the default for all job types and methods
except Guess=Only and/or ZIndo.
Regular
The five highest occupied and five lowest virtual orbitals are printed, along with the density matrices and
a full (orbital by orbital and atom by atom) Mulliken population analysis. Since the size of the output
depends on the square of the size of the molecule, it can become quite substantial for larger molecules.
Full
Same as the Regular population analysis, except that all orbitals are printed. This is the default for
Guess=Only jobs.
Always
Perform a population analysis at every optimization step rather than just the initial and final ones.
Orbitals[=N]
AllOrbitals
Perform a population analysis of the highest N occupied and lowest N virtual orbitals, including the
atomic contributions to each MO (see the examples). N defaults to 10. AllOrbitals may also be specified
instead of Orbitals=N to request analysis of all orbitals. For open shell calculations, both alpha and beta
orbitals are included.
ThreshOrbitals=N
Set the minimum contribution percentage to include in individual orbital population analysis. The default
is 10.

Population Analysis Options

Bonding
Do a bonding population analysis in addition to the standard analysis. This is a Mulliken population
analysis in which only density terms involving pairs of basis functions on different centers are retained.
MBS
Perform minimum basis set Mulliken population analysis [110, 181]. NoMBS tells the program not to
perform MBS Mulliken population analysis.
Hirshfeld
Perform Hirshfeld population analysis [638–640]. CM5 atomic charges [641] are computed along with
Hirshfeld charges. CM5 is a synonym for Hirshfeld. The HirshfeldEE option requests interatomic elec-
trostatic interactions as well.
Biorthogonalize
Biorthogonalize unrestricted molecular orbitals in order to maximally align electron pairs.
SaveBiorth
Save biorthogonalized orbitals in the checkpoint file over the canonical MOs.
DCT
272 Chapter 5. List of Gaussian Keywords

Compute Ciofini’s DCT charge transfer diagnostic [642, 643] for whichever unrelaxed excited-state den-
sity/densities are available and, if a relaxed density was requested, for that as well.
NaturalTransitionOrbitals
Requests Natural Transition Orbital analysis [644] of a CI-Singles or TD-DFT excited state. Must be
accompanied by Density=(Check,Transition=N) in order to specify which transition density is to be used
to generate the orbitals. To print the orbitals from several states of interest, run successive Pop=NTO
Density=(Check,Transition=N) Guess=Only jobs after the initial excited state calculation. NTO is a
synonym for this option.
SaveNaturalTransitionOrbitals
Save the generated orbitals in the checkpoint file, replacing the canonical ones if the density was read-in
from there. SaveNTO is a synonym for this option. If you want to visualize the orbitals, you need to
write them back to the checkpoint file. It is a good idea to do so with a copy of the checkpoint file for
each state. After the initial excited state calculation (using %Chk=ex.chk), use a technique like the
following to generate visualization data for each state:

$ g16 <<END Run a Guess=Only job just to

generate orbitals.
%OldChk=excited.chk Work on copy of original check-
point file.
%Chk=staten.chk Checkpoint file for this state.
# Geom=AllCheck ChkBas Guess=Only
Density=(Check,Transition=n) Pop=SaveNTO Repeat for each state.
END End of Gaussian input file.

Charge Save Options

NoOrthogonalize
Suppress orthogonalization of saved Pop=(SaveMixed,NoOrthogonalize) orbitals (primarily for visualiz-
ing raw NBO results).
SaveType
Computed atomic charges can be stored on the checkpoint file for use in a later MM calculation with
Geom=Check. The options Pop=SaveMulliken, Pop=SaveESP, Pop=SaveNPA, Pop=SaveCM5, and so
on can be used to save the corresponding charges. In the case of a multilayer ONIOM calculation, only
explicitly computed charges are saved by default: i.e., charges for atoms in the QM layer(s). Any atomic
charges present in the input file will not be used and they will be replaced by the newly fitted charges
saved by these options.
The additional option Uncharged will keep the atomic charges present in the input file and only fit charges
on uncharged atoms in the QM layers(s). The option combinations Pop=(Uncharged, SaveMulliken),
Pop=(Uncharged, SaveCM5) and so on will save both the original atomic charges plus the newly fitted
charges for the atoms that were originally uncharged.

Natural Orbital-Related Options

NaturalOrbitals
Do a natural orbital analysis of the total density. NO is a synonym for NaturalOrbitals.
5.62 Population 273

NOAB
Do separate natural orbital analyses for the α and β densities. NaturalSpinOrbitals is a synonym for
NOAB.
AlphaNatural
Do separate natural orbital analyses for the α and β densities, but store only the α densities for use in a
.wfn file (see Output=WFN). NOA is a synonym for AlphaNatural.
BetaNatural
Do separate natural orbital analyses for the α and β densities, but store only the β densities for use in a
.wfn file (see Output=WFN). NOB is a synonym for BetaNatural.
SpinNatural
Generate natural orbitals for the spin density (with α considered positive).
By default, natural orbitals are not included in the checkpoint file. Use a second job step of this form to
place the natural orbitals into the checkpoint file:

--Link1--
%Chk=name
# Guess=(Save,Only,NaturalOrbitals) Geom=AllCheck ChkBasis

Run the formchk utility on the resulting checkpoint file to prepare the orbitals for visualization.

Options For Generating Electrostatic Potential-Derived Charges

MK
Produce charges fit to the electrostatic potential at points selected according to the Merz-Singh-Kollman
scheme [645, 646]. ESP and MerzKollman are synonyms for MK. The data file for Antechamber (the
AMBER program for generating RESP charges) can be generated using Pop=MK IOp(6/50=1) and spec-
ifying the file name on a separate line at the end of the Gaussian input file.
MKUFF
Uses the MK fitting but using UFF radii, which are defined for the full periodic table.
CHelp
Produce charges fit to the electrostatic potential at points selected according to the CHelp scheme [647].
CHelpG
Produce charges fit to the electrostatic potential at points selected according to the CHelpG scheme [648].
HLY
Specifies the Hu, Lu, and Yang charge fitting method [649].
HLYGAt
Specifies the Hu, Lu, and Yang charge fitting method, but using Gaussian’s standard atomic densities
instead of those of HLY. The authors of HLY only parametrized the atomic densities required for the
model for the first 18 elements. This is an alternative version that uses the HLY fitting scheme but with
Gaussian’s standard atomic densities, which are available for the entire periodic table. For systems which
can be done either way, the difference in atomic charges is usually between 1% and 5%.
Dipole
When fitting charges to the potential, constrain them to reproduce the dipole moment. ESPDipole is a
synonym for Dipole.
274 Chapter 5. List of Gaussian Keywords

AtomDipole
When fitting charges to the potential, also fit a point dipole at each atomic center.
ReadRadii
Read in alternative radii (in Angstroms) for each element for use in fitting potentials. These are read as
pairs of atomic symbol and radius, terminated by a blank line.
ReadAtRadii
Read in alternative radii (in Angstroms) for each atom for use in fitting potentials. These are read as pairs
of atom number and radius, terminated by a blank line.

NBO-Related Options (Version 3)

NBO
Requests a full Natural Bond Orbital analysis, using NBO version 3 [14–21].
NCS
Requests a partitioning of the NMR shielding tensors (computed using GIAOs) into magnetic contribu-
tions from bonds and lone pairs using the Natural Chemical Shielding analysis of Bohmann et al. [650],
which is based upon the NBO analysis method. By default, an analysis of the isotropic shielding is
performed. NoNCS skips this analysis.
NCSDiag
Requests an NCS analysis of the diagonal tensor elements.
NCSAll
Requests an NCS analysis of all tensor components.
NPA
Requests just the Natural Population Analysis phase of NBO.
NBORead
Requests a full NBO analysis, with input controlling the analysis read from the input stream. Use this
option to specify keywords for NBO. Refer to the NBO documentation for details on this input.
NBODel
Requests NBO analysis of the effects of deletion of some interactions. Only possible with SCF methods.
Implies that NBO input will be read; refer to the NBO documentation for details. Note that NBO input
starts in column 2 so that the UNIX shell does not interpret the initial $.
SaveNBOs
Save natural bond orbitals in the checkpoint file (for later visualization).
SaveNLMOs
Save natural localized molecular orbitals in the checkpoint file (for later visualization).
SaveMixed
Save the NBOs for the occupied orbitals and the NLMOs for the unoccupied orbitals in the checkpoint
file (for later visualization).

NBO-Related Options (Version 6)

An interface to NBO version 6 is provided. Pop=NPA6, Pop=NBO6, Pop=NBO6Read and Pop=NBO6Delete

request use of the separate NBO6 program via the external interface. The script required to run NBO6 and the
program itself must be obtained from Frank Weinhold (nbo6.chem.wisc.edu).
 5.62 Population 275

5.62.2 Related Keywords

Density, Output=WFN

5.62.3 Examples
Orbital-by-Orbital Population Analysis. The following route section requests population analysis of the
lowest 3 virtual orbitals and the highest 3 occupied orbitals:
# UHF/6-311+G(d) Pop=Orbitals=3
Here is the resulting output from a calculation on FeO+ quartet:

Atomic contributions to Alpha molecular orbitals:

Alpha occ 16 OE=-0.923 is Fe1-d=1.00
Alpha occ 17 OE=-0.699 is O2-p=0.88
Alpha occ 18 OE=-0.690 is O2-p=0.68 Fe1-s=0.21
Alpha vir 19 OE=-0.253 is Fe1-s=0.70 Fe1-p=0.27
Alpha vir 20 OE=-0.188 is Fe1-p=0.71 O2-p=0.29
Alpha vir 21 OE=-0.133 is Fe1-p=1.04

Atomic contributions to Beta molecular orbitals:

Beta occ 13 OE=-0.801 is O2-p=0.79
Beta occ 14 OE=-0.783 is Fe1-d=1.00
Beta occ 15 OE=-0.758 is O2-p=0.89
Beta vir 16 OE=-0.241 is Fe1-s=0.81 Fe1-p=0.17
Beta vir 17 OE=-0.139 is Fe1-p=0.91 Fe1-d=0.14

Note that both alpha and beta orbital information is included. For each orbital, the output reports the orbital
energy (labeled OE and given in atomic units), followed by the fractional contribution of all basis functions of
a given angular momentum for each relevant atom.
This is an example of a system where it is hard to tell the spin state of the system, because the canonical α
and β orbitals are quite different. If you subsequently run a Guess=(Read,Only,BiOrthogonalize) Pop=Orbital
calculation to analyze the results, then the program transforms the α and β orbitals to match up as much as
possible (occupied and virtual separately). In this case, orbital energies for the transformed orbitals are nor
given. Rather, the Pop=Orbital analysis reports the overlaps between the pairs of corresponding orbitals (i.e., α
19 with β 19), with a value of 1 indicating 100% correspondence. Instead of labeling the orbitals as occupied
or virtual, they are labeled:

Docc Doubly occupied: alpha and beta are occupied, with a match of 90% or better.
Asing, Bsing Singly occupied: alpha without matching beta occupied, or lower occupieds which
do not match up with any orbital of the opposite spin.
Dvir Virtual orbital with nearly the same alpha and beta orbitals.
AVir, BVir Virtual orbital which does not match up with any of the other opposite-spin virtuals.

The program lists the orbitals which match another orbital only once within the output. Also, for each
unpaired excess alpha spin occupied orbital, there is always some beta virtual orbital which matches it, and the
276 Chapter 5. List of Gaussian Keywords

latter are also omitted.

Here is the output for FeO+ quartet, which has 3 more alpha electrons than beta but which turns out to
really have 4 unpaired alpha occupieds and one unpaired beta occupied (the lowest doubly occupied and highest
unoccupied orbitals have been cut from the output):

Atomic contributions to molecular orbitals:

Docc. orb 13 abOv=0.999 is Fe1-d=1.00
Docc. orb 14 abOv=0.990 is O2-p=0.72 Fe1-s=0.14 Fe1-d=0.14
Asing orb 15 abOv=0.316 is Fe1-d=0.99
Asing orb 16 abOv=1.000 is Fe1-d=0.94
Asing orb 17 abOv=1.000 is Fe1-d=0.91
Asing orb 18 abOv=1.000 is Fe1-d=0.91
Dvirt orb 19 abOv=1.000 is O2-s=1.92 Fe1-s=-0.67 O2-p=-0.43 Fe1-p=0.14
Dvirt orb 20 abOv=1.000 is Fe1-s=0.52 Fe1-p=0.37
Bsing orb 15 abOv=0.316 is O2-p=0.92

Orbitals 1-14 are doubly occupied. Alpha orbital 15 and beta orbital 15 are different singly occupied
orbitals; all 4 unpaired alpha spins are on the Fe, and the one unpaired beta spin is on the oxygen. There are no
unmatched alpha and beta virtuals within the default range of orbitals analyzed.
Fragment Level Decomposition. If fragment information is present, the output also reports populations
over fragments. For Pop=Orbital jobs, the decomposition of each orbital by fragment is reported.
Default output including fragment populations:
Mulliken charges with hydrogens summed into heavy atoms:
1
1 Pd -0.265855
2 P 0.346314
3 P 0.346314
4 Cl -0.168156
5 Cl -0.168156
6 C 0.060982
7 C 0.060982
8 C -0.106213
9 C -0.106213
Sum of Mulliken charges with hydrogens summed into heavy atoms = 0.00000
Condensed to fragments (all electrons):
1 -0.265855
2 -0.168156
3 -0.168156
4 0.060982
5 0.060982
6 0.480203

Pop=Orbital output:
Alpha occ 60 OE=-0.247 is Cl4-p=0.22 Cl5-p=0.22 P3-p=0.12 P2-p=0.12
Fr6=0.36 Fr2=0.22 Fr3=0.22
 5.63 Pressure 277

Sample NBO 3 Input. The following input file requests a bond order analysis using NBO 3:

# B3LYP/6-31G(d,p) Pop=NBORead

Example of NBO bond orders

0 1
C 0.000000 0.665676 0.000000
H 0.919278 1.237739 0.000000
H -0.919239 1.237787 0.000000
C 0.000000 -0.665676 0.000000
H -0.919278 -1.237739 0.000000
H 0.919239 -1.237787 0.000000

$nbo bndidx $end

5.63 Pressure

Specifies the pressure to be used for thermochemistry analysis (in atmospheres). The value should be
specified as an option:
# · · · Pressure=1.5
The default is 1 atmosphere.

5.63.1 Options
Default
Restores the default pressure if a different value was returned by Geom=AllCheck.

5.64 Prop

This properties keyword tells Gaussian to compute electrostatic properties [97, 609, 610, 651]. By default,
the potential, electric field, and electric field gradient at each nucleus are computed. The density used for the
electrostatic analysis is controlled by the Density keyword.

5.64.1 Options
Property Selection Options
EFG
Specifies that potential, field and field gradient are to be computed. This is the default.
Potential
Specifies that the potential but not the field or field gradient are to be computed. NoPotential suppresses
computation of the electric potential and higher properties.
Field
Specifies that the potential and field, but not the field gradient, are to be computed.
 278 Chapter 5. List of Gaussian Keywords

EPR
Compute the anisotropic hyperfine coupling constants (i.e., spin-dipole EPR terms) [97, 609, 610].

Input Source-Related Options

If both Read and Opt are specified, the order of the input sections is fixed points (Read), then optimized
points (Opt).
Read
Causes the program to read a list of additional centers at which properties will be computed from the
input stream. The Cartesian coordinates of each center in angstroms are read in free field, with one
center per line, in the standard orientation.
Opt
Causes the program to read a list of centers as in Prop=Read, but then to locate the minimum in the
electric potential closest to each specified point.
FitCharge
Fit atomic charges to the electrostatic potential at the van der Waals surface.
Dipole
Constrain fitted charges to the dipole moment.
Grid
Specifies that the potential is to be calculated at one or more grids of points and written to an external file
(generally superseded by the cubegen utility). This option requests mapping of the electric potential over
a 2D grid of points. The points can be specified as a uniform rectangular grid, as an arbitrary collection
read from an auxiliary file (both described below), or via the input format used by cubegen.
Three additional input lines are required for a uniform grid:

KTape,XO,YO,ZO Fortran unit for write, coords. of map’s lower left cor-
ner.
N1,X1,Y1,Z1 # grid rows & vertical step size.
N2,X2,Y2,Z2 # grid column & horizontal step size.

For points read from an auxiliary file, a single line of input supplies all of the necessary information:
N,NEFG,LTape,KTape
The coordinates of N points in Angstroms will be read from unit LTape, in format 3F20.12. LTape defaults
to 52. The potential (NEFG=3), potential and field (NEFG=2), or potential, field, and field gradient
(NEFG=1) will be computed and written to unit KTape. For example, the following input indicates that
19,696 points for the electrostatic potential (code 3) will be read from Fortran unit 10, with output written
to Fortran unit 11:
19696,3,10,11

5.64.2 Availability
HF, all DFT methods, CIS, TD, MP2, MP3, MP4(SDQ), CID, CISD, CCD, CCSD, and QCISD.

5.64.3 Related Keywords

Density, Cubegen
 5.65 Pseudo 279

5.65 Pseudo

This keyword requests that a model potential be substituted for the core electrons. The Cards option is
by far its most-used mode. Gaussian supports a new effective core potential (ECP) input format (similar to
that used by ExtraBasis) which is described in the Format tab. When reading-in pseudopotentials, do not give
them the same names as any internally-stored pseudopotentials: CEP, CHF, LANL1, LANL2, LP-31, SDD,
and SHC.
If used with ONIOM, the Pseudo and keyword applies to all layer of the ONIOM. If you want to read in
ECPs only for one ONIOM layer, then use the GenECP keyword instead.
Without any options, this keyword defaults to Pseudo=Read.

5.65.1 Options
Read
Read pseudopotential data from the input stream. Input is described in the next subsection below. Cards
is a synonym for Read.
SOScal
When reading pseudopotentials from input using Pseudo=Read, scale the spin-orbit coefficients (if present)
by 2/L as appropriate for published CRENBL potentials. The default is not to scale, which is appropriate
for Dolg (Stuttgart) potentials.
CHF
Requests the Coreless Hartree-Fock potentials. This option is normally used with the LP-31G basis sets.
SHC
Requests the SHC potentials.
LANL1
Requests the LANL1 potentials.
LANL2
Requests the LANL2 potentials.
Old
Read pseudopotential data using the old format (used by Gaussian 92 and earlier versions).

5.65.2 Format
Full ECP Input Format

Effective Core Potential operators are sums of products of polynomial radial functions, Gaussian radial
functions and angular momentum projection operators. ECP input therefore specifies which potential to use on
each atomic center, and then includes a collection of triplets of:
(coefficient, power of R, exponent)
for each potential for each term in each angular momentum of the ECP. Since only the first few angular mo-
mentum components have different terms, the potential is expressed as (1) terms for the general case, typically
d or f and higher projection, and (2) the extra terms for each special angular momentum. Thus for an LP-31G
potential, which includes special s and p projected terms, the input includes the general (d and higher) term, the
s-d term (i.e., what to add to the general term to make the s component) and the p-d term.
All ECP input is free-format. Each block is introduced by a line containing the center numbers (from the
 280 Chapter 5. List of Gaussian Keywords

molecule specification) and/or atomic symbols, specifying the atoms and/or atoms types to which it applies
(just as for general basis set input-see the discussion of the Gen keyword). The list ends with a value of 0.
The pseudopotential for those centers/atoms follows:
Name,Max,ICore
Name of the potential, maximum angular momentum of the potential (i.e., 2 if there are special s and p
projections, 3 if there are s, p, and d projections), and number of core electrons replaced by the potential.
If Name matches the name of a previous potential, that potential is reused and no further input other than
the terminator line is required.
For each component (I=1 to Max) of the current potential, a group of terms is read, containing the follow-
ing information:
Title
A description of the block, not otherwise used.
NTerm
Number of terms in the block.
NPower,Expon,Coeff[,SO]
Power of R, exponent, and coefficient for each of the NTerm terms. NPower includes the R2 Jacobian
factor. The optional SO coefficient is for use with ECP basis sets which include this term.

Simplified ECP Input Format

Gaussian adds flexibility to ECP input by allowing it to include pre-defined basis sets names. An ECP
definition may be replaced by a line containing the standard keyword for a pre-defined basis set. In this case,
the ECPs within the specified basis set corresponding to the specified atom type(s) will be used for that atom
(see the examples).

5.65.3 Keywords
In Pseudo input, keywords for these ECPs are of the form XYn where n is the number of core electrons
which are replaced by the pseudopotential and X denotes the reference system used for generating the pseu-
dopotential (S for a single-valence-electron ion or M for a neutral atom).
Y specifies the theoretical level of the reference data: HF for Hartree-Fock, WB for Wood-Boring quasi-
relativistic and DF for Dirac-Fock relativistic. For one- or two-valence electron atoms SDF is a good choice;
otherwise MWB or MDF is recommended (although for small atoms or for the consideration of relativistic
effects, the corresponding SHF and MHF pseudopotentials may be useful).

5.65.4 SD ECP Availability

The Stuttgart/Dresden ECPs are not uniformly available across the periodic table. The following table
shows the availability of the various XY combinations, along with valid values for n. The Defaults columns list
the equivalencies for the SDD keyword (which selects an all electron basis set through Cl and ECPs thereafter)
and when IOp(3/6) is set to 6 (which selects ECPs for all elements).
Note: These ECPs are not available for elements 87 (Fr), 88 (Ra), and 105 and higher.

IOp(3/6=6) SDD keyword Valid values of n for given values of X and Y

Z Atom Default Default MWB SDF SHF MDF MHF
5.65 Pseudo 281

1 H D95 D95
2 He D95 D95
3 Li SDF2 D95
4 Be SDF2 D95 2
5 B MWB2 D95 2 2
6 C MWB2 D95 2 2
7 N MWB2 D95 2 2
8 O MWB2 D95 2 2
9 F MWB2 D95 2 2
10 Ne MWB2 D95 2 2
11 Na SDF10 6-31G 10
12 Mg SDF10 6-31G 10
13 Al MWB10 D95 10 10
14 Si MWB10 D95 10 10
15 P MWB10 D95 10 10
16 S MWB10 D95 10 10
17 Cl MWB10 D95 10 10
18 Ar MWB10 6-31G 10 10
19 K MWB10 MWB10 10 18 18
20 Ca MWB10 MWB10 10 18 18
21 Sc MDF10 MDF10 10 10
22 Ti MDF10 MDF10 10 10
23 V MDF10 MDF10 10 10
24 Cr MDF10 MDF10 10 10
25 Mn MDF10 MDF10 10 10
26 Fe MDF10 MDF10 10 10
27 Co MDF10 MDF10 10 10
28 Ni MDF10 MDF10 10 10
29 Cu MDF10 MDF10 28 10 10
30 Zn MDF10 MDF10 28 28 10 10
31 Ga MWB28 MWB28 28 28
32 Ge MWB28 MWB28 28 28 28
33 As MWB28 MWB28 28 28
34 Se MWB28 MWB28 28 28
35 Br MWB28 MWB28 28 28
36 Kr MWB28 MWB28 28 28
37 Rb MWB28 MWB28 28 36 36
38 Sr MWB28 MWB28 28 36 36
39 Y MWB28 MWB28 28 28
40 Zr MWB28 MWB28 28 28
41 Nb MWB28 MWB28 28 28
282 Chapter 5. List of Gaussian Keywords

42 Mo MWB28 MWB28 28 28
43 Tc MWB28 MWB28 28 28
44 Ru MWB28 MWB28 28 28
45 Rh MWB28 MWB28 28 28
46 Pd MWB28 MWB28 28 28
47 Ag MWB28 MWB28 28 46 28
48 Cd MWB28 MWB28 28 28
49 In MWB46 MWB46 46 46
50 Sn MWB46 MWB46 46 46
51 Sb MWB46 MWB46 46 46
52 Te MWB46 MWB46 46 46
53 I MWB46 MWB46 46 46 46
54 Xe MWB46 MWB46 46 46
55 Cs MWB46 MWB46 46 54 54
56 Ba MWB46 MWB46 46 54
57 La MWB28 MWB28 28, 46, 47 46, 47
58 Ce MWB28 MWB28 28, 47, 48 47, 48
59 Pr MWB28 MWB28 28, 48, 49 48, 49
60 Nd MWB28 MWB28 28, 49, 50 49, 50
61 Pm MWB28 MWB28 28, 50, 51 50, 51
62 Sm MWB28 MWB28 28, 51, 52 51, 52
63 Eu MWB28 MWB28 28, 52, 53 52, 53
64 Gd MWB28 MWB28 28, 53, 54 53, 54
65 Tb MWB28 MWB28 28, 54, 55 54, 55
66 Dy MWB28 MWB28 28, 55, 56 55, 56
67 Ho MWB28 MWB28 28, 56, 57 56, 57
68 Er MWB28 MWB28 28, 57, 58 57, 58
69 Tm MWB28 MWB28 28, 58, 59 58, 59
70 Yb MWB28 MWB28 28, 59 59
71 Lu MWB60 MWB60 28, 60 60
72 Hf MWB60 MWB60 60 60
73 Ta MWB60 MWB60 60 60
74 W MWB60 MWB60 60 60
75 Re MWB60 MWB60 60 60
76 Os MWB60 MWB60 60 60
77 Ir MWB60 MWB60 60 60
78 Pt MWB60 MWB60 60 60
79 Au MWB60 MWB60 60 78 60 60
80 Hg MWB60 MWB60 60, 78 60 60, 78
81 Tl MWB78 MWB78 78 78
82 Pb MWB78 MWB78 78 78
 5.65 Pseudo 283

83 Bi MWB78 MWB78 78 78
84 Po MWB78 MWB78 78 78
85 At MWB78 MWB78 78 78
86 Rn MWB78 MWB78 78 78
89 Ac MWB60 MWB60 60 60
90 Th MWB60 MWB60 60 60
91 Pa MWB60 MWB60 60 60
92 U MWB60 MWB60 60 60
93 Np MWB60 MWB60 60 60
94 Pu MWB60 MWB60 60 60
95 Am MWB60 MWB60 60 60
96 Cm MWB60 MWB60 60 60
97 Bk MWB60 MWB60 60 60
98 Cf MWB60 MWB60 60 60
99 Es MWB60 MWB60 60 60
100 Em MWB60 MWB60 60 60
101 Md MWB60 MWB60 60 60
102 No MWB60 MWB60 60 60
103 Lr MWB60 MWB60 60 60
104 Rf 92

5.65.5 Related Keywords

ChkBasis, ExtraBasis, Gen, GenECP

5.65.6 Examples
Specifying an ECP. This input file runs an RHF/LP-31G calculation on hydrogen peroxide, with the basis
set and ECP data read from the input file:
# HF/Gen Pseudo=Read Test

Hydrogen peroxide
0,1
O
H,1,R2
O,1,R3,2,A3
H,3,R2,1,A3,2,180.,0

R2=0.96
R3=1.48
A3=109.47

General basis set input

****
284 Chapter 5. List of Gaussian Keywords

O 0 ECPs for the oxygen atoms.

OLP 2 2 ECP name=OLP, applies to d & higher, replaces 2 electrons.
D component Description for the general terms.
3 Number of terms to follow.
1 80.0000000 -1.60000000
1 30.0000000 -0.40000000
2 1.0953760 -0.06623814
S-D projection Corrections for projected terms (lowest angular momentum).
3
0 0.9212952 0.39552179
0 28.6481971 2.51654843
2 9.3033500 17.04478500
P-D Corrections for projected terms (highest angular momentum).
2
2 52.3427019 27.97790770
2 30.7220233 -16.49630500
Blank line indicates end of the ECP block.

The basis set data follows the molecule specification section. The first line of the ECP data requests that a
potential be read in (type 7) for atoms number 1 and 3 (the oxygen atoms). No potential is to be used for atoms
2 and 4 (the hydrogen atoms).
The second line of ECP data begins the input for the centers requiring a read-in potential: in this case,
oxygen atoms. The potential on these centers is named OLP, it is a general term and applies to angular mo-
mentum 2 (d) and higher, and the potential replaces two electrons. Next comes a title for the general term (D
component), and the number of components of that term (3); the individual components follow on the next 3
lines. Next come the corrections for the projected terms in two sections, lowest angular momentum first. Each
section again consists of a title line, the number of terms to follow, and then the terms themselves.
Using Standard Basis Set Keywords to Specify ECPs. The following input file illustrates the use of the
simplified ECP input format:
# Becke3LYP/Gen Pseudo=Read Opt Test

HF/6-31G(d) Opt of Cr(CO)6

0 1
Cr 0.0 0.0 0.0
molecule specification continues · · ·

C O 0
6-31G(d)
****
Cr 0
LANL2DZ
****

Cr 0 ECP for chromium atom.

LANL2DZ Use the ECP in this basis set.
 5.66 Punch 285

5.66 Punch

This output specification keyword allows the user to “punch” – in more modern parlance, send to a separate
output file – useful information at various points in the calculation. The output is disposed of in whatever
manner is usual for Fortran alternate-unit output under the appropriate operating system (for example, unit 7 is
sent to the file fort.7 under UNIX). Options are used to specify what information should be output. All of these
options can be combined, except that only one of MO and NaturalOrbitals can be requested. Note, however,
that they are distinct and non-interacting. For example, Punch(MO, GAMESS) sends both the molecular orbital
and GAMESS input information to the file; it does not format the MO information in GAMESS input format.

5.66.1 Options

Archive
Requests that a summary of the important results of the calculation be punched. This output is in the
same format used by the Browse Quantum Chemistry Database System.
Title
Outputs the title section.
Coord
Outputs the atomic numbers and Cartesian coordinates in a form which could be read back into Gaussian.
Derivatives
Outputs the energy, Cartesian nuclear coordinate derivatives, and second derivatives in format 6F12.8,
suitable for later use with Opt=FCCards.
MO
Outputs the orbitals in a format suitable for Guess=Cards input.
NaturalOrbitals
Outputs natural orbitals (for the density selected with the Density keyword).
HondoInput
Outputs an input deck for one version of Hondo, which is probably easily modified to fit most others.
GAMESSInput
Outputs an input deck for GAMESS.
All
Outputs everything except natural orbitals.

5.66.2 Related Keywords

Output, chkchk -p

5.67 QCI

This method keyword requests a Quadratic CI calculation [194], including single and double substitutions.
Note that this keyword requests only QCISD and does not include the triples correction [652, 653] by default
(see T in Options).
 286 Chapter 5. List of Gaussian Keywords

5.67.1 Options
T
Requests a Quadratic CI calculation including single and double substitutions with a triples contribution
to the energy added [194].
E4T
Requests a Quadratic CI calculation including single and double substitutions with a triples contribution
to the energy and also an evaluation of MP4 triples. Must be specified with the T option.
TQ
Requests a Quadratic CI calculation including single and double substitutions with an energy contribution
from triples and quadruples [134] added.
SaveAmplitudes
Saves the converged amplitudes in the checkpoint file for use in a subsequent calculation (e.g., using a
larger basis set). Using this option results in a very large checkpoint file, but also may significantly speed
up later calculations.
ReadAmplitudes
Reads the converged amplitudes from the checkpoint file (if present). Note that the new calculation can
use a different basis set, method (if applicable), etc. than the original one.
T1Diag
Computes the Q1 diagnostic of T. J. Lee and coworkers [195, 654]. Note that Q1 is analogous to the T1
diagnostic for CCSD when it is computed using QCISD instead of the Coupled Cluster method.
FC
All frozen core options are available with this keyword; a frozen core calculation is the default. See the
discussion of the FC options for full information.
Conver=N
Sets the convergence calculations to 10−N on the energy and 10−(N−2) on the wavefunction. The default
is N=7 for single points and N=8 for gradients.
MaxCyc=n
Specifies the maximum number of cycles. The default is 50.

5.67.2 Availability
Analytic energies and gradients for QCISD, numerical gradients for QCISD(T), and numerical frequencies
for all methods.

5.67.3 Related Keywords

CCSD

5.67.4 Examples
The predicted energy from a QCISD calculation appears in the output in the final QCISD iteration:

DE(CORR)= -.54999890D-01 E(CORR)= -.7501966245D+02

When QCISD(T) is specified, the preceding output is followed by the energy including the non-iterative
triples contribution:
 5.68 Restart 287

QCISD(T)= -.75019725718D+02

5.68 Restart
This keyword restarts a previously-failed job. This method is primarily intended for long jobs that involve
sufficiently large amounts of intermediate data, so that saving the restart data in the checkpoint file would
make the checkpoint file unmanageably enormous, which would defeat the purpose of having a checkpoint file
separate from the read-write file. This procedure depends on naming the read-write file so that it will be saved
if the job terminates abnormally, and then using it to restart.
For example, in a frequency calculation you would include following Link 0 commands:

%RWF=myrwf
%NoSave
%Chk=mychk
#P Freq · · ·

input continues· · ·

By default, any file which is named with a % line is retained when the job finishes. The %NoSave after
the %RWF overrides this default, so that the read-write file will still be deleted if the job finishes normally (but
will be left behind if the job terminates early).
Be careful about these points:
♢ The checkpoint file is often useful after the job finishes, so one typically places it after the %NoSave.
♢ The read-write file may be huge and should be put on a suitable file system. For example, the checkpoint file
can be placed in a regular user directory, which might have only a moderate amount of free space and/or
be NFS-mounted. However, the read-write file for a job large enough to be worth restarting should be on
a large, local scratch file system.
♢ A restartable job is one for which execution was stopped before completion. Jobs that finish with an error
message such as convergence failure or exceeding number of optimization steps require user intervention.

5.68.1 Availability
Analytic frequency calculations, including properties like ROA and VCD with ONIOM; CCSD and EOM-
CCSD calculations; NMR; Polar=OptRot; CID, CISD, CCD, QCISD and BD energies. Calculations that com-
pute multiple geometries, such as geometry optimizations, IRCs, and numerical frequency calculations, are
better just restarted off the checkpoint file as before.

5.68.2 Related Keywords

Freq, EOM

5.68.3 Examples
The following input file will restart a job set up as described above:

%RWF=myrwf
%NoSave
 288 Chapter 5. List of Gaussian Keywords

%Chk=mychk
#P Restart

No other keywords are required in the route section, and no other input is needed.

5.69 SAC-CI
The keyword selects the Symmetry Adapted Cluster/Configuration Interaction (SAC-CI) methods of Nakat-
suji and coworkers [655–677]. For detailed information on this method, consult the SAC-CI documentation
available at the following web site: www.qcri.or.jp/sacci/. For review articles, see [661, 663, 678].
SAC-CI jobs must specify a reference state for the subsequent excited states calculations. For closed shell
systems, the default RHF wavefunction used by SAC-CI is appropriate. For open shell ground states, you
must either select an ROHF ground state wavefunction by including ROHF in the route section in addition to
SAC-CI, or you must specify a closed shell state for the ground state calculation using the AddElectron or
SubElectron option. See the examples for more information.

Spin State Options

Singlet=(additional-options)
Specifies that singlet states are to be calculated. The parenthesized list of suboptions specifies the desired
states and other calculation parameters. Other spin state selection options are CationDoublet (Doublet is
a synonym), AnionDoublet, Triplet, Quartet, Quintet, Sextet and Septet. More than one spin state may
be specified.

5.69.1 Input
In the options that follow, SpinState is replaced by the name of the desired spin state.
SpinState=(NState=(i1 ,i2 ,· · · ))
Sets the number of states of the specified type to be calculated for the various irreducible representations
of the molecule’s point group. Up to eight values may be specified, depending on the molecular symmetry
(e.g., 8 for D2h , 4 for C2v , and so on). The shorthand form NState=N specifies a value of N for each
irreducible representation. Degeneracies are handled by assuming the closest linear symmetry (e.g., D2
for Td ).
SpinState=(Density)
Calculate unrelaxed density matrices and perform Mulliken population analysis for all computed SAC-CI
states of spin SpinState. See the examples for more information.
SpinState=(SpinDensity)
Calculate spin density matrices for all computed SAC-CI states of spin SpinState. Implies the FullActive
option as well.
SpinState=(NoTransitionDensity)
By default, the transition density and oscillator strength are calculated between the SAC ground state
and the SAC-CI singlet excited states when SpinState is Singlet, and between the lowest SAC-CI states
and SAC-CI excited states for other spin states. NoTransitionDensity disables these calculations for the
corresponding spin state.
TargetState=(SpinState=s, Symmetry=m, Root=n)
 5.69 SAC-CI 289

Specifies the target state for a geometry optimization or a gradient calculation, or for use with the Den-
sity keyword. S is the keyword indicating its spin multiplicity (i.e., Singlet, Doublet, etc.), m is the
irreducible representation number of its point group, and n is the solution number in the desired spin
state (determined by a previous energy calculation).
AddElectron
Add one electron to the open shell reference SCF configuration. This is the default for such systems for
CationDoublet, Doublet, Quartet and Sextet.
SubElectron
Subtract one electron from the open shell reference SCF configuration. This is the default for such
systems for AnionDoublet.
TransitionFrom=(SpinState=s, Symmetry=m, Root=n)
Specifies the initial state for calculating transition density matrices. S is the keyword indicating its spin
multiplicity (i.e., Singlet, Doublet, etc.), m is the irreducible representation number of its point group,
and n is the solution number in the desired spin state (as for TargetState above).
AllProperties
Calculate multipole moments through hexadecapole, all nth moments to the 4th moment, all electrostatic
properties and the diamagnetic terms (shielding and susceptibility). This option applies to all spin states
which specify the Density suboption.
NoProperty
Don’t calculate any molecular properties.
SelectCISOnly
Terminate the calculation after the CIS initial guess has been calculated. You can use this option to
determine the state number of a particular state in which you are interested (e.g., for TargetState). See
the examples for an alternative method.
SACOnly
Performs only the calculation for the reference state and does not compute any excited states.

5.69.2 Options

Additional Options for Expert Users

For this set of options, SpinState below is replaced by the name of the desired spin state.
SpinState=(MaxR=N)
Set the maximum excitation level to N.
SpinState=(NonVariational)
Solve the SAC-CI equations for non-symmetric matrices. Variational proceeds by diagonalizing sym-
metrized matrices, and it is the default. Note that this option only applies to the excited state portion of
the calculation (the ground state calculation always uses a nonvariational procedure).
SpinState=(InCoreDiag)
Force use of the in-core algorithm.
SpinState=(Iterative=item)
Force the use of an iterative algorithm. item specifies the initial guess type: SInitial for CIS and SDInitial
for CISD.
290 Chapter 5. List of Gaussian Keywords

Direct
Requests to use the direct algorithm for the SAC/SAC-CI SD-R calculations. Direct is not compatible
with General-R, WithoutR2S2, FullUnlinked, InCoreDiag, and InCoreSAC. The direct SAC-CI code uses
different values of internal thresholds, which correspond to the conventional SAC-CI calculations with
NoUnlinkedSelection keywords. Therefore, the results obtained with the direct SAC-CI code are usually
different from the results with the conventional SAC-CI code. The direct SAC-CI code is efficient and
therefore strongly recommended. (available in Rev. B01 and later 1 ) [673].
FC
All frozen core options are available with this keyword; a frozen core calculation is the default. See the
discussion of the FC options for full information.
In general, the size of the active space greatly affects the accuracy of SAC-CI calculations. For this
reason, using a full orbital window is recommended. Full is the default for geometry optimizations and
gradient calculations.
LMO=type
Use the specified type of localized MO as reference orbitals. The available types are PM (Pipek-Mezey)
and Boys.
Window=(M[,N])
Means that the SAC/SAC-CI calculation is done within the M-th to N-th active orbital space (M < N
in the energy order). Window=(M[,N]) is a synonym for ReadWindow=(M[,N]). If spin densities at the
nuclei are of interest, as for Electron Spin Resonance or hyperfine splitting, then the core orbitals must
be included in the window.
CorePrWindow=(M,N)
Activates the calculation of core-excited/core-ionized states and specifies core orbitals from which an
electron is excited or ionized in the core-electron processes; M and N specify the range of core orbitals.
This keyword is used with the FullActive or Window keyword to include core-orbitals in the active space
(available in Rev. C01 and later 2 ).
MacroIteration=N
Requests the use of N macroiterations within an optimization step. The default value of N is 0.
InCoreSAC
For solution of the SAC equations using the in-core algorithm.
MaxItDiag=N
Set the maximum number of diagonalization iterations. The default is 64 and the maximum is 999.
MaxItSAC=N
Set the maximum number of iterations for solving the SAC equations. The default is 999.
MaxItLin=N
Set the maximum number of iterations allowed to solve the SAC linear equations. The maximum is 999.
DConvDiag=M
Set the diagonalization energy convergence criteria to 10−M .
DConvSAC=M

1 This is relevant to G09, not G16. – Noted by the editor.

2 This is relevant to G09, not G16. – Noted by the editor.
5.69 SAC-CI 291

Set the energy convergence criteria to 10−M when solving the SAC equations.
SD-R
Perform the calculation using singles and doubles linked excitation operators. This is the default.
General-R
Perform the calculation including linked excitation operators through sextuples.
LevelOne
Set the thresholds for selection of the double excitation operators to the lowest recommended level.
LevelThree is the most accurate level, and it is the default. LevelTwo is intermediate in accuracy between
the other two levels.
WithoutDegeneracy
By default, perturbation selection is performed so that degeneracies are retained. This option suppresses
this test, resulting in reduced computational requirements. Use of this option is not recommended for
production use.
NoLinkedSelection
Disables perturbation selection thresholds for linked operators (i.e., all operators are included).
NoUnlinkedSelection
Disables perturbation selection thresholds for unlinked operators (i.e., all operators are included).
FullUnlinked
Include all types of unlinked terms. Forces the use of the in-core algorithm.
In order to include all terms, all three of NoLinkedSelection, NoUnlinkedSelection, and FullUnlinked
are required, currently at a considerable performance penalty.
WithoutR2S2
Ignore R2S2 unlinked integrals. This option results in a tradeoff between decreased accuracy and com-
putational requirements.
EgOp
Generate quadruple and higher-order linked operators in the General-R scheme via the exponential gen-
eration algorithm. This is the default for single point energy calculations. The highest order excitation
level is specified via the MaxR option (up to a maximum of 6). Perturbation selection thresholds are set
via the LevelOne, LevelTwo and LevelThree options.
FullRGeneration
Generate all higher-order linked operators in the General-R scheme up to MaxR=4 and then perform
perturbation selection as above. This is the default for gradient calculations and geometry optimizations.

These options are used to ensure consistency between all points in multipoint calculation types like poten-
tial energy surface scans. The Scan calculation must be performed three times: at the first point with BeforeG-
SUM, then at some or all subsequent points with CalcGSUM and then finally at all points with AfterGSUM.
The actual results are provided by the final calculation. This procedure is only valid for singlet, triplet, ionized
and electron-attached states, and it is not compatible with the General-R option.
BeforeGSUM
Initialize a series of linked calculations. Use this option in a calculation at the first point.
CalcGSUM
Collect data and determine the thresholds and operator selections at specified points in order to form a
 292 Chapter 5. List of Gaussian Keywords

consistent set which can then be used at every point.

AfterGSUM
Perform SAC-CI calculations at each point using the GSUM data collected previously with the CalcG-
SUM option.

These options can be used to increase the program default settings after a failed job has indicated that a
resource shortfall was the problem.
MaxR2Op=N
Set the maximum number of R2 operators after perturbation selection to N. The default is 100,000.
MaxEgOp=N
Set the maximum number of operators in the General-R method to N. The default is 5,000.

5.69.3 Availability
Energy, analytical energy gradient, geometry optimization, and numerical frequencies.
Geometry optimizations default to using a full window. Specifying a different frozen core option for an
optimization will result in numerical gradient calculations and correspondingly poorer performance.

5.69.4 Related Keywords

Density

5.69.5 Examples
If you want to locate the lowest two singlet excited states, you could use a route like the following:
# SAC-CI=(Singlet=(NState=8))/6-31G(d) NoSymm · · ·
This will search for 8 singlet states, ignoring symmetry. The two lowest excited states will probably be among
those found by the calculation.
Alternatively, you could use the following route:
# SAC-CI=(Singlet=(NState=4))/6-31G(d) · · ·
This calculation will locate the lowest four singlet excited states for each irreducible representation.
To specify the desired number of singlet excited states for each irreducible representation for a molecule
with C2v symmetry, use a route like this one:
# SAC-CI=(Singlet=(NState=(2,2,1,2)))/6-31G(d) · · ·
Direct SAC-CI. To use the direct SAC-CI code, use the following route:
# SAC-CI=(Direct,Singlet=(· · · ),· · · )/6-31G(d) · · ·
Locating States with an Inexpensive Initial Calculation. You can use a preliminary, lower-accuracy
calculation in order to locate a desired excited state at reduced computational cost. For example, the following
route will locate 4 singlet excited states of each symmetry type:
# SAC-CI=(Singlet=(NState=4),LevelOne)/6-31G(d) · · ·
This job could be followed by a normal (LevelThree) calculation for the state(s) of interest. For example:
# SAC-CI=(Singlet=(1,0,1,0))/6-31G(d) · · ·
Calculations on Open Shell Systems. To predict excited states for vinyl radical, a neutral doublet radical,
you could use a route like the following:
# ROHF/6-31G(d) SAC-CI=(Doublet=(NState=3),Quartet=(NState=3)) · · ·
5.69 SAC-CI 293

This specifies the use of an ROHF wavefunction for the ground state, and it computes three doublet and three
quartet excited states for each irreducible representation. You could use a similar approach for the triplet ground
state of methylene.
Geometry Optimizations. To optimize a specific excited state, use the TargetState option:
# Opt SAC-CI=(Singlet=(Nstate=4),
TargetState=(SpinState=Singlet,Symmetry=1,Root=2))/6-31G(d) · · ·
Computing Densities and Molecular Properties. To compute the unrelaxed density and population
analysis for all predicted excited states, use a route like this one:
# SAC-CI=(Singlet=(· · · ,Density),Triplet=(· · · ,Density))/6-31G(d) · · ·
If you wanted to compute the unrelaxed density and population analysis only for the triplet states, then
you would omit the Density suboption to the Singlet option.
To compute the relaxed density and population analysis for only one specified state, use a route like the
following:
# SAC-CI=(Singlet=(NState=4),TargetState=(· · · )) Density=Current · · ·
Note that this job will be much more computationally expensive than the previous one as it requires a full
gradient calculation.
SAC-CI Output. SAC-CI calculations produce a table like the following for each requested spin state
(this example is for singlet states):

--------------------------------------------------------------------
Transition dipole moment of singlet state from SAC ground state
--------------------------------------------------------------------
Symmetry Sol Excitation Transition dipole moment (au) Osc.
energy (eV) X Y Z strength
--------------------------------------------------------------------
A1 0 0.0 Excitations are from this state.
A1 1 8.7019 0.0000 0.0000 0.4645 0.0460
A1 2 18.9280 0.0000 0.0000 -0.4502 0.0940
A1 3 18.0422 0.0000 0.0000 -0.8904 0.3505
A1 4 18.5153 0.0000 0.0000 0.0077 0.0000
A2 1 7.1159 0.0000 0.0000 0.0000 0.0000
A2 2 18.2740 0.0000 0.0000 0.0000 0.0000
B1 1 1.0334 -0.2989 0.0000 0.0000 0.0023
B1 2 18.7395 -0.6670 0.0000 0.0000 0.2042
B1 3 22.1915 -0.1500 0.0000 0.0000 0.0122
B1 4 15.8155 0.8252 0.0000 0.0000 0.2639
B2 1 11.0581 0.0000 0.7853 0.0000 0.1671
B2 2 15.6587 0.0000 1.5055 0.0000 0.8696
B2 3 24.6714 0.0000 -0.7764 0.0000 0.3644
B2 4 23.5135 0.0000 -0.1099 0.0000 0.0070
---------------------------------------------------------------------

Note that the various excited states are grouped by symmetry type – and not in order of increasing energy
– in the output.
 294 Chapter 5. List of Gaussian Keywords

5.70 Scale
Specifies the frequency scale factor to be used for thermochemistry analysis. The value should be specified
as an option:
# · · · Scale=0.95
The default is 1.0 except for compound methods where the scale factor is implicit in being the definition
of the method used.

5.70.1 Options
Default
Restores the default scale factor for harmonic frequencies if a different value was retrieved by Geom=AllCheck.

5.71 Scan
This calculation type keyword requests that a potential energy surface (PES) scan be done. A rigid PES
scan is performed, which consists of single point energy evaluations over a rectangular grid involving selected
internal coordinates. The molecular structure must be defined using Z-matrix coordinates. The number of steps
and step size for each variable are specified on the variable definition lines, following the variable’s initial value.
For example:

R1 1.41 3 0.05
A1 104.5 2 1.0
A2 120.0

This input causes variable R1 to be stepped 3 times by 0.05. Thus, four R1 values (1.41, 1.46, 1.51 and
1.56) will be done for each combination of other variables. Similarly, 3 values for A1 (104.5, 105.5 and 106.5)
will be used, and A2 will be held fixed at 120.0. All in all, a total of 12 energy evaluations will be performed.
Any number of variables can be stepped. The units of the step-sizes are controlled by the Units keyword and
default to Angstroms and degrees.
A relaxed PES scan (with geometry optimization at each point) is requested with the Opt keyword.
If any scanning variable breaks symmetry during the calculation, then you must include NoSymm in the
route section of the job, or the job will fail with an error.

5.71.1 Options
Restart
Restarts a PES scan calculation. A failed scan calculation may be restarted from its checkpoint file by
simply repeating the route section of the original job, adding the Restart option to the Scan keyword. No
other input is required.

5.71.2 Related Keywords

Opt

5.71.3 Examples
Output files from PES scans conclude with a table summarizing the results for the job:
 5.72 SCF 295

Scan completed.

Summary of the potential surface scan:

N R A SCF
---- --------- --------- -----------
1 0.9600 104.5000 -38.39041
2 1.0100 104.5000 -38.41306
3 1.0600 104.5000 -38.42336
4 0.9600 105.5000 -38.39172
5 1.0100 105.5000 -38.41430
6 1.0600 105.5000 -38.42453
7 0.9600 106.5000 -38.39296
8 1.0100 106.5000 -38.41547
9 1.0600 106.5000 -38.42564
10 0.9600 107.5000 -38.39412
11 1.0100 107.5000 -38.41657
12 1.0600 107.5000 -38.42668
---- --------- --------- -----------

Chapter 6 of Exploring Chemistry with Electronic Structure Methods [152, pages 238–44, 255–58] pro-
vides a detailed discussion of potential energy surface scans.

5.72 SCF
This keyword controls the functioning of the SCF procedure. Options are used to specify the desired
behavior, alternate algorithms, and so on.
The default SCF procedure uses a combination of EDIIS [679] and CDIIS, with no damping or Fermi
broadening. In Gaussian 16, SCF=Tight is the default.
The SCF=QC option is often helpful with difficult conversion cases. For difficult-to-converge ROHF
wavefunctions, where QC cannot be used, add Use=L506 to the route section.
See reference [680] for a discussion of SCF convergence and stability.

5.72.1 Options
Algorithm Selection Options
DIIS
DIIS calls for and NoDIIS prohibits use of Pulay’s Direct Inversion in the Iterative Subspace (DIIS)
extrapolation method [681].
CDIIS
Use only CDIIS. CDIIS implies Damp as well.
Fermi
Requests temperature broadening during early iterations [682], combined with CDIIS and damping.
NoFermi suppresses Fermi broadening and is the default. By default, Fermi also implies Damp and
also includes level shifting.
296 Chapter 5. List of Gaussian Keywords

Damp
Turn on dynamic damping of early SCF iterations. NoDamp is the default. However, damping is enabled
if SCF=Fermi or SCF=CDIIS is requested. Note that damping and EDIIS do not work well together.
NDamp=N
Allow dynamic damping for up to N SCF iterations (the default is 10).
QC
Calls for the use of a quadratically convergent SCF procedure [683]. By default this involves linear
searches when far from convergence and Newton-Raphson steps when close (unless the energy goes up).
This method is slower than regular SCF with DIIS extrapolation but is more reliable. SCF=QC is not
available for restricted open shell (RO) calculations.
XQC
Add an extra SCF=QC step in case the first-order SCF has not converged. XQC defaults to MaxConven-
tional=32.
YQC
Provides a new algorithm that is useful for difficult SCF convergence cases involving very large molecules.
It does steepest descent and then scaled steepest descent as in QC, but then switches to regular SCF in-
stead of quadratic convergence, using the quadratic algorithm only if the regular SCF fails to converge.
YQC defaults to MaxConventional=32.
MaxConventionalCycles=N
Sets the limit on conventional SCF cycles during SCF=XQC and SCF=YQC to N.
PseudoDiagonalization=N
Use pseudo-diagonalization in Link 502 whenever possible, with full diagonalization only at the early
cycles, at the end, and every N th cycle in between. PDiag is a synonym for this option. This is the default
for semi-empirical methods (the default is N=30).
FullDiagonalization
Forces full diagonalization in Link 502. This is the default for HF and DFT. FDiag is a synonym for this
option.
SD
Does steepest descent SCF.
SSD
Does scaled steepest descent SCF.
SaveKPoint
Save k-point information at the conclusion of the SCF. NoSaveKPoint says not to save this data, and it is
the default except for numerical frequency calculations for which SaveKPoint is the default.
DM
Calls for use of the direct minimization SCF program [684]. It is usually inferior to SCF=QC and retained
for backwards compatibility and as a last resort. Available only for RHF closed shell and UHF open shell
calculations.
VShift[=N]
Shift orbital energies by N*0.001 (i.e., N milliHartrees); N defaults to 100. This option disables automatic
archiving. N=-1 disables level shifting; NoVShift is equivalent to this setting.
5.72 SCF 297

MaxCycle=N
Changes the maximum number of SCF cycles permitted to N; the default is 64 (or 512 for SCF=DM and
SCF=QC).
FullLinear
Specifies that L508 (SCF=QC, SD, or SSD) should do full linear searches at each iteration. By default, a
full minimization is done only if the initial microiteration caused the energy to go up.
FinalIteration
FinalIteration performs and NoFinalIteration prevents a final non-extrapolated, non-incremental iteration
after an SCF using DIIS or a direct SCF has converged. The default is NoFinalIteration.
IncFock
Forces use of incremental Fock matrix formation. This is the default for direct SCF. NoIncFock prevents
the use of incremental Fock matrix formation, and it is the default for conventional SCF.
Pass
For in-core calculations, saves the integrals on disk as well, to avoid recomputing them in Link 1002.
Only useful for frequency jobs in conjunction with SCF=InCore. NoPass forces integrals to be recom-
puted during each in-core phase.
TightLinEq
Use tight convergence in linear equation solution throughout SCF=QC. By default, the convergence
criterion is tightened up as the rotation gradient is reduced.
VeryTightLinEq
Use even tighter convergence in the linear equation solutions (microiterations) throughout the QCSCF.
This option is sometimes needed for nearly linearly-dependent cases. VTL is a synonym for VeryTight-
LinEq.

Integral Storage Options

Direct
Requests a direct SCF calculation, in which the two-electron integrals are recomputed as needed. This
is the default SCF procedure in Gaussian. This is possible for all available methods, except for MCSCF
second derivatives and anything using complex orbitals.
InCore
Insists that the SCF be performed storing the full integral list in memory. This is done automatically in a
direct SCF calculation if sufficient memory is available. SCF=InCore is available to force in-core storage
or abort the job if not enough is available. NoInCore prohibits the use of the in-core procedure, for both
the SCF and CPHF.
Conventional
The two-electron integrals are stored on disk and read-in each SCF iteration. NoDirect is a synonym for
Conventional.

Options Related to Convergence and Cutoffs

PtDensity=N
Specifies N points per Angstrom2 (N>0) or -N tesserae (N<0). The default is 5.
Conver=N
298 Chapter 5. List of Gaussian Keywords

Sets the SCF convergence criterion to 10−N . SCF convergence requires both <10−N RMS change in the
density matrix and <10−(N−2) maximum change in the density matrix. Note that the energy change is
not used to test convergence; however, an SCF 10−N RMS density matrix change typically corresponds
to a 10−2N change in energy in atomic units. For GVB and CASSCF calculations, SCF convergence
is determined not by change in the density matrix, but rather in terms of the orbital change and energy
change, respectively.
VarAcc
Use modest integral accuracy early in direct SCF, switching to full accuracy later on. This is the default
for direct SCF, and it can be turned off via NoVarAcc. VarInt is a synonym for VarAcc, and NoVarInt is
a synonym for NoVarAcc.
Tight
Use normal, tight convergence in the SCF. This is the default. Synonymous with TightIntegrals.
Big
Turns off optional O(N 3 ) steps to speed up very large calculations (>5000 basis functions).
MaxNR=N
Sets the maximum rotation gradient for a Newton-Raphson step in SCF=QC and SCF=YQC to 10−N .
Below this threshold the program switches to the QC SCF procedure (if using SCF=QC), or to the regular
SCF procedure (if using SCF=YQC). Above this, scaled steepest descent is used; above 100 times this,
steepest descent is used. The default value for N is 2.

Symmetry-Related Options

IDSymm
Symmetrize the density matrix at the first iteration to match the symmetry of the molecule (“initial density
symmetrize”). NoIDSymm is the default.
DSymm
Symmetrize the density matrix at every SCF iteration to match the symmetry of the molecule (“density
symmetrize”). NoDSymm is the default. DSymm implies IDSymm.
NoSymm
Requests that all orbital symmetry constraints be lifted. It is synonymous with Guess=NoSymm and
Symm=NoSCF.
Symm
Retain all symmetry constraints: make the number of occupied orbitals of each symmetry type (abelian
irreducible representation) match that of the initial guess. Use this option to retain a specific state of the
wavefunction throughout the calculation. It is the default only for GVB calculations.
IntRep
Calls for the SCF procedure to account for integral symmetry by replicating the integrals using the sym-
metry operations. Allows use of a short integral list even if the wavefunction does not have the full
molecular symmetry. Available for L502 (the default for RHF, ROHF and UHF) and L508 (SCF=QC).
FockSymm
Calls for the SCF procedure to account for integral symmetry (use of the petite integral list) by sym-
metrizing the Fock matrices. This is the default. FSymm is a synonym for FockSymm.
 5.73 SCRF 299

Restart-Related Options
Save
Save the wavefunction on the checkpoint file every iteration, so the SCF can be restarted. This is the
default for direct SCF. NoSave suppresses saving the wavefunction.
Restart
Restart the SCF from the checkpoint file. SCF=DM cannot be restarted. SCF=Restart skips steps which
are not necessary when restarting an SCF calculation, but which are necessary when reading in a guess
from a calculation with a different basis set or at a different geometry. In contrast, if you want to start
a new SCF using the restart information from a calculation with a different geometry and/or a different
basis set, use Guess=Restart.

5.73 SCRF
This keyword requests that a calculation be performed in the presence of a solvent by placing the solute in
a cavity within the solvent reaction field.
The Polarizable Continuum Model (PCM) using the integral equation formalism variant (IEFPCM) is
the default SCRF method. This method creates the solute cavity via a set of overlapping spheres. It was
initially devised by Tomasi and coworkers and Pascual-Ahuir and coworkers [685–687], and it has been further
developed in Gaussian by the Tomasi, Barone and Mennucci groups as well as Gaussian, Inc. researchers and
collaborators [349, 352, 353, 360, 366, 367, 410, 688–702]. This model corresponds to SCRF=PCM. See [703]
for a review. The model of Chipman [704] is closely related to this method [705].
Gaussian also offers the SMD variation of IEFPCM of Truhlar and workers [706] via the SMD option.
This is the recommended choice for computing ∆G of solvation.
Other available models are IPCM, which uses a static isodensity surface for the cavity [707], the Self-
Consistent Isodensity PCM (SCIPCM) model [707], and the Onsager model [708–713], which places the solute
in a spherical cavity within the solvent reaction field.
In Gaussian 16, we use a continuous surface charge formalism that ensures continuity, smoothness and
robustness of the reaction field, which also has continuous derivatives with respect to atomic positions and
external perturbing fields [701]. This is achieved by expanding the apparent surface charge that builds up at the
solute-solvent interface in terms of spherical Gaussian functions located at each surface element in which the
cavity surface is discretized. Discontinuities in the surface derivatives are removed by effectively smoothing
the regions where the spheres intersect. This formalism, initially proposed in 1999 by Karplus and York for
the conductor screening model [714], never received the attention it deserved. We developed and generalized it
within the framework of the PCM family of solvation methods in G09, and it is the default method for building
the solute’s cavity and computing the reaction field.
The PCM method in Gaussian 16 includes an external iteration procedure whereby the program computes
the energy in solution by making the solvent reaction field self-consistent with the solute electrostatic potential
(the latter being generated from the computed electron density with the specified model chemistry) [715, 716].
The difference with the standard approach (based on the variational approach or linear response theory) can be
illustrated with MP2. The default procedure computes the solvent effect on the SCF density and then applies
MP2 perturbation, while the external iteration approach computes the solvent effect self-consistently with re-
spect to the MP2 density. While this technique is of primary interest for studying excited state processes such
 300 Chapter 5. List of Gaussian Keywords

fluorescence, it can also be used for ground state calculations with theoretical methods that provide gradients:
e.g. post-SCF methods. Use the ExternalIteration option to specify this method.

Solvation and Excited States

There are two basic approaches available for modeling excited states in solution:
♢ Computing the lowest excited states in the solvent environment. This approach adds SCRF to a normal
excited state calculation such as TD or CIS. This technique employs a linear response formalism by
adding the necessary terms to the excited state method equations (thereby including the solvent effects
on the excited states) [349, 698]. The geometry of a specific excited state can be optimized in solution
with CIS or TD [717].
♢ A single excited state can be modeled via a state-specific approach. In this case, the program computes
the energy in solution by making the electrostatic potential generated by the excited state density self
consistent with the solvent reaction field [715, 716], using the external iteration technique.
For excited state calculations in solution, there is a distinction between equilibrium and non-equilibrium
calculations. The solvent responds in two different ways to changes in the state of the solute: it polarizes its
electron distribution, which is a very rapid process, and the solvent molecules reorient themselves (e.g., by a
rotation), a much slower process. An equilibrium calculation describes a situation where the solvent had time
to fully respond to the solute (in both ways), e.g., a geometry optimization (a process that takes place on the
same time scale as molecular motion in the solvent). A non-equilibrium calculation is appropriate for processes
which are too rapid for the solvent to have time to fully respond, e.g. a vertical electronic excitation.
Equilibrium solvation is the default for CIS and TD-DFT excited state geometry optimizations. Non-
equilibrium is the default for CIS and TD-DFT energies using the default PCM procedure, and equilibrium is
the default for calculations using the external iteration approach (SCRF=ExternalIteration). See the examples
for the method for computing non-equilibrium external iteration calculations.
For EOM-CCSD calculations in solution, the solvation approaches of Cammi and Caricato are available
[360, 366, 367]. The PTED method is available with the PTED option. Other methods discussed in [360] are
also available via IOp(9/116).
By default, CASSCF PCM [695] calculations correspond to equilibrium calculations with respect to the
solvent reaction field/solute electronic density polarization process. Calculation of non equilibrium solute-
solvent interaction involving two different electronic states (e.g. the initial and final states of a vertical transi-
tion) can be performed using the NonEq=type PCM keyword, in two separate job steps (see PCM in the Input
section).

5.73.1 Input
Keywords and options specifying details for a PCM calculation (i.e., the default SCRF=PCM or SCRF=CPCM)
may be specified in an additional blank-line terminated input section provided that the Read option is also spec-
ified. Keywords within this section follow general Gaussian input rules. The available keywords are listed in a
separate subsection following the examples.
For the Onsager model (SCRF=Dipole), the solute radius in Angstroms and the dielectric constant of the
solvent are read as two free-format real numbers on one line from the input stream. A suitable solute radius
is computed by a gas-phase molecular volume calculation (in a separate job step); see the discussion of the
Volume keyword.
 5.73 SCRF 301

For the IPCM and SCIPCM models, the input consists of a line specifying the dielectric constant of the
solvent and an optional isodensity value (the default for the latter is 0.0004).

5.73.2 Options
Specifying the Solvent

Solvent=item
Selects the solvent in which the calculation is to be performed. Note that the solvent may also be specified
in the input stream in various ways for the different SCRF methods. If unspecified, the solvent defaults
to water. item is a solvent name chosen from the list at the end of this section.

Selecting the SCRF Method

PCM
Performs a reaction field calculation using the integral equation formalism model (IEFPCM). This is the
default. Some details of the formalism and the implementation have changed with respect to Gaussian
03, as described in [701]. IEFPCM is a synonym for PCM.
When PCM is used for an anisotropic or ionic solvent, then items in the PCM input section must be used
to select the anisotropic and ionic dielectric models for these types of solvents, using the Read option.
The continuous surface charge formalism is also not available with such solvents, and no derivatives can
be computed.
CPCM
Performs a PCM calculation using the CPCM polarizable conductor calculation model [410, 691].
Dipole
Performs an Onsager model reaction field calculation.
IPCM
Performs an IPCM model reaction field calculation. Isodensity is a synonym for IPCM.
SCIPCM
Performs an SCIPCM model reaction field calculation, i.e. the SCRF calculation uses a cavity determined
self-consistently from an isodensity surface.

SMD Model

SMD
Do an IEFPCM calculation with radii and non-electrostatic terms for Truhlar and coworkers’ SMD solva-
tion model [706]. This is the recommended choice for computing ∆G of solvation, which accomplished
by performing gas phase and SCRF=SMD calculations for the system of interest and taking the differ-
ence the resulting energies. You can define a new solvent for use with SMD by providing additional input
via the SCRF=Read option (see “Additional Input” for details).

PCM Non-Equilibrium Solvation

NonEquilibrium=action
Save or retrieve data for non-equilibrium solvation. action is one of the following:
♢ Save or Write: Save the slow/inertial charges in the checkpoint file (from which they will be retrieved
in a subsequent non-equilibrium solvation calculation).
302 Chapter 5. List of Gaussian Keywords

♢ Read or Load: Read the slow/inertial charges for use in the current non-equilibrium solvation calcula-
tion.
♢ CCSave or CCWrite: Save the slow/inertial correlation charges for use in a subsequent non-equilibrium
solvation coupled cluster calculation.
♢ CCRead or CCLoad: Retrieve the slow/inertial correlation charges for use in the current non-equilibrium
solvation coupled cluster calculation.

External Iteration PCM

ExternalIteration
Does a self-consistent PCM calculation performing an external iteration through Link 124. This approach
computes the energy in solution by making the solute’s electrostatic potential self-consistent with the sol-
vent reaction field [715, 716]. ExternalIteration is available only for energy calculations. SelfConsistent
and SC are synonyms for this option.
1stVac
Do the first iteration in an external iteration PCM calculation in solution. 1stVac is equivalent to DoVac-
uum, which is now deprecated.
1stPCM
Do not do the first iteration in an external iteration PCM calculation in solution. 1stPCM is equivalent to
SkipVacuum and NoVacuum, which are now deprecated.
Restart
Restarts a PCM external iteration calculation from the checkpoint file.

IEFPCM and CPCM Other Options

SolventAccessibleSurface
For PCM, use a cavity representing the solvent-accessible surface. Only suitable for single-point cal-
culations, but useful for cases with unusual cavities, snapshots from MD with explicit solvent, etc.
SCRF=SAS is a synonym for this option.
AsymmetricIEFPCM
Perform asymmetric isotropic IEFPCM rather than the default of symmetric isotropic IEFPCM. Asym-
metricIEFPCM was the default in Gaussian 09.
SCRF=AIEFPCM is a synonym for this option. Not valid with CPCM.
PTED
Use the perturbation theory and density approach (PTED) to PCM-CCSD coupling [360, 366] for an
EOM-CCSD calculation in solution. Other schemes discussed in [360] are available via IOp(9/116).
CorrectedLinearResponse
Do a state-specific correction to the energy of a CIS/RPA/TD-DFT SCRF excited state, according to
[718]. CorrectedLR is a synonym for this option.
Read
Indicates that a separate section of keywords and options providing calculation parameters should be read
from the input stream. This must be specified for anisotropic and ionic solvents.
Checkpoint
Retrieves the SCRF information from the checkpoint file.
5.73 SCRF 303

Modify
Retrieves the SCRF information from the checkpoint file, and also reads modifications from the input
stream.
ONIOMPCM=k
Performs an ONIOM calculation in solution [719, 720] according to the scheme selected by the code
letter k, for which these are the valid values:

A The reaction field is computed self-consistently using the integrated ONIOM den-
sity (available only for energies, and not available for semi-empirical methods).
B The reaction field is computed for the real-system at the low-level and the corre-
sponding polarization charges are used as external charges in the sub-calculations
on the model-systems (available only for energies).
C The reaction field is computed only for the real-system at the low-level while the
sub-calculations on the model-systems are performed assuming zero reaction field
(i.e., gas phase). This selection is available for energies, optimizations and frequen-
cies.
X The reaction field is computed separately in each sub-calculation always using the
cavity of the real-system. This is the default if ONIOM and SCRF are specified
(available for energies, optimizations and frequencies).

G09Defaults
Sets defaults for PCM solvation back to those used in Gaussian 09.
G03Defaults
Modify the PCM defaults in order to reproduce the results of a Gaussian 03 PCM calculation as closely
as possible. Note that perfect agreement is not always possible due to improvements in the program.

Onsager (SCRF=Dipole) Model Options

A0=val
Sets the value for the solute radius a0 in the route section (rather than reading it from the input stream of
an SCRF=Dipole calculation). If this option is included, then Solvent or Dielectric must also be included.
Dielectric=val
Sets the value for the dielectric constant of the solvent. This option overrides Solvent if both are specified.

IPCM Model Options

GradVne
Use Vne basins for the numerical integration.
GradRho
Use density basins for the numerical integration. The job may fail if non-nuclear attractors are present.

SCIPCM Model Options

UseDensity
Force the use of the density matrix in evaluating the density.
UseMOs
Force the use of MOs in evaluating the density.
 304 Chapter 5. List of Gaussian Keywords

GasCavity
Use the gas phase isodensity surface to define the cavity rather than solving for the surface self-consistently.
This is mainly a debugging option.

Save/Retrieve PCM Charges

SaveQ
Write the PCM charges on the checkpoint file. SaveQ can be specified together with LoadQ. WriteQ is a
synonym for this option.
LoadQ
Read the PCM charges on the checkpoint file. Note that the molecular geometry and the cavity must
match exactly to use the saved charges. SaveQ can be specified together with LoadQ. ReadQ is a synonym
for this option.

Produce Input for COSMO/RS

COSMORS
Produces the data file used by COSMO/RS and other programs.

5.73.3 Availability
The following table details the availability of the various SCRF=PCM calculation types by theoretical
method:

Method Energy (Ext. Iter.) Energy Opt Freq 3rd Order Propsa NMR
MM no yes yes yes no no
AM1, PM3, PM3MM, PM6, PDDG no yes yes yes no no
HF, DFT yes yes yes yes yes yes
MP2 yes yesb yesb yesb yesb,c yesb
MP3, MP4(SDQ), CCSD, QCISD yes yesb no no no no
CASSCF yes yes yes yese no no
CIS yes yesd yesd yesd no no
TD yes yesd yesd yesd no no
ZIndo no yes no no no no
a For example, Freq=Raman, ROA or VCD;
b Computed via SCF MO polarization;
c Raman intensities are computed numerically (i.e., as with Freq=NRaman);
d Using the linear response approach;
e Numerical frequencies only.

CASSCF frequencies with PCM solvation must be done numerically using Freq=Numer.
Restarting SCRF Calculations. SCRF=ExternalIteration and SCRF=IPCM jobs can be restarted from
the read-write file by using the Restart option. SCRF=SCIPCM calculations that fail during the SCF iterations
should be restarted via the SCF=Restart keyword.
Non-Default Methods. The IPCM model is available for HF, DFT, MP2, MP3, MP4(SDQ), QCISD,
CCD, CCSD, CID, and CISD energies only. The SCIPCM model is available for HF and DFT energies and
 5.73 SCRF 305

optimizations and numerical frequencies. The Onsager (SCRF=Dipole) model is available for HF, DFT, MP2,
MP3, MP4(SDQ), QCISD, CCD, CCSD, CID, and CISD energies, and for HF and DFT optimizations and
frequency calculations. However, the Opt Freq keyword combination may not be used in SCRF=Dipole calcu-
lations.

5.73.4 Related Keywords

SCF, Volume

5.73.5 Examples
PCM Energy. In general, energy output from the default SCRF method appears in the normal way within
the output file. For example, here are the sections of the output file containing the predicted energy from a
Hartree-Fock and from an MP2 PCM calculation:

Hartree-Fock SCRF calculation:

SCF Done: E(RHF) = -99.4687828290 A.U. after 8 cycles
Convg = 0.2586D-08 -V/T = 2.0015

MP2 SCRF calculation:

E2 = -0.1192799427D+00 EUMP2 = -0.99584491345297D+02

The predicted energy in solution includes all computed corrections (unlike in Gaussian 03 output).
Additional output lines may appear when various PCM options are included. For example, the following
output is produced by an HF SCRF=SMD calculation:

SCF Done: E(RHF) = -99.4687828290 A.U. after 8 cycles

Convg = 0.2586D-08 -V/T = 2.0015
SMD-CDS (non-electrostatic) energy (kcal/mol) = 0.54
(included in total energy above)

For external iteration SCRF calculations, the final energy is computed by Link 124, which controls the
external iteration, and is reported in a separate output section, which will appear very near the end of the output
file, as in the following example:
--------------------------------------------------------------------
Self-consistent PCM results
===========================
<psi(f)| H |psi(f)> (a.u.) = -99.577537 (A)
<psi(f)|H+V(f)/2|psi(f)> (a.u.) = -99.584002 (B)
(Polarized solute)-Solvent (kcal/mol) = -4.06 (C)
--------------------------------------------------------------------
Partition over spheres:
Sphere on Atom Surface Charge GEl GCav GDR
1 H1 15.27 -0.157 -2.36 0.00 0.00
2 F2 32.58 0.157 -1.70 0.00 0.00
--------------------------------------------------------------------
Predicted energy value for external iteration and state-specific SCRF calculations
After PCM corrections, the energy is -99.5840023899 a.u.
306 Chapter 5. List of Gaussian Keywords

--------------------------------------------------------------------

Line (A) reports the energy computed using the polarized solute wavefunction and the gas phase Hamilto-
nian, line (B) reports energy computed using the polarized solute wavefunction and the Hamiltonian in solution,
line (C) reports the interaction energy between the polarized solute and the solvent, which corresponds to the
integral < Ψ( f )|V ( f )/2|Ψ( f ) > (in kcal/mol), and the final line reports the predicted energy incorporating all
PCM corrections.
Fluorescence example: Emission (Fluorescence) from First Excited State (n → π ∗ ) of Acetaldehyde
Here we study the cycle:

Figure 5.4: Acetaldehyde Excitation and Emission Cycle

The primary process of interest is the emission, but this example shows how to study the complete cycle
including the solvent effects.
Step 1: Ground state geometry optimization and frequencies (equilibrium solvation). This is a stan-
dard Opt Freq calculation on the ground state including PCM equilibrium solvation.
%chk=01-ac
# B3LYP/6-31+G(d,p) Opt Freq SCRF=(Solvent=Ethanol)

Acetaldehyde ground state

0 1
C
C,1,RA
X,2,1.,1,A
O,2,RB,3,A,1,180.,0
X,1,1.,2,90.,3,0.,0
H,1,R1,2,A1,5,0.,0
H,1,R23,2,A23,5,B23,0
H,1,R23,2,A23,5,-B23,0
H,2,R4,1,A4,3,180.,0

RA=1.53643
RB=1.21718
R1=1.08516
R23=1.08688
R4=1.10433
5.73 SCRF 307

A=62.1511
A1=110.51212
A23=109.88119
A4=114.26114
B23=120.56468

Here is the energy of the ground state optimized geometry in solution:

SCF Done: E(RB3LYP) = -153.851761719 A.U. after 1 cycles
Step 2: Vertical excitation with linear response solvation. This is a TD-DFT calculation of the vertical
excitation, therefore at the ground state equilibrium geometry, with the default solvation: linear response, non-
equilibrium. We perform a single-point TD-DFT calculation, which defaults to non-equilibrium solvation. The
results of this job will be used to identify which state or states are of interest and their ordering. These results
give a reasonable description of the solvation of the excited state, but not quite as good as that from a state-
specific solvation calculation. In this case, we see that the n → π ∗ state is the first excited state. Next, we will
use the state-specific method to produce a better description of the vertical excitation step.
%oldchk=01-ac
%chk=02-ac
# B3LYP/6-31+G(d,p) TD=NStates=6 SCRF=(Solvent=Ethanol) Geom=Check Guess=Read

Acetaldehyde: linear response vertical excited states

0 1

The vertical excitation (absorption) to first excited state from the non-equilibrium solvation linear response
calculation:
Excited State 1: Singlet-A" 4.3767 eV 283.28 nm f=0.0000 <S**2>=0.000
Thus, the ground state to first excited state absorption is at 283.28 nm, computed via the linear-response ap-
proach.
Step 3: State-specific solvation of the vertical excitation. This will require two job steps: first the
ground state calculation is done, specifying the NonEquilibrium=Save option, in order to store the information
about non-equilibrium solvation based on the ground state. Second, the actual state-specific calculation is
done, reading in the necessary information for non-equilibrium solvation using NonEquilibrium=Read option,
and specifying the checkpoint file from Step 1:
%oldchk=01-ac
%chk=03-ac
# B3LYP/6-31+G(d,p) SCRF=(Solvent=Ethanol,NonEquilibrium=Save)
Geom=Check Guess=Read

Acetaldehyde: prepare for state-specific non-eq solvation

by saving the solvent reaction field from the ground state

0 1

--link1--
%chk=03-ac
308 Chapter 5. List of Gaussian Keywords

# B3LYP/6-31+G(d,p) TD(NStates=6,Root=1) Geom=Check Guess=Read

SCRF=(Solvent=Ethanol,ExternalIteration,NonEquilibrium=Read)

Acetaldehyde: read non-eq solvation from ground state and

compute energy of the first excited with the state-specific method

0 1

Here is the energy of first excited state – at the ground state optimized geometry – from the non-equilibrium
solvation state-specific calculation:
After PCM corrections, the energy is -153.687679826 a.u.
Subtracting this energy from the ground state energy (from step 1) gives the ground state to first excited state
absorption including the state-specific solvation correction: at 277.69 nm.
Step 4: Relaxation of the excited state geometry. Next, we perform a TD-DFT geometry optimization,
with equilibrium, linear response solvation, in order to find the minimum energy point on the excited state
potential energy surface. Since this is a TD-DFT optimization, the program defaults to equilibrium solvation.
As is typical of such cases, the molecule has a plane of symmetry in the ground state but the symmetry is
broken in the excited state, so the ground state geometry is perturbed slightly to break symmetry at the start of
the optimization. We retrieve the geometry and other data from the checkpoint file from Step 2:
%oldchk=02-ac
%chk=04-ac
# B3LYP/6-31+G(d,p) TD=(Read,NStates=6,Root=1) SCRF=(Solvent=Ethanol)
Geom=Modify Guess=Read Opt

Acetaldehyde: excited state opt

Modify geometry to break Cs symmetry
since first excited state is A"

0 1

4 1 2 3 10.0
5 1 2 7 -50.0

Here are the results for the first excited state after the geometry optimization of first excited state in solution
(equilibrium geometry):
Excited State 1: Singlet-A 3.2074 eV 386.55 nm f=0.0013 <S**2>=0.0
This state for optimization and/or second-order correction.
Total Energy, E(TD-HF/TD-KS) = -153.705918726

Step 5: Vibrational frequencies of the excited state structure. Now we run a frequency calculation to
verify that the geometry located in step 4 is a minimum. The results could also be used as part of a Franck-
Condon calculation if desired. This is a numerical frequency calculation.
%oldchk=04-ac
%chk=05-ac
# B3LYP/6-31+G(d,p) TD=(Read,NStates=6,Root=1) Freq
SCRF=(Solvent=Ethanol) Geom=Check Guess=Read
5.73 SCRF 309

Acetaldehyde excited state freq

0 1

The frequency calculation is used to confirm that the geometry optimized in Step 4 is a minimum on the
excited state potential energy surface.
Step 6: Emission state-specific solvation (part 1). This step does state-specific equilibrium solvation of
the excited state at its equilibrium geometry, writing out the solvation data for the next step via the NonEquilib-
rium=Save option.
%oldchk=05-ac
%chk=06-ac
# B3LYP/6-31+G(d,p) TD=(Read,NStates=6,Root=1) Geom=Check Guess=Read
SCRF=(Solvent=Ethanol,ExternalIteration,NonEquilibrium=Save)

Acetaldehyde emission state-specific solvation

at first excited state optimized geometry

0 1

Here is the energy of first excited state – at its optimized geometry – from the equilibrium solvation state-
specific calculation:
After PCM corrections, the energy is -153.707148980 a.u.
Step 7: Emission to final ground state (part 2). Finally, we compute the ground state energy with
non-equibrium solvation, at the excited state geometry and with the static solvation from the excited state.
%oldchk=06-ac
%chk=07-ac
# B3LYP/6-31+G(d,p) SCRF=(Solvent=Ethanol,NonEquilibrium=Read)
Geom=Check Guess=Read

Acetaldehyde: ground state non-equilibrium

at excited state geometry.

0 1

Here is the energy of ground state from a non-equilibrium solvation calculation in solution, using the
first excited state optimized geometry and the solvent reaction field in equilibrium with the first excited state
density):
SCF Done: E(RB3LYP) = -153.822024722 A.U. after 10 cycles
The difference between the energies from steps 6 and 7 gives the vertical emission energy. In this case, the first
excited state to ground state emission, including the state-specific solvation correction, is at 396.63 nm.
Steps 1, 2, and 4 would be sufficient to compute the excitation and emission energies in the gas-phase
(along with step 5 to confirm the nature of stationary point). They are not sufficient when solvent effects are
included because the energies computed in step 4 correspond to the ground state solvent reaction field, while
the emission takes place in the reaction field created in response to the excited state charge distribution. This is
what is accounted for properly in steps 6 and 7.
 310 Chapter 5. List of Gaussian Keywords

If the band shape is to be calculated, then in the gas phase one would simply run a calculation with
Freq=(ReadFC,FC,Emission), giving the checkpoint file from step 1 as the main checkpoint file for the job,
and providing the name of the checkpoint file from step 5 in the input stream to specify the other state. For
the solvated band shape, one must do Freq=(ReadFC,FC,Emission,ReadFCHT) using the checkpoint files for
steps 1 and 5, but also providing the state-specific emission energy in the input section for the Franck-Condon
calculation.

5.73.6 Additional Input

Additional Input for PCM Calculations
Additional input keywords may be specified for PCM SCRF calculations (including ones using the SMD
model). Note that many of the available parameters are designed for expert users; experimenting with modifi-
cations to the standard settings is strongly discouraged for production calculations.
These keywords are placed in a separate input section, terminated as usual by a blank line, as in this
example which tightens the convergence threshold for the iterative calculation of the PCM polarization charges
and sets the electrostatic scaling factor for the cavity sphere radii:

# B3LYP/6-31G(d) 5D SCRF(Solvent=Ethanol,Read)

PCM extra input example.

0 1
molecule specification

QConv=10 Input section for PCM keywords

Alpha=1.1
Blank line terminates PCM input

The PCM input section ends as usual with a blank line.

The available keywords for controlling PCM calculations are listed below, arranged in groups of related
items.

Defining Solvent Parameters

The solvent for the PCM calculation is generally specified using the normal Solvent option to the SCRF
keyword. You can use the following keywords to override some default values for known solvents.

Eps=x Specifies the static (or zero-frequency) dielectric constant of the solvent.
EpsInf=x Specifies the dynamic (or optical) dielectric constant of the solvent. For SMD cal-
culations, it should be set to the square of the solvent’s refractive index at 293 K.
RSolv=x Specifies the solvent radius (in Angstroms). Relevant only when using AddSph or
Surface=SAS.

Unspecified parameters default to the values for the solvent specified with the Solvent option (or to water
if this option is omitted).
5.73 SCRF 311

Defining Solvents for SMD Calculations

The items needed to define a solvent differ for the SMD method. Here is an example of an SMD calcu-
lation that defined ethanol manually via a PCM input section. Note that the final five items are SMD-specific
keywords. Note that all 7 items are required and that all values must be specified as real numbers. For full
details about these parameters, see [706]. As of this writing, the vast majority of the solvents in the Minnesota
Solvent Descriptor Database have solvent keywords defined (see “Solvents”).

# B3LYP/6-31G(d) 5D SCRF(SMD,Solvent=Generic,Read)

Water in solution with ethanol, defined as generic SMD solvent.

0 1
O
H,1,0.94
H,1,0.94,2,104.5
Input section for PCM keywords
Eps=24.852 ε
EpsInf=1.852593 n2
HbondAcidity=0.37 α
HbondBasicity=0.48 β
SurfaceTensionAtInterface=31.62 γ
CarbonAromaticity=0. ϕ
ElectronegativeHalogenicity=0. ψ
Blank line terminates PCM input

Calculation Method Variations

NonEq=item Compute and save the non-equilibrium reaction field after the completion of
an HF, DFT or CASSCF calculation using SCRF(Read), or at the end of any
SCRF(ExternalIteration,Read) calculation. NonEq=Write says to save the data in
the checkpoint file. Use NonEq=Read to retrieve it from the checkpoint file in a
subsequent calculation.
Dis Computes and includes in the total energy the solute-solvent dispersion interaction
energy using the model of Floris and Tomasi [721, 722]. The default is NoDis. This
option cannot be used in a SCRF=SMD calculation.
Rep Includes the solute-solvent repulsion interaction energy in the total energy using the
model of Floris and Tomasi [721, 722]. The default is NoRep. This option cannot
be used in a SCRF=SMD calculation.
Cav Includes the solute cavitation energy in the total energy using the model of Pierotti
[723]. The default is NoCav. This option cannot be used in a SCRF=SMD calcula-
tion.
312 Chapter 5. List of Gaussian Keywords

CavityFieldEffects Includes the effects of the cavity-field interaction energy (also known as local field
effect) in the total energy according to the model of Cammi and co-workers [724].
The default is not to include this effect.
CF=Eps=x Specifies a different value for the static dielectric constant to be used in the cavity-
field energy contribution. This is useful to modulate the magnitude of the cavity-
field effects.
CF=EpsInf=x Specifies a different value for the dynamic (optical) dielectric constant to be used
in the cavity-field energy contribution. This is useful to modulate the magnitude of
the cavity-field effects.
FitPot Performs analysis of the solute-solvent interaction energy in terms of atomic or
atomic groups additive contributions. This analysis involves a fitting of atomic
charges to the molecular electrostatic potential in solution.
Iterative Solves the PCM electrostatic problem to calculate polarization charges through an
iterative method.
MxIter=N Specifies the maximum number of iterations allowed to the iterative solution of the
electrostatic problem. 400 is the default.
QConv=type|N Sets the convergence threshold for the iterative calculations of the PCM polarization
charges to 10−N or to one of the following predefined types: VeryTight (10−12 ),
Tight (10−9 ) and Sleazy (10−6 ). The default is QConv=Tight.
SC=QConv=x Specifies the convergence for the PCM polarization charges during the external
iteration procedure.
MaxExtIt=x Specify the maximum number of iterations allowed during the external iteration
procedure.

Anisotropic and Ionic Solvents

Anisotropic Performs a PCM calculation for an anisotropic solvent according to the IEFPCM
formalism. The 3-rank symmetric tensor representing the dielectric constant must
be specified as the values for these six additional keywords: EPSX, EPSY, EPSZ,
EUPHI, EUTHE, and EUPSI (all of them take a parameter: e.g., EPSX=value).
Ionic Performs a PCM calculation for ionic solution according to the IEFPCM formalism.
The ionic strength in mol/dm3 has to be specified as the value to the keyword DISM.

Specifying the Molecular Cavity

By default, the program builds up the cavity using the UFF radii, which places a sphere around each solute
atom, with the radii scaled by a factor of 1.1. There are also three United Atom (UA) models available.
The cavity can be extensively modified in the PCM input section: changing sphere parameters and the
general cavity topology, adding extra spheres to the cavity built by default, and so on. The whole molecular
cavity can be also provided by the user in the input section.
Radii=model : Indicates the topological model and/or the set of atomic radii used. Available models and sets
are:
♢ UFF: Uses radii from the UFF force field. Hydrogens have individual spheres (explicit hydrogens).
5.73 SCRF 313

This is the default.

♢ UA0: Uses the United Atom Topological Model applied on atomic radii of the UFF force field for
heavy atoms. Hydrogens are enclosed in the sphere of the heavy atom to which they are bonded.
This was the default in Gaussian 03.
♢ UAHF: Uses the United Atom Topological Model applied on radii optimized for the HF/6-31G(d)
level of theory.
♢ UAKS: Uses the United Atom Topological Model applied on radii optimized for the PBE1PBE/6-
31G(d) level of theory.
♢ Pauling: Uses the Pauling (actually Merz-Kollman) atomic radii (uses explicit hydrogens).
♢ Bondi: Uses the Bondi atomic radii (uses explicit hydrogens).

Surface=type : Specify the type of molecular surface representing the solute-solvent boundary. Available
options are:

♢ VDW: Van der Waals surface. Uses atomic radii (scaled) and skips the generation of “added spheres”
to smooth the surface. This is the default.
♢ SES: Solvent Excluding Surface. The surface is generated by the atomic or group spheres and by
the spheres created automatically to smooth the surface (“added spheres”). This was the default in
Gaussian 03.
♢ SAS: Solvent Accessible Surface. The radius of the solvent is added to the unscaled radii of atoms
and/or atomic groups.

ModifySph : Alters parameters for one or more spheres. The modified spheres can be indicated in the PCM
input in lines following this keyword having the following format:
atom radius [alpha]
where atom is the atom number or element type.
ExtraSph=N : Adds N user-defined spheres to the cavity. Parameters of the spheres can be specified in lines
following this keyword using the following format:
X Y Z radius [alpha]
where X,Y,Z are the Cartesian coordinates in the standard orientation.
NSph=N : The cavity is built just from the N spheres provided by the user, specified on lines of the following
format:
atom_number radius [alpha] – or – X Y Z radius [alpha]
where X,Y,Z are the Cartesian coordinates in the standard orientation. Specifying spheres by atom number
mimics standard cavity behavior, while specifying Cartesian produces a fixed cavity which does not move
with the structure.
PDens=x Sets the average density of integration points on the surface, in units of Angstrom−2 . 5.0 is the
default. Increasing this value results in a finer surface discretization.
Alpha=scale Specifies the electrostatic scaling factor by which the sphere radius is multiplied. The default
value is 1.1.
SphereOnH=N When using a United Atom Topological model, places an individual sphere on the hydrogen
at the Nth position in the atoms list.
SphereOnAcidicHydrogens When using a United Atom Topological model, puts individual spheres on acidic
hydrogens (those bonded to N, O, S, P, Cl and F atoms).
 314 Chapter 5. List of Gaussian Keywords

OFac=x Specifies the overlap index between two interlocking spheres Pascual-Ahuir94 for SES added spheres.
Decreasing this index results in a smaller number of added spheres. The default value is 0.89.
RMin=x Sets the minimum radius in Angstroms for SES added spheres. Increasing this value results in a
smaller number of added spheres. The default value is 0.2.
GeomView Create the file points.off describing the cavity. This file contains input for the GeomView program
(see www.geomview.org), which can be used to visualize the molecular cavity.

5.73.7 Solvents
The following solvent keywords are accepted with the SCRF=Solvent option. We list the ε values here
for convenience, but be aware it is only one of many internal parameters used to define solvents. Thus, simply
changing the ε value will not define a new solvent properly.

♢Water: ε =78.3553 ♢2-Heptanone: ε =11.658 ♢HexanoicAcid: ε =2.6

♢Acetonitrile: ε =35.688 ♢2-Hexanone: ε =14.136 ♢IodoBenzene: ε =4.5470
♢Methanol: ε =32.613 ♢2-MethoxyEthanol: ε =17.2 ♢IodoEthane: ε =7.6177
♢Ethanol: ε =24.852 ♢2-Methyl-1-Propanol: ε =16.777 ♢IodoMethane: ε =6.8650
♢IsoQuinoline: ε =11.00 ♢2-Methyl-2-Propanol: ε =12.47 ♢IsoPropylBenzene: ε =2.3712
♢Quinoline: ε =9.16 ♢2-MethylPentane: ε =1.89 ♢m-Cresol: ε =12.44
♢Chloroform: ε =4.7113 ♢2-MethylPyridine: ε =9.9533 ♢Mesitylene: ε =2.2650
♢DiethylEther: ε =4.2400 ♢2-NitroPropane: ε =25.654 ♢MethylBenzoate: ε =6.7367
♢Dichloromethane: ε =8.93 ♢2-Octanone: ε =9.4678 ♢MethylButanoate: ε =5.5607
♢DiChloroEthane: ε =10.125 ♢2-Pentanone: ε =15.200 ♢MethylCycloHexane: ε =2.024
♢CarbonTetraChloride: ε =2.2280 ♢2-Propanol: ε =19.264 ♢MethylEthanoate: ε =6.8615
♢Benzene: ε =2.2706 ♢2-Propen-1-ol: ε =19.011 ♢MethylMethanoate: ε =8.8377
♢Toluene: ε =2.3741 ♢3-MethylPyridine: ε =11.645 ♢MethylPropanoate: ε =6.0777
♢ChloroBenzene: ε =5.6968 ♢3-Pentanone: ε =16.78 ♢m-Xylene: ε =2.3478
♢NitroMethane: ε =36.562 ♢4-Heptanone: ε =12.257 ♢n-ButylBenzene: ε =2.36
♢Heptane: ε =1.9113 ♢4-Methyl-2-Pentanone: ε =12.887 ♢n-Decane: ε =1.9846
♢CycloHexane: ε =2.0165 ♢4-MethylPyridine: ε =11.957 ♢n-Dodecane: ε =2.0060
♢Aniline: ε =6.8882 ♢5-Nonanone: ε =10.6 ♢n-Hexadecane: ε =2.0402
♢Acetone: ε =20.493 ♢AceticAcid: ε =6.2528 ♢n-Hexane: ε =1.8819
♢TetraHydroFuran: ε =7.4257 ♢AcetoPhenone: ε =17.44 ♢NitroBenzene: ε =34.809
♢DiMethylSulfoxide: ε =46.826 ♢a-ChloroToluene: ε =6.7175 ♢NitroEthane: ε =28.29
♢Argon: ε =1.430 ♢Anisole: ε =4.2247 ♢n-MethylAniline: ε =5.9600
♢Krypton: ε =1.519 ♢Benzaldehyde: ε =18.220 ♢n-MethylFormamide-mixture: ε =181.56
♢Xenon: ε =1.706 ♢BenzoNitrile: ε =25.592 ♢n,n-DiMethylAcetamide: ε =37.781
♢n-Octanol: ε =9.8629 ♢BenzylAlcohol: ε =12.457 ♢n,n-DiMethylFormamide: ε =37.219
♢1,1,1-TriChloroEthane: ε =7.0826 ♢BromoBenzene: ε =5.3954 ♢n-Nonane: ε =1.9605
♢1,1,2-TriChloroEthane: ε =7.1937 ♢BromoEthane: ε =9.01 ♢n-Octane: ε =1.9406
♢1,2,4-TriMethylBenzene: ε =2.3653 ♢Bromoform: ε =4.2488 ♢n-Pentadecane: ε =2.0333
♢1,2-DiBromoEthane: ε =4.9313 ♢Butanal: ε =13.45 ♢n-Pentane: ε =1.8371
♢1,2-EthaneDiol: ε =40.245 ♢ButanoicAcid: ε =2.9931 ♢n-Undecane: ε =1.9910
♢1,4-Dioxane: ε =2.2099 ♢Butanone: ε =18.246 ♢o-ChloroToluene: ε =4.6331
♢1-Bromo-2-MethylPropane: ε =7.7792 ♢ButanoNitrile: ε =24.291 ♢o-Cresol: ε =6.76
♢1-BromoOctane: ε =5.0244 ♢ButylAmine: ε =4.6178 ♢o-DiChloroBenzene: ε =9.9949
♢1-BromoPentane: ε =6.269 ♢ButylEthanoate: ε =4.9941 ♢o-NitroToluene: ε =25.669
♢1-BromoPropane: ε =8.0496 ♢CarbonDiSulfide: ε =2.6105 ♢o-Xylene: ε =2.5454
♢1-Butanol: ε =17.332 ♢Cis-1,2-DiMethylCycloHexane: ε =2.06 ♢Pentanal: ε =10.0
♢1-ChloroHexane: ε =5.9491 ♢Cis-Decalin: ε =2.2139 ♢PentanoicAcid: ε =2.6924
♢1-ChloroPentane: ε =6.5022 ♢CycloHexanone: ε =15.619 ♢PentylAmine: ε =4.2010
 5.74 Semi-Empirical Methods 315

♢1-ChloroPropane: ε =8.3548 ♢CycloPentane: ε =1.9608 ♢PentylEthanoate: ε =4.7297

♢1-Decanol: ε =7.5305 ♢CycloPentanol: ε =16.989 ♢PerFluoroBenzene: ε =2.029
♢1-FluoroOctane: ε =3.89 ♢CycloPentanone: ε =13.58 ♢p-IsoPropylToluene: ε =2.2322
♢1-Heptanol: ε =11.321 ♢Decalin-mixture: ε =2.196 ♢Propanal: ε =18.5
♢1-Hexanol: ε =12.51 ♢DiBromomEthane: ε =7.2273 ♢PropanoicAcid: ε =3.44
♢1-Hexene: ε =2.0717 ♢DiButylEther: ε =3.0473 ♢PropanoNitrile: ε =29.324
♢1-Hexyne: ε =2.615 ♢DiEthylAmine: ε =3.5766 ♢PropylAmine: ε =4.9912
♢1-IodoButane: ε =6.173 ♢DiEthylSulfide: ε =5.723 ♢PropylEthanoate: ε =5.5205
♢1-IodoHexaDecane: ε =3.5338 ♢DiIodoMethane: ε =5.32 ♢p-Xylene: ε =2.2705
♢1-IodoPentane: ε =5.6973 ♢DiIsoPropylEther: ε =3.38 ♢Pyridine: ε =12.978
♢1-IodoPropane: ε =6.9626 ♢DiMethylDiSulfide: ε =9.6 ♢sec-ButylBenzene: ε =2.3446
♢1-NitroPropane: ε =23.73 ♢DiPhenylEther: ε =3.73 ♢tert-ButylBenzene: ε =2.3447
♢1-Nonanol: ε =8.5991 ♢DiPropylAmine: ε =2.9112 ♢TetraChloroEthene: ε =2.268
♢1-Pentanol: ε =15.13 ♢e-1,2-DiChloroEthene: ε =2.14 ♢TetraHydroThiophene-s,s-dioxide: ε =43.962
♢1-Pentene: ε =1.9905 ♢e-2-Pentene: ε =2.051 ♢Tetralin: ε =2.771
♢1-Propanol: ε =20.524 ♢EthaneThiol: ε =6.667 ♢Thiophene: ε =2.7270
♢2,2,2-TriFluoroEthanol: ε =26.726 ♢EthylBenzene: ε =2.4339 ♢Thiophenol: ε =4.2728
♢2,2,4-TriMethylPentane: ε =1.9358 ♢EthylEthanoate: ε =5.9867 ♢trans-Decalin: ε =2.1781
♢2,4-DiMethylPentane: ε =1.8939 ♢EthylMethanoate: ε =8.3310 ♢TriButylPhosphate: ε =8.1781
♢2,4-DiMethylPyridine: ε =9.4176 ♢EthylPhenylEther: ε =4.1797 ♢TriChloroEthene: ε =3.422
♢2,6-DiMethylPyridine: ε =7.1735 ♢FluoroBenzene: ε =5.42 ♢TriEthylAmine: ε =2.3832
♢2-BromoPropane: ε =9.3610 ♢Formamide: ε =108.94 ♢Xylene-mixture: ε =2.3879
♢2-Butanol: ε =15.944 ♢FormicAcid: ε =51.1 ♢z-1,2-DiChloroEthene: ε =9.2
♢2-ChloroButane: ε =8.3930

5.74 Semi-Empirical Methods

There are a variety of semi-empirical methods available in Gaussian 16. The AM1 and the PM3 methods
have been reimplemented [725–727] to use the standard integral processing infrastructure (rather than using
code from the public-domain MOPAC). In addition to increased efficiency, this change also provides analytic
gradients and frequencies. PM6 and PDDG are also implemented in this way. The remaining semi-empirical
methods use the modified version of MOPAC in Link 402, and they are discussed on their individual pages.
♢ AM1: Requests a semi-empirical calculation using the AM1 Hamiltonian [519, 521, 522, 527, 728–734].
♢ PM3: Requests a semi-empirical calculation using the PM3 Hamiltonian [735, 736]. The parameter for
Li has been updated as specified in [734]. PM3MM specifies the PM3 model including the optional
molecular mechanics correction for HCON linkages.
♢ PM6: Requests a semi-empirical calculation using the PM6 Hamiltonian [737]. The PDDG variation is also
available [340, 738–741].
♢ PM7: Requests a semi-empirical calculation using the PM7 Hamiltonian as modified by Throssel and Frisch
for continuous potential energy surfaces [742]. PM7R6 is a synonym. The original PM7 method of
Stewart [743] can also be requested with the PM7MOPAC keyword.
Standard parameters for supported atoms are generated automatically by the program unless the NoGen-
erate option is specified. Additional and/or alternate ones can also be read-in in several ways (see the options).
Read-in parameters take precedence over internal ones when both are used.
 316 Chapter 5. List of Gaussian Keywords

Using PM7 with Third-Row and Higher Elements

For some systems containing these elements, instabilities can exists in the PM7 wavefunction. There may
be difficulties getting the wavefunction to converge. This is less common for lighter elements and is most likely
to occur for transition metal complexes. In such cases, the first option is to try an alternate SCF algorithm: e.g.,
SCF=YQC. If this fails, other options are to use a different initial guess or read in the density from a calculation
using a different method (see the Guess keyword).
In some cases, the PM7 wavefunction that is found may not be the lowest energy SCF solution. This too
is most common for transition metals and so caution is advised when performing calculations on transition
metals. A straightforward way of testing the wavefunction is to use the Stable keyword.

5.74.1 Options

Generate
Generate the standard parameters for the specified method. This is the default. NoGenerate says not to
generate any standard parameters; all parameters must be read in.
Input
Read parameters from the input stream in Gaussian’s format. Any parameter can be specified or overrid-
den. The input section must be terminated by a blank line. Cards is a synonym for Input.
MOPACExternal
Read parameters from the input stream in MOPAC’s external format and units. Most but not all parame-
ters can be changed. The input section must be terminated by a blank line.
Both
Read parameters from the input stream, first in Gaussian’s format, followed by more parameters in
MOPAC’s format. Both input sections must be terminated by a blank line.
Checkpoint
Read parameters from the checkpoint file. Chk and Read are synonymous with Checkpoint.
TCheckpoint
Read parameters from the checkpoint file if present; otherwise generate them.
RWF
Read parameters from the read-write file.
Print
Print parameters used for elements in the current job in Gaussian’s format. This is the default if param-
eters are read from the input file. NoPrint says not to print parameters, and it is the default if standard
parameters are used.
PrintAll
Print parameters for all elements (in Gaussian’s format), even the ones that are not present in the molecule
specification.
Zero
Print all parameters including the ones that are zero. The default is NonZero, which says to print only
non-zero parameters.
Old
Use the old MOPAC-based code. Second derivatives are done numerically. Applies only to AM1 and
 5.74 Semi-Empirical Methods 317

PM3. The default is New, which says to use the new implementation described above.

5.74.2 Specifying Semi-Empirical Parameters

Semi-empirical parameters can be specified in two different formats, Gaussian and MOPAC, via the Input
and MOPACExternal options (respectively). We begin with the native Gaussian semi-empirical parameter
format, which is very general.
Here’s an example in Gaussian format, for FeCH (actual output may wrap differently):

Initial section of global parameters.

Method=40 CoreType=2 PM6R6=0.0000124488 PM6R12=0.0000007621
****
H Parameters for hydrogen.
PQN=1 NValence=1 F0ss=0.5309794634 ZetaOverlap=1.2686410000 U=-0.4133181193
Beta=-0.3069665271 CoreKO=0.9416560046 KON=0,0,0,0.9416560046 EISol=-0.4133181193
EHeat=0.0830298228
GCore=0.0016794859,0.8557539899,3.3750716603 DCore=1,3,1.8737858033,2.2435870000
****
C Parameters for carbon.
PQN=2,2 NValence=4 F0ss=0.4900713271 F0sp=0.4236511476 F0pp=0.3644399975 F2pp
=0.1978513243
G1sp=0.0790832988
ZetaOverlap=2.0475580000,1.7028410000
U=-1.8775102825,-1.4676916178
Beta=-0.5653970441,-0.2745883502 DDN=0,1,0.7535642510 DDN=1,1,0.7192361890
CoreKO=1.0202596487 KON=0,0,0,1.0202596487 KON=1,0,1,1.2918442312 KON=0,1,1,1.0202596487
KON=2,1,1,0.7626764584 EISol=-4.2335803497 EHeat=0.2723305520 DipHyp=1.5070417957
GCore=0.0032154961,0.5881175739,2.5208171825 DCore=1,4,0.2878149911,0.2165060000
DCore=2,3,1.6101301385,3.2139710000 DCore=3,3,1.7155258339,16.1800020000
DCore=4,3,2.2293611369,25.0358790000 DCore=5,3,1.5446719761,1.8748590000
DCore=6,5,1.3831173494,0.8135100000,3.1644797074,9.2800000000
****
Fe Parameters for iron.
PQN=4,4,3 NValence=8 F0ss=0.2931506917 F0sp=0.2861621092 F0pp=0.2797829041
F0sd=0.3417747898 F0pd=0.3378189937 F0dd=0.5580709105 F2pp=0.1567537881 F2pd
=0.1236661383
F2dd=0.2945882511 F4dd=0.1921227725 G1sp=0.2072870321 G1pd=0.1102204721 G2sd
=0.0588483485
G3pd=0.0671224585 Rsppd=0.1364112343 Rsdpp=0.1031169651 Rsddd=0.1510228569
ZetaOverlap=1.4791500000,6.0022460000,1.0807470000
Zeta1C=1.4591520000,1.3926140000,2.1619090000
U=-2.5913804076,-2.3138503107,-3.8083983722
Beta=0.2950096563,-0.0413709206,-0.1288993981 DDN=0,1,0.0896587028 DDN=1,1,0.3534210933
DDN=0,2,1.6776352014 DDN=1,2,0.0796789968 DDN=2,2,1.3085519205 CoreKO=1.2720920000
KON=0,0,0,1.7056074374 KON=1,0,1,0.2359511557 KON=0,1,1,1.7056074374 KON
=2,1,1,0.4977547907
KON=2,0,2,1.6958541322 KON=1,1,2,0.2947417183 KON=0,2,2,0.8959434914 KON
=2,2,2,1.2449263774
EISol=-15.6859079709 EHeat=0.1582446241 DipHyp=0.1793070893
DCore=1,3,0.4521755746,0.0251950000 DCore=6,3,2.1121277473,0.3668350000
DCore=7,3,1.3232002016,0.1553420000 DCore=8,3,0.9135254945,0.1364220000
318 Chapter 5. List of Gaussian Keywords

DCore=9,3,2.2726610620,3.6573500000 DCore=15,3,1.3586804751,0.4312910000
DCore=16,3,0.5233514967,0.0334780000 DCore=17,3,0.6507784269,0.0194730000
DCore=19,3,1.0583544172,6.0000000000 DCore=26,3,1.4397774115,1.8468900000
****

The following items are specified in the global section:

Method An integer corresponding to the desired semi-empirical method. This value should
correspond to the method specified in the route section as a check. The values are
8 for AM1, 9 for PM3, 10 for PM3MM, 40 for PM6 and 41 for PDDG.
CoreType Type of core repulsion terms, where 1 means AM1, PM3, or PDDG, and 2 means
PM6.
PeptideFC Force constant for peptide linkages. Only valid for with PM3MM.
RIJScale Ri j scale factor for the AM1 O-H and N-H bonds.
PM6R6 R6 parameter for the PM6 core repulsion.
PM6R12 R12 parameter for the PM6 core repulsion.

The following items specify the parameters for an element:

PQN Principal quantum numbers for each shell (s, p, d). Determines which basis func-
tions are used on the element.
NValence Number of valence electrons.
ZetaOverlap Slater exponents for basis functions used in the calculation of the overlap contribu-
tion to the core Hamiltonian.
Zeta1C Slater exponents for basis functions used in the computation of those one-center
two-electron integrals that were not specified explicitly.
F0*, G*, Rs* Slater-Condon parameters for one-center two-electron integrals. If any of these
items are not specified, they are computed from the Zeta1C exponents. When inter-
nal parameters are printed, all values are included regardless of whether they were
computed from Zeta1C or a specific value. The full list of these parameters is: F0ss,
F0sp, F0pp, F0sd, F0pd, F0dd, F2pp, F2pd, F2dd, F4dd, G1sp, G1pd, G2sd, G3pd,
Rsppd, Rsdpp and Rsddd.
U Diagonal core Hamiltonian matrix elements, one per angular momentum.
Beta Off-diagonal core Hamiltonian parameters, one per angular momentum.
DDN Point-charge distance parameters for multipole-approximated two-center two-
electron integrals. Each instance has the form L1,L2,Value and applies to charge
distributions involving one basis function of angular momentum L1 and one of an-
gular momentum L2. If any are needed but are not specified, they are computed
from the Zeta1C exponents.
5.74 Semi-Empirical Methods 319

KON Klopman-Ohno parameters for two-center two-electron integrals. Required but un-
specified items are computed by matching the one-center limit to the one-center in-
tegrals given by the Slater-Condon parameters and Zeta1C, and using the specified
or defaulted DD values. Each instance is of the form LT,L1,L2,Value and applies
to the LT angular momentum component of the product of functions of angular
momentum L1 and L2.
CoreKO Klopman-Ohno parameter used in nuclear attraction terms. If not specified, the
0,0,0 (L=0 SS) parameter is used.
EHeat Heat of formation of the isolated atom.
EISol Energy of the isolated atom. If not provided, it is computed from the other parame-
ters and a standard electronic configuration for the atom.
DipHyp Dipole moment hybridization parameter.
DCore Core repulsion parameters. Each instance is of the form El,IType,Value1,Value2.
Each term specifies the core repulsion between the current element and the element
El. IType specifies the bond type: 1 for usual AM1, 2 for AM1 N-H and O-H, 3
usual PM6, 4 PM6 O-H, 5 PM6 CC triple bond, and 6 PM6 Si-O. There will be one
or two parameters values, depending on the specific functional form.

MOPAC-style semi-empirical parameter input. If you request PM6=MOPACExternal or AM1=MOPACExternal,

then an input section is read giving parameters in the same formation used by the External keyword in MOPAC.
This is less general than the native Gaussian format, but includes the most common parameters. Refer to the
MOPAC documentation for details. The units expected by Gaussian in this format are those expected by
MOPAC, which are a mixture of atomic and other units.
The following table gives the correspondence between MOPAC External labels and the native Gaussian
input:

MOPAC Gaussian
USS,UPP,UDD U
ZS,ZP,ZD ZetaOverlap
ZSN,ZPN,ZDN Zeta1C
BetaS,BetaP,BetaD Beta
GSS,GPP,· · · ,FODD,· · · F0ss,F0pp, etc.†
DD2 DDN=0,1,Value
DD3 DDN=1,1,Value
DD4 DDN=0,2,Value
DD5 DDN=1,2,Value
DD6 DDN=2,2,Value
PO1 KON=0,0,0,Value
PO2 KON=1,0,1,Value
PO3 KON=2,1,1,Value
PO4 KON=2,0,2,Value
PO5 KON=1,1,2,Value
320 Chapter 5. List of Gaussian Keywords

PO6 KON=2,2,2,Value
PO7 KON=0,1,1,Value
PO8 KON=0,2,2,Value
PO9 CoreKO
EHeat EHeat
EISol EISol
AlpB_NN,XFac_NN DCore=NN,3,Alpha,XFac
† Note that MOPAC’s GSP and GP2 are linear combinations of F0sp and G1sp. Gaussian uses the standard
Slater-Condon names and parameter definitions.

Here is example MOPAC External data for Cr, printed by MOPAC using its debug option:
PARAMETER VALUES USED IN THE CALCULATION

NI TYPE VALUE UNIT

24 USS -34.86433900 EV ONE-CENTER ENERGY FOR S
24 UPP -26.97861500 EV ONE-CENTER ENERGY FOR P
24 UDD -54.43103600 EV ONE-CENTER ENERGY FOR D
24 ZS 3.28346000 AU ORBITAL EXPONENT FOR S
24 ZP 1.02939400 AU ORBITAL EXPONENT FOR P
24 ZD 1.62311900 AU ORBITAL EXPONENT FOR D
24 BETAS -5.12261500 EV BETA PARAMETER FOR S
24 BETAP 3.92671100 EV BETA PARAMETER FOR P
24 BETAD -4.23055000 EV BETA PARAMETER FOR D
24 GSS 8.85557242 EV ONE-CENTER INTEGRAL (SS,SS)
24 GPP 5.05309383 EV ONE-CENTER INTEGRAL (PP,PP)
24 GSP 5.58863066 EV ONE-CENTER INTEGRAL (SS,PP)
24 GP2 4.42952965 EV ONE-CENTER INTEGRAL (PP*,PP*)
24 HSP 0.64803936 EV ONE-CENTER INTEGRAL (SP,SP)
24 ZSN 1.61985300 AU INTERNAL EXPONENT FOR S - (IJ,KL)
24 ZPN 0.84826600 AU INTERNAL EXPONENT FOR P - (IJ,KL)
24 ZDN 1.40501500 AU INTERNAL EXPONENT FOR D - (IJ,KL)
24 F0DD 9.86923654 EV SLATER-CONDON PARAMETER F0DD
24 F2DD 5.20966257 EV SLATER-CONDON PARAMETER F2DD
24 F4DD 3.39760602 EV SLATER-CONDON PARAMETER F4DD
24 F0SD 6.15013600 EV SLATER-CONDON PARAMETER F0SD
24 G2SD 2.00030000 EV SLATER-CONDON PARAMETER G2SD
24 F0PD 5.63536196 EV SLATER-CONDON PARAMETER F0PD
24 F2PD 1.91648791 EV SLATER-CONDON PARAMETER F2PD
24 G1PD 1.58022558 EV SLATER-CONDON PARAMETER G1PD
24 G3PD 0.96233144 EV SLATER-CONDON PARAMETER G3PD
24 DD2 0.28669123 BOHR CHARGE SEPARATION, SP, L=1
24 DD3 2.91433601 BOHR CHARGE SEPARATION, PP, L=2
24 DD4 1.12394737 BOHR CHARGE SEPARATION, SD, L=2
24 DD5 0.81804068 BOHR CHARGE SEPARATION, PD, L=1
24 DD6 1.23219554 BOHR CHARGE SEPARATION, DD, L=2
24 PO1 1.53639890 BOHR KLOPMAN-OHNO TERM, SS, L=0
24 PO2 0.72875078 BOHR KLOPMAN-OHNO TERM, SP, L=1
24 PO3 1.96024483 BOHR KLOPMAN-OHNO TERM, PP, L=2
24 PO4 0.94950312 BOHR KLOPMAN-OHNO TERM, SD, L=2
 5.75 SP 321

24 PO5 1.66105265 BOHR KLOPMAN-OHNO TERM, PD, L=1

24 PO6 1.08400979 BOHR KLOPMAN-OHNO TERM, DD, L=2
24 PO7 1.53639890 BOHR KLOPMAN-OHNO TERM, PP, L=0
24 PO8 1.37859617 BOHR KLOPMAN-OHNO TERM, DD, L=0
24 PO9 1.53639890 BOHR KLOPMAN-OHNO TERM, CORE
24 CORE 6.00000000 E CORE CHARGE
24 EHEAT 95.00000000 KCAL/MOL HEAT OF FORMATION OF THE ATOM (EXP)
24 EISOL -185.72482255 EV TOTAL ENERGY OF THE ATOM (CALC)
24 ALPB_24 4.65541900 ALPB factor
24 XFAC_24 10.31860700 XFAC factor

5.74.3 Availability

Energies, optimizations and frequencies.

Parameters are stored in the program for the following elements:
♢ AM1: H, Li-F, Mg-Cl, Cr, Zn, Ge, Br, Sn, I and Hg.
♢ PM3: H, Li-F, Na-Cl, K, Ca, Cr, Zn-Br, Rb, Sr, Cd-I, Cs, Ba and Hg-Bi.
♢ PM6: H-Ba and Lu-Bi.
♢ PM7: H-La and Lu-Bi.

5.74.4 Related Keywords

CNDO, INDO, MNDO, MINDO3

5.74.5 Examples

The energy from these calculations appears in the output file as follows:

SCF Done: E(RAM1) = -0.943839275843E-01 A.U. after 6 cycles AM1

SCF Done: E(RPM3) = -0.850201514485E-01 A.U. after 6 cycles PM3
SCF Done: E(RPM6) = -0.864068239687E-01 A.U. after 7 cycles PM6
SCF Done: E(RPM7) = -0.919784216493E-01 A.U. after 7 cycles PM7

The energy printed is the heat of formation as computed by the model. Energies for other semi-empirical
methods are reported similarly.

5.75 SP

This calculation type keyword requests a single-point energy calculation. It is the default when no calcu-
lation type keyword is specified.

5.75.1 Availability

All methods.

5.75.2 Examples

See the discussions of the various methods keywords for examples of their energy output formats.
 322 Chapter 5. List of Gaussian Keywords

5.76 Sparse
The Sparse keyword says to use sparse matrix storage for performance enhancement of large calculations
(above around 400 atoms) [744]. The keyword’s option allows you to specify the cutoff value for considering
matrix elements to be zero.
See the Program Development-Related Keywords for options to this keyword.

5.76.1 Options
Loose
Use loose cutoffs: 5.0−5
Medium
Use medium cutoffs: 5.0−7
Tight
Use tight cutoffs: 1.0−10
N
Set the cutoff to 10−N
None
Overrides the default of Sparse for ONIOM layers.

5.77 Stable
This calculation type method requests that the stability of the Hartree-Fock or DFT wavefunction be tested.
Gaussian has the ability to test the stability of a single-determinant wavefunction with respect to relaxing
various constraints [745, 746](see also [680]). These include:
♢ Allowing an RHF determinant to become UHF.
♢ Allowing orbitals to become complex.
♢ Reducing the symmetry of the orbitals.
Note that analytic frequency calculations are only valid if the wavefunction has no internal instabilities.
In examining the results prior to a frequency calculation, it suffices to see if any singlet instabilities exist for
restricted wavefunctions or if any instabilities (singlet or triplet) exist for unrestricted wavefunctions. Møller-
Plesset calculations are only valid if the wavefunction has no internal instabilities within the constrained sym-
metry. In examining the results prior to a Møller-Plesset calculation, an internal instability only affects the
validity of the results if the pairs of orbitals mixed are of the same spatial symmetry. The validity of restricted
Møller-Plesset energies based on wavefunctions which are unstable with respect to becoming UHF is also
questionable [747].
By default, only real instabilities (i.e., not complex) are sought. The code which checks for a complex
stability (Link 902) is older and less reliable and should not be used unless complex orbitals are of interest.

5.77.1 Options
RExt
Test for external real instability as well as internal instability (the default).
Int
Test for internal instability (a lower determinant with the same constraints) only.
 5.77 Stable 323

RRHF
Constrain the wavefunction testing or reoptimization to be real, spin-restricted. Synonymous with Sin-
glet.
RUHF
Constrain the wavefunction testing or reoptimization to be real, spin-unrestricted. Synonymous with
Triplet.
CRHF
Allow testing for real to complex instabilities in spin-restricted wavefunctions.
CUHF
Allow testing for real to complex instabilities in spin-unrestricted wavefunctions.
Opt
If an instability is found, reoptimize the wavefunction with the appropriate reduction in constraints,
repeating stability tests and reoptimizations until a stable wavefunction is found. RepOpt is a synonym
for Opt. NoOpt prevents reoptimization and is the default. See also the QCOnly option below.
1Opt
Redo the SCF once if an instability is detected.
Direct
Forces a direct calculation. This is the default.
MO
Forces a stability calculation using transformed two-electron integrals (i.e., in the MO basis).
AO
Forces a calculation using the AO integrals (written to disk), avoiding an integral transformation. The
AO basis is seldom an optimal choice, except for small molecules on systems having very limited disk.
It is the default when SCF=Conven is also specified.
InCore
Forces an in-core algorithm.
ICDiag
Forces in-core full diagonalization of the matrix formed in memory from transformed integrals. It implies
the use of MO integrals.
QCOnly
Suppresses the use of the regular SCF procedure (i.e., non quadratic convergence: Link 502) during later
SCF calculations of the Stable=Opt iterations. This is the default.
XQC
Try to use the regular SCF procedure (Link 502) before quadratic convergence SCF (Link 508) for later
SCF calculations of the Stable=Opt iterations.
Restart
Restarts the calculation off the checkpoint file. Also implies SCF=Restart.

5.77.2 Availability

HF and DFT methods.

 324 Chapter 5. List of Gaussian Keywords

5.77.3 Related Keywords

SCF

5.78 Symmetry
This keyword specifies the uses of molecular symmetry within the calculation. By default, the program
attempts to identify the point group of the molecule. If symmetry is in use, the molecule may be rotated to a
different coordinate system, called the standard orientation, before the calculation is performed. Derivatives
are then rotated back to the original (input) orientation. Orbitals are printed in the standard orientation. Input
for properties and background charge distributions must be specified in the standard orientation.
By default, symmetry is used wherever possible to reduce CPU, disk storage, and I/O requirements. The
NoSymmetry keyword prevents molecule reorientation and causes all computations to be performed in the input
orientation (although the program still attempts to identify the appropriate point group). Symmetry use can be
completely disabled by Symmetry=None; use this option if NoSymm generates an error when identifying the
point group.

5.78.1 Options
Int
Int enables and NoInt disables use of integral symmetry (use of the petite list). Synonymous with
Int=[No]Symm.
Grad
NoGrad disables and Grad enables use of symmetry in integral derivative evaluation.
SCF
NoSCF disables and SCF enables use of N3 symmetry in SCF, which is used by default only for GVB cal-
culations. Symm=NoSCF is equivalent to Guess=LowSym and combining all irreducible representations
together.
Loose
Tells the program to use looser cutoffs in determining symmetry at the first point. It is designed for use
with suboptimal input geometries. Tight says to use the regular criteria at the first point, and it is the
default.
Follow
Try to follow point group/orientation during optimization.
PG=group
Use no more symmetry than that found in the specified point group.
Axis=[X|Y|Z ]
Specify axis to help specify subgroup.
CenterOfCharge
Use the center of atomic charges in determining the standard orientation. This is the default. COC is a
synonym for this option.
CenterOfMass
Use the center of atomic masses in determining the standard orientation. COM is a synonym for this
option.
 5.79 TD 325

None
Do not assign point group and bypass all symmetry processing.
PrintOrientation
Print the standard orientation to high precision.
SaveOrientation
Mark the standard orientation as the input orientation.
On
Turn on symmetry when it would otherwise be off. This can cause wrong answers, so it should only be
used if you know what you’re doing!

5.78.2 Related Keywords

Int, SCF

5.79 TD
This method keyword requests an excited state calculation using the time-dependent Hartree-Fock or DFT
method [717, 748–753]; analytic gradients [717, 753] and frequencies [754–756] are available in Gaussian 16.
For a review of using TD-DFT to predict excited state properties, see [757, 758].
Time-dependent DFT calculations can employ the Tamm-Dancoff approximation, via the TDA keyword.
TD-DFTB calculations can also be performed [759].
Note that the normalization criteria used is < X +Y |X −Y >= 1.
Electronic circular dichroism (ECD) analysis is also performed during these calculations [760–765].

5.79.1 Options
General Options
Singlets
Solve only for singlet excited states. Only effective for closed-shell systems, for which it is the default.
Triplets
Solve only for triplet excited states. Only effective for closed-shell systems.
50-50
Solve for half triplet and half singlet states. Only effective for closed-shell systems.
Root=N
Specifies the “state of interest”. The default is the first excited state (N=1).
NStates=M
Solve for M states (the default is 3). If 50-50 is requested, NStates gives the number of each type of state
for which to solve (i.e., the default is 3 singlets and 3 triplets).
The keyword Read may also be specified as the parameter to the NStates option. In this case, the number
of states to compute is read from the input stream. This features is typically used in EET calculations.
Add=N
Read converged states off the checkpoint file and solve for an additional N states. This option implies
Read as well.
Read
326 Chapter 5. List of Gaussian Keywords

Reads initial guesses for the states off the checkpoint file. Note that, unlike for SCF, an initial guess for
one basis set cannot be used for a different one.
Restart
This option restarts a TD calculation after the last completed geometry. A failed frequency job may be
restarted from its checkpoint file by simply repeating the route section of the original job, adding the
Restart option to the keyword/option. No other input is required.
EqSolv
Whether to perform equilibrium or non-equilibrium PCM solvation. NonEqSolv is the default except for
excited state optimizations and when the excited state density is requested (e.g., with Density=Current or
All).
IVOGuess
Force use of IVO guess. This is the default for TD Hartree-Fock. NoIVOGuess forces the use of canonical
single excitations for guess, and it is the default for TD-DFT. The HFIVOGuess option forces the use of
Hartree-Fock IVOs for the guess, even for TD-DFT.
SOS
Do sum-over states polarizabilities, etc. By default, all excited states are solved for. A list of frequencies
at which to do the sums is read in. Zero frequency is always done and need not be in the list.
NonAdiabaticCoupling
Requests that the ground-to-excited-state non-adiabatic coupling be computed [766, 767]. NAC is a
synonym for this option. NoNonAdiabaticCoupling and NoNAC suppress this behavior. The default is
NoNAC when computing energies or energies+gradients because the extra cost is non-trivial. The default
is NAC during frequency calculations where the extra cost is negligible.
Conver=N
Sets the convergence calculations to 10−N on the energy and 10−(N−2) on the wavefunction. The default
is N=4 for single points and N=6 for gradients.

Energy Range Options

An energy range can be specified for CIS and TD excitation energies using the following options to CIS,
TD and TDA.
GOccSt=N
Generate initial guesses using only active occupied orbitals N and higher.
GOccEnd=N
Generate initial guesses: if N>0, use only the first N active occupied orbitals; if N<0, do not use the
highest |N| occupieds.
GDEMin=N
Generate guesses having estimated excitation energies ≥ N/1000 eV.
DEMin=N
Converge only states having excitation energy ≥ N/1000 eV; if N=-2, read threshold from input; if N<-2,
set the threshold to |N|/1000 Hartrees. [768, 769]
IFact=N
Specify factor by which the number of states updated during initial iterations is increased. The default
for IFact is Max(4,g) where g is the order of the Abelian point group.
 5.79 TD 327

WhenReduce=M
Reduce to the desired number of states after iteration M. The default for WhenReduce is 1 for TD and 2
for TDA. Larger values may be needed if there are many states in the range of interest.

5.79.2 Availability
Energies, gradients and frequencies using Hartree-Fock or a DFT method.
Gradients and frequencies are not available for functionals for which third and fourth derivatives are not
implemented: the exchange functionals G96, P86, PKZB, wPBEh and PBEh; the correlation functional PKZB;
the hybrid functionals OHSE1PBE and OHSE2PBE.

5.79.3 Related Keywords

CIS, ZIndo, Output

5.79.4 Examples
Here is the key part of the output from a TD excited states calculation:

Excitation energies and oscillator strengths:

Excited State 1: Singlet-A2 4.0147 eV 308.83 nm f=0.0000 <S**2>=0.000

8 -> 9 0.70701
This state for optimization and/or second-order correction.
Copying the excited state density for this state as the 1-particle RhoCI
density.

Excited State 2: Singlet-B1 9.1612 eV 135.34 nm f=0.0017 <S**2>=0.000

6 -> 9 0.70617

Excited State 3: Singlet-B2 9.5662 eV 129.61 nm f=0.1563 <S**2>=0.000

8 -> 10 0.70616

The results on each state are summarized, including the spin and spatial symmetry, the excitation energy,
the oscillator strength, the S2 , and (on the second line for each state) the largest coefficients in the CI expansion.
The ECD results appear slightly earlier in the output as follows:

1/2[<0|r|b>*<b|rxdel|0> + (<0|rxdel|b>*<b|r|0>)*]
Rotatory Strengths (R) in cgs (10**-40 erg-esu-cm/Gauss)
state XX YY ZZ R(length) R(au)
1 0.0000 0.0000 0.0000 0.0000 0.0000
2 0.0000 0.0000 0.0000 0.0000 0.0000
3 0.0000 0.0000 0.0000 0.0000 0.0000
1/2[<0|del|b>*<b|r|0> + (<0|r|b>*<b|del|0>)*] (Au)
state X Y Z Dip. S. Osc.(frdel)
1 0.0000 0.0000 0.0000 0.0000 0.0000
2 -0.0050 0.0000 0.0000 0.0050 0.0033
3 0.0000 -0.2099 0.0000 0.2099 0.1399
 328 Chapter 5. List of Gaussian Keywords

5.80 Temperature
Specifies the temperature to be used for thermochemistry analysis (in Kelvin). The value should be speci-
fied as an option:
# · · · Temperature=300
The default is 298.15 K.

5.80.1 Options
Default
Restore the default temperature if a different value was retrieved by Geom=AllCheck.

5.81 Test
This keyword suppresses the automatic creation of an archive entry (formerly intended for the Browse
Quantum Chemistry Database System). Its antonym is Archive, which is the default. Note that archive entries
may be extracted from Gaussian log files after the fact using the pluck utility.

5.82 TestMO
The cutoffs used in computing and storing integrals and the convergence criteria applied in SCF and CPHF
calculations are appropriate for most molecules and basis sets. However, if a nearly linearly dependent basis set
is used, very large MO coefficients may occur and, in combination with the finite accuracy of other terms, lead
to substantial numerical errors. By default, CPHF and post-SCF calculations are aborted if any MO coefficient
is larger than 1000. (Note that this corresponds to a coefficient of 1012 for the contribution of an AO integral
to an MO integral involving four virtual orbitals.) The NoTestMO keyword suppresses this check. It should be
used only after careful thought. TestMO is the default.

5.83 TrackIO
This keyword requests routine-by-routine statistics of I/O and CPU usage.

5.83.1 Related Keywords

#P

5.84 Transformation
This keyword controls the algorithm used for integral transformation, as well as the types of transformed
integrals produced.

5.84.1 Options
Integral Transformation Algorithm Options
The default is the smallest set of integrals the method can use.
Direct
Requests that the direct transformation routines be used. Equivalent to L804. Link 804 will select
between the in-core, fully direct, and semi-direct methods automatically. This is the default.
 5.85 Units 329

InCore
Forces use of the in-core algorithm in Link 804.
Force
Forces an AO-to-MO integral transformation to be done during a single-point SCF calculation.
FullDirect
Forces use of the fully direct (MO integrals in core) method in Link 804.
SemiDirect
Forces use of the semi-direct algorithm in Link 804.

Integral Selection Options

Full
Forces a transformation over all orbitals (i.e., including transformed integrals involving all virtuals).
ABCD is a synonym for Full.
IJAB
Produce only <IJ||AB> integrals.
IAJB
Produce <IJ||AB> and <IA||JB> integrals.
IJKL
Produce <IJ||AB>, <IA||JB>, and <IJ||KL> integrals.
IJKA
Produce <IJ||AB>, <IA||JB>, <IJ||KL>, and <IJ||KA> integrals.
IABC
Produce <IJ||AB>, <IA||JB>, <IJ||KL>, <IJ||KA>, and <IA||BC> integrals.

5.85 Units

The Units keyword controls the units used in the Z-matrix for distances and angles and related values,
such as step-sizes in numerical differentiation. The defaults are Angstroms and degrees.

5.85.1 Options
Ang
Distances are in Angstroms (this is the default).
AU
Distances are in atomic units (Bohrs).
Deg
Angles are in degrees (the default).
Rad
Angles are in radians.

5.85.2 Restrictions

The Charge, Cube and Massage keywords are not affected by the setting of the Units keyword, and their
input is always interpreted in units of Angstroms and degrees.
 330 Chapter 5. List of Gaussian Keywords

5.86 Volume

This keyword requests that the molecular volume be computed, defined as the volume inside a contour
of 0.001 electrons/Bohr3 density. The density to be used can be specified with the Density keyword. Since a
Monte-Carlo integration is done, the computed volume is only accurate to about two significant figures, but
this is sufficient to estimate a radius for use with the Onsager solvent reaction field model. The recommended
radius (which is 0.5 Å larger than the radius corresponding to the computed volume) is printed in the output.
Since other, more accurate solvent models are available in Gaussian 16, this keyword has applicability
only in preparation for frequency calculations using SCRF=Dipole.

5.86.1 Options
Tight
Requests an increased density of points for more accurate integration. By default, the volume is computed
to an accuracy of about 10%. Use of this option is recommended if the computed molecular volume is
needed more quantitatively.

5.86.2 Availability
Hartree-Fock, all DFT methods, CIS, MP2, MP3, MP4(SDQ), CID, CISD, CCD, CCSD, and QCISD.

5.86.3 Related Keywords

SCRF=Dipole

5.87 W1 Methods

These method keywords request the W1 methods of Martin [107, 770]:

♢ The W1U keyword specifies the W1 method modified to use UCCSD instead of ROCCSD for open shell
systems [771] (the ROCCSD method is that of Handy, Pople and coworkers [543]).
♢ W1BD requests a related method which replaces coupled cluster with BD [771]. This method is both more
expensive and more accurate than CBS-QB3 and G3 (true for all W1 methods); we recommend using
W1BD when you require very accurate energies.
♢ W1RO is the W1 method described in [107] with a slightly improved scalar relativistic correction as de-
scribed in [771].

5.87.1 Options
SP
Perform only a single-point energy evaluation using the specified compound model chemistry. No zero-
point or thermal energies are included.
NoOpt
Perform the frequencies and single-point energy calculation for the specified model chemistry at the input
geometry. Freq=TProjected is implied. This option is not meaningful or accepted for methods such as
G1, which use different geometries for the frequencies and the single-point steps. StartFreq is a synonym
for NoOpt.
 5.87 W1 Methods 331

ReadAmplitudes
Reads the converged amplitudes from the checkpoint file (if present). Note that the new calculation can
use a different basis set, method (if applicable), etc. than the original one.
SaveAmplitudes
Saves the converged amplitudes in the checkpoint file for use in a subsequent calculation (e.g., using a
larger basis set). Using this option results in a very large checkpoint file, but also may significantly speed
up later calculations.
The ReadAmplitudes option is the default for all W1 methods. SaveAmplitudes is also the default for
W1BD.
Restart
Restart an incomplete W1 calculation.
ReadIsotopes
This option allows you to specify alternatives to the default temperature, pressure, frequency scale factor
and/or isotopes – 298.15 K, 1 atmosphere, no scaling, and the most abundant isotopes (respectively). It is
useful when you want to rerun an analysis using different parameters from the data in a checkpoint file.
Be aware, however, that all of these can be specified in the route section (Temperature, Pressure and Scale
keywords) and molecule specification (the Iso parameter), as in this example:

#T Method/6-31G(d) JobType Temperature=300.0 · · ·

···

0 1
C(Iso=13)
···

ReadIsotopes input has the following format:

temp pressure [scale] Values must be real numbers.

isotope mass for atom 1
isotope mass for atom 2
···
isotope mass for atom n

Where temp, pressure, and scale are the desired temperature, pressure, and an optional scale factor for
frequency data when used for thermochemical analysis (the default is unscaled). The remaining lines hold
the isotope masses for the various atoms in the molecule, arranged in the same order as they appeared
in the molecule specification section. If integers are used to specify the atomic masses, the program will
automatically use the corresponding actual exact isotopic mass (e.g., 18 specifies 18 O, and Gaussian uses
the value 17.99916).

5.87.2 Examples
Calculation Summary Output. After all of the output for the component job steps, Gaussian prints a
table of results for these methods. Here is the key part of the output from a W1BD calculation:
 332 Chapter 5. List of Gaussian Keywords

Results before spin correction.

Temperature= 298.150000 Pressure= 1.000000
E(ZPE)= 0.016919 E(Thermal)= 0.019783
W1BD (0 K)= -39.139927 W1BD Energy= -39.137063
W1BD Enthalpy= -39.136119 W1BD Free Energy= -39.158277

W1U spin correction:

G.P.F. Wood, L. Radom, G.A. Petersson, E.C. Barnes, M.J. Frisch
and J.A. Montgomery, Jr., JCP 125, 94106 (2006).

DE(Spin)= -0.000051

W1Bsc Electronic Energy -39.156897 Predicted energy.

Spin-corrected results.
Temperature= 298.150000 Pressure= 1.000000
E(ZPE)= 0.016919 E(Thermal)= 0.019783
W1Bsc(0 K)= -39.139978 W1Bsc Energy= -39.137114
W1Bsc Enthalpy= -39.136170 W1Bsc Free Energy= -39.158328

The predicted energy is given between the ordinary and spin-corrected thermochemistry analysis tables.
The energy labels thus have the following meanings (spin-corrected W1BD is used as an example):

W1Bsc (0 K) Zero-point-corrected electronic energy: E0 = Eelec + ZPE

W1Bsc Energy Thermal-corrected energy: E = E0 + Etrans + Erot + Evib
W1Bsc Enthalpy Enthalpy computed using the spin-corrected W1BD predicted energy: H = E + RT
W1Bsc Free Energy Gibbs Free Energy computed using the spin-corrected W1BD predicted energy: G
= H - TS

5.88 Window Keyword and Frozen Core Options

These options specify which inner orbitals are frozen in post-SCF calculations. Gaussian 16 added some
additional options to the ones previously available in the program [772]. See also BD for BD-specific choices.
The Window keyword performs an analogous function but takes its input as parameters in the route section
rather than from the input stream. It requests that L801 perform the setup for a frozen-core calculation during
jobs (e.g., single-point SCF) which would otherwise not set up a window.

5.88.1 Options
Frozen Core Options to Post SCF Methods Keywords
FC
This specifies a “frozen core” calculation, and it implies that inner-shells are excluded from the correla-
tion calculation. This is the default calculation mode. Note that FC, Full, RW, and Window are mutually
exclusive. It is equivalent to FreezeG2 for the 6-31G and 6-311G basis sets and to FreezeNobleGasCore
for all other basis sets, except that the outer s and p core orbitals of 3rd row and later alkali and alkaline
earth atoms are not frozen (in accord with the G2/G3/G4 conventions).
5.88 Window Keyword and Frozen Core Options 333

FreezeNobleGasCore
In post-SCF calculations, the largest noble gas core is frozen. FrzNGC is a synonym for this option.
FreezeInnerNobleGasCore
In post-SCF calculations, the next to largest noble gas core is frozen. That is, the outermost core orbitals
are retained. FrzINGC and FC1 are synonyms for this option.
FreezeG2
Freeze orbitals according to the G2 convention: d orbitals of main group elements are frozen, but the
outer sp core of 3rd row and later alkali and alkaline earth elements are kept in the valence.
FreezeG3
Freeze orbitals according to the G3 convention.
FreezeG4
Freeze orbitals according to the G4 convention.
Full
This specifies that all electrons be included in a correlation calculation.
RW
The “read window” option means that specific information about which orbitals are retained in the post-
SCF calculation will be given in the input file. ReadWindow is a synonym for RW.
The required input section consists of a line specifying the starting and ending orbitals to be retained,
followed by a blank line. A value of zero indicates the first or last orbital, depending on where it is used.
If the value for the first orbital is negative (-m), then the highest m orbitals are retained; if the value for
the last orbital is negative (-n), then the highest n orbitals are frozen. If m is positive and n is omitted,
n defaults to 0. If m is negative and n is omitted, then the highest |m| occupied and lowest |m| virtual
orbitals are retained.
Here are some examples for a calculation on C4 H4 :

0,0 Equivalent to Full.

5,0 Freezes the 4 core orbitals and keeps all virtual orbitals (equivalent to
FC if the basis has a single zeta core).
5,-4 Freezes the four core orbitals and the highest four virtual orbitals. This
is the appropriate frozen core for a basis with a double-zeta core.
6,22 Retains orbitals 6 through 22 in the post-SCF phase. For example, since
C4 H4 has 28 electrons, if this is a closed-shell calculation, there will be
14 occupied orbitals, 5 of which will be frozen, so the post-SCF calcula-
tion will involve 9 occupied orbitals (orbitals 6-14) and 8 virtual orbitals
(orbitals 15-22).
-6 Retains orbitals 9 through 20.

ChkWindow
The window read in during a previous job is recovered from the checkpoint file.
ListWindow
Reads a list of orbitals to freeze from the input stream, terminated by a blank line. Two lists are read for
unrestricted calculations. A range of orbitals can be specified, e.g.: 2 7-10 14.
 334 Chapter 5. List of Gaussian Keywords

The Window Keyword

Window=(m[,n])
Window=parameter
This keyword performs the same function as the ReadWindow option, but takes its input as parame-
ters in the route section rather than from the input stream. It is typically used with Output=(Matrix,
MO2ElectronIntegrals).
The Window keyword accepts one or two integers as parameters (as with the corresponding option). It
also accepts the following parameters, which have the same meanings as the correspondingly-named options:
FC, FreezeNobleGasCore, FreezeInnerNobleGasCore, FreezeG2, FreezeG3, FreezeG4, and Full.

5.89 ZIndo
This method keyword requests an excited state energy calculation using the ZIndo/S method [773–781].
Note that ZIndo calculations must not specify a basis set keyword.

5.89.1 Options
Singlets
Solve only for singlet excited states. Only effective for closed-shell systems, for which it is the default.
Triplets
Solve only for triplet excited states. Only effective for closed-shell systems.
50-50
Solve for half triplet and half singlet states. Only effective for closed-shell systems.
Root=N
Specifies the “state of interest”. The default is the first excited state (N=1).
NStates=M
Solve for M states (the default is 3). If 50-50 is requested, NStates gives the number of each type of state
for which to solve (i.e., the default is 3 singlets and 3 triplets).
Add=N
Read converged states off the checkpoint file and solve for an additional N states.
Window=(m[,n])
The two values specify the starting and ending orbitals to be used. The default is to use all orbitals. A
value of zero indicates the first or last orbital, depending on where it is used. If the value for the first
orbital is negative (-m), then the highest m orbitals are retained; the value for the last orbital is negative
(-n), then the highest n orbitals are frozen. If m is positive and n is omitted, n defaults to 0. If m is
negative and n is omitted, then the highest |m| occupied and lowest |m| virtual orbitals are retained.

5.89.2 Availability
Energies only. The Density keyword is ignored for ZIndo calculations.

5.89.3 Related Keywords

CIS, TD
 6. Utility Programs

Most utilities are available for both UNIX and Windows versions of Gaussian. However, be sure to consult
the release notes accompanying the program for information pertaining to specific operating systems.
The GAUSS_MEMDEF environment variable may be used to increase the memory available to utilities
which do not offer such an option themselves. Its value should be set to the desired amount of memory. The
default unit is words; the specified value can also be followed by a suffix indicating other units (e.g., GB for
gigabytes).
The following lists the available utilities and their functions (starred items are included on the Gaussian
16W Utilities menu):
♢ c8616
Converts checkpoint files from previous program versions to Gaussian 16 format.
♢ chkchk*
Displays the route and title sections from a checkpoint file.
♢ cubegen*
Standalone cube generation utility.
♢ cubman*
Manipulates Gaussian-produced cubes of electron density and electrostatic potential (allowing them to
be added, subtracted, and so on).
♢ formchk*
Converts a binary checkpoint file into an ASCII form suitable for use with visualization programs and
for moving checkpoint files between different types of computer systems.
♢ freqchk*
Prints frequency and thermochemistry data from a checkpoint file. Alternate isotopes, temperature, pres-
sure and scale factor can be specified for the thermochemistry analysis.
♢ freqmem
Determines memory requirements for frequency calculations.
 336 Chapter 6. Utility Programs

♢ gauopt
Performs optimizations of variables other than molecular coordinates.
♢ ghelp
On-line help for Gaussian.
♢ mm
Standalone molecular mechanics program.
♢ newzmat*
Conversion between a variety of molecular geometry specification formats.
♢ testrt*
Route section syntax checker and non-standard route generation.
♢ unfchk*
Convert a formatted checkpoint file back to its binary form (e.g., after moving it from a different type of
computer system).

6.1 c8616
The c8616 utility converts checkpoint files from Gaussian 86 through Gaussian 09 to Gaussian 16 format.
It takes the name of the checkpoint file as its argument and transforms it in place so that the reformatted file has
the same name as the original one. For example, the following command converts the checkpoint file taxol.chk
in the Gaussian scratch directory to Gaussian 16 format:
$ c8616 $GAUSS_SCRDIR/taxol.chk

6.2 chkchk
The chkchk utility displays the route and title sections from a checkpoint file, and indicates other infor-
mation that is present within it. It is useful for determining the contents of random checkpoint files whose
purpose has been forgotten and whose names are non-descriptive. It takes the name of the checkpoint file as its
argument. Here is an example of its use:
$ chkchk important
Checkpoint file important.chk:
Title: Opt freq for pentaprismane
Route: #P opt freq b3lyp/6-311+g(2d,p)
Version: ES64L-G16RevB.01
NAtoms= 4 ICharg= 0 Multip= 1
Atomic coordinates present.
AO basis is present.
MO coefficients present.
Cartesian force constants present.
This checkpoint is from a job which completed successfully.
Internal force constants may be present.
An OT bucket is present. The stored data is from a(n) Optimization job.
Total number of points stored = 1.
Number of statistics per point= 2.

The -p option may be used to print additional information from the checkpoint file, including the molecular
coordinates, the basis set in Gen format, and the molecular orbitals in the correct format for Guess=Cards. This
6.2 chkchk 337

information may be redirected to a file for later use as input to Gaussian or another program.
Here is an example:

$ chkchk -p myfile >newjob.gjf

$ cat newjob.gjf
Checkpoint file myfile.chk:
Title: DMABN: Opt freq from saddle point found by first opt: acetonitrile
Route: #N Geom=AllCheck Guess=TCheck SCRF=Check GenChk
B3LYP/6-311+G(2d,p) Freq
Atomic coordinates (Angstroms): Molecular structure
0 1
N 2.258424299166 -0.051967437933 -0.108610457679
C 0.911965883667 -0.011528021623 -0.025315883831
···

AO basis set (Overlap normalization): Basis set in format for Gen keyword
Atom N1 Shell 1 S 6 bf 1 - 1 4.267803417278 -0.098204225521 -0.205244020181

0.6293480000D+04 0.1969788147D-02
0.9490440000D+03 0.1496128592D-01
···
Atom N1 Shell 2 SP 3 bf 2 - 5 4.267803417278 -0.098204225521 -0.205244020181

0.3063310000D+02 0.1119060795D+00 0.3831191864D-01

···

(5D15.8) MOs in format for Guess=Cards

1 Alpha MO OE=-0.15587059D+02
0.55760173D+00 0.46815568D+00-0.15193125D-03 0.20920429D-03 0.73161643D-03
0.58391570D-02-0.61620240D-04-0.80819280D-04-0.30786697D-03-0.40418785D-02
···

357 Alpha MO OE= 0.37351112D+02

0.81138955D-01-0.87165085D-01 0.52591067D-03 0.25976528D-03-0.27428643D-03
0.35549516D-01-0.44238173D-02-0.13061602D-02 0.11962956D-02-0.14464014D+00

Input for Opt=FCCards (Energy,Forces,Force Constants): Forces for use with Opt=FCCards
-0.4554698501440964D+03
0.00000485 0.00000348 0.00000040 -0.00000441 0.00000421 -0.00000731
0.00000048 0.00000292 -0.00000191 -0.00000112 0.00000014 -0.00000354
···

Internal force constants may be present.

An OT bucket is present. The stored data is from a(n) Optimization job.
Total number of points stored = 1.
Number of statistics per point= 2.

Note that some editing of the generated input file may be required prior to use.
 338 Chapter 6. Utility Programs

6.3 cubegen
Gaussian includes a standalone utility for generating cubes from the data in a formatted checkpoint file
(equivalent to the previous Cube keyword). The utility is named cubegen, and it has the following syntax:
cubegen nprocs kind fchkfile cubefile npts format cubefile2
The parameters, which are not case-sensitive, have the following meanings:
nprocs
Number of shared memory processors used for electrostatic potential calculations. A value of 0 is equiv-
alent to 1 (it is the default). Note that this parameter must be included if other parameters are specified.
Previously this parameter was used to specify the amount of memory to allocate. The GAUSS_MEMDEF
environment variable should be used instead.
kind
A keyword specifying the type of cube to generate:

MO=n Molecular orbital n. The keywords Homo, Lumo, All, OccA (all alpha occu-
pied), OccB (all beta occupied), Valence (all valence orbitals) and Virtuals (all
virtual orbitals) may also be used in place of a specific orbital number. There
is no default for n, and an error will occur if it is omitted. AMO and BMO can
be similarly used to select only alpha or beta orbitals (respectively). For open
shell systems, Homo selects both alpha and beta orbitals.
Density=type Total density of the specified type. The type keyword is one of the single
density selection options that are valid with the Density keyword: SCF, MP2,
CC, CI, and so on (note that Current is not supported). The fdensity, falpha
and fbeta forms request the use of full instead of frozen core densities. The
default is SCF.
Spin=type Spin density (difference between α and β densities) of the specified type.
Alpha=type Alpha spin density of the specified type.
Beta=type Beta spin density of the specified type.
Potential=type Electrostatic potential using the density of the specified type.
Gradient Compute the density and gradient.
Laplacian Compute the Laplacian of the density (∇2 ρ ).
NormGradient Compute the norm of the density gradient at each point.
CurrentDensity=I Magnitude of the magnetically-induced (GIAO) current density, where I is the
applied magnetic field direction (X, Y or Z).
ShieldingDensity=IJN Magnetic shielding density. I is the direction of the applied magnetic field, J
is the direction of the induced field (X, Y or Z), and N is the number of the
nucleus for which the shielding density (GIAO) is to be calculated.

fchkfile
Name of the formatted checkpoint file. cubegen will prompt for this filename if it is not specified.
cubefile
Name of the output cube file; test.cube is the default if it is not explicitly specified (i.e., specifying the
name of the checkpoint file does not change the default cube filename).
 6.3 cubegen 339

npts
Number of points per side in the cube. A value of 0 selects the default value of 803 points distributed
evenly over a rectangular grid generated automatically by the program (not necessarily a cube). Positive
values of npts similarly specify the number of points per “side”; e.g., 100 specified a grid of 1,000,000
(1003 ) points.
The values -2, -3 and -4 correspond to the keywords Coarse, Medium and Fine and to values of 3
points/Bohr, 6 points/Bohr and 12 points/Bohr (respectively). Negative values of npts ≤-5 specify spac-
ing of npts*10−3 Angstroms between points in the grid.
A value of -1 says to read the cube specification from the input stream or from a second cube file (see
below), according to the following format:

IFlag, X0 , Y0 , Z0 Output unit number and initial point.

N1 , X1 , Y1 , Z1 Number of points and step-size in the X-direction.
N2 , X2 , Y2 , Z2 Number of points and step-size in the Y-direction.
N3 , X3 , Y3 , Z3 Number of points and step-size in the Z-direction.

IFlag is the output unit number. If IFlag is less than 0, then a formatted file will be produced; otherwise,
an unformatted file will be written.
If N1 <0 the input cube coordinates are assumed to be in Bohr, otherwise, they are interpreted as Angstroms.
|N1 | is used as the number of X-direction points in any case; N2 and N3 specify the number of points in
the Y and Z directions, respectively. Note that the three axes are used exactly as specified; they are not
orthogonalized, so the grid need not be rectangular.
The value -5 says to read in an arbitrary list of points from standard input. If you enter this input by hand,
terminate the input with an end-of-file (i.e., Ctrl-D under Unix). Alternatively, you can redirect standard
input to a file containing the list of points (do not place a blank line or Ctrl-D at the end of the file).
format
Format of formatted output files: h means include header (this is the default); n means don’t include
header. This parameter is ignored when unformatted cube files are produced.
cubefile2
If specified, the size for the generated cube is taken from this file. This option is useful when creating
cubes for later arithmetic operations such as difference densities.
In order for the cube dimensions to be taken from the specified cube file, the npts parameters must be -1,
and the specified file must have been created with a header.
If no parameters are specified, cubegen will prompt for fchkfile and run the following:
cubegen 1 density=scf test.cube 80 h
This generates a file named test.cube (with header) containing the SCF density in a rectangular grid of 803
points.

6.3.1 Output File Formats

All values in the cube file are in atomic units, regardless of the input units.
Densities, the norm of the density gradient, the Laplacian of the density, and the potential are scalars (i.e.
one value per point, NVal=1). A gradient cube contains the density plus the vector gradient of the density, so it
 340 Chapter 6. Utility Programs

has four values per point (NVal=4): i.e. the value of the density plus the X, Y, and Z components of its gradient.
Cube files have one row per record (i.e., N1 *N2 records each of length N3 *NVal). For formatted output,
each row is written out in format (6E13.5). In this case, if N3 *NVal is not a multiple of six, then there may be
blank space in some lines.
For example, schematically, cube files will look like this:

NAtoms, X-Origin, Y-Origin, Z-Origin, NVal NVal is the # of values/point

N1, X1, Y1, Z1 # of increments in the slowest running direction
N2, X2, Y2, Z2
N3, X3, Y3, Z3 # of increments in the fastest running direction
IA1, Chg1, X1, Y1, Z1 Atomic number, charge, and coordinates of the first atom
···
IAn, Chgn, Xn, Yn, Zn Atomic number, charge, and coordinates of the last atom
(N1*N2) records, each length N3*NVal Values of the density at each point in the grid

Note that a separate write is used for each record.

For molecular orbital output, NAtoms will be less than zero, and an additional record follows the data for
the final atom (in format 10I5 if the file is formatted):
NMO, (MO(I),I=1,NMO) Number of MOs and their numbers
If NMO orbitals were evaluated, then each record is NMO *N3 long and has the values for all orbitals at each
point together (in this case NMO =NVal).

6.3.2 Reading Cube Files with Fortran Programs

If one wishes to read the values of a cube file back into an array dimensioned X(NVal,N3 ,N2 ,N1 ), code like
the following Fortran loop may be used:

Do 10 I1 = 1, N1
Do 10 I2 = 1, N2
Read(n,’(6E13.5)’) ((X(IVal,I3,I2,I1),IVal=1,NVal)I3=1,N3)
10 Continue

where n is the unit number corresponding to the cube file.

6.4 cubman
The cubman program manipulates cubes of values of electron density and electrostatic potential as pro-
duced by Gaussian. The program prompts for an operation to perform and then the names of the necessary
files. The possible operations and their associated subcommands are:
add
Add two cubes to produce a new one.
copy
Copy a cube, possibly converting it from formatted to unformatted or vice versa.
diff
Compute properties of the difference between two cubes, without writing out a new cube.
 6.5 Example 341

prop
Computes the properties of a single cube.
subtract
Subtracts two cubes to produce a new cube.
scale
Scale a cube by a constant factor, producing a new cube.
square
Multiply a cube by itself to produce a new cube.
sprod
Take the scalar product of vectors in two cubes, producing a new cube of scalars.
vprod
Take the vector product of 3-vectors in two cubes, producing a new cube of 3-vectors.
magnitude
Compute the magnitude of vectors in a cube, producing a new cube of scalars.
normalize
Normalize the vectors in a cube, producing a new cube of vectors.
select
Select among the values per point and produce a new cube.
toxyz
Convert a cube into a simple list: X,Y,Z,Value,Value, · · · format.
All operation subcommands can be abbreviated to the shortest unique form.

6.5 Example
Here are some annotated sample runs with cubman (user input is shown in boldface type, and output has
been condensed slightly due to space considerations):
$ cubman
Action [Add, Copy, Difference, Properties, SUbtract, SCale, SQuare]? p
Input file? b.cube
Is it formatted [no,yes,old]? y
Opened special file b.cube.
Input file titles:
First excited state of propellane Title line from the job
CI Total Density Contents of cube file

SumAP= 13.39263 SumAN= .00000 SumA= 13.39263 Statistics about cube contents
CAMax= 3.35320 XYZ= .18898 -1.32280 .000004
CAMin= .00000 XYZ= -9999.00000 -9999.00000 -9999.00000

DipAE= -.8245357658 .7624198057 .1127178115

DipAN= -.0000060000 -.0000060000 .0000000000
DipA= -.8245417658 .7624138057 .1127178115

$ cubman
Action [Add, Copy, Difference, Properties, SUbtract, SCale, SQuare]? su
First input? b.cube
 342 Chapter 6. Utility Programs

Is it formatted [no,yes,old]? y
Opened special file b.cube.
Second input? a.cube
Is it formatted [no,yes,old]? y
Opened special file a.cube.
Output file? c.cube File to hold the new cube
Should it be formatted [no,yes,old]? y
Opened special file c.cube.
Input file titles:
First excited state of propellane Title from first file
CI Total Density Contents of first cube
Input file titles:
Propellane HF/6-31G* Title from second file
SCF Total Density Contents of second cube
Output file titles: Composite title used for new file
First excited state of propellane || Propellane HF/6-31G*
CI Total Density - SCF Total Density Difference to be computed

SumAP= 13.39263 SumAN= .00000 SumA= 13.39263 Statistics for first cube
CAMax= 3.35320 XYZ= .18898 -1.32280 .000004
CAMin= .00000 XYZ= -9999.00000 -9999.00000 -9999.00000

SumBP= 13.38168 SumBN= .00000 SumB= 13.38168 Statistics for second cube
CBMax= 3.39683 CBMin= .00000

SumOP= .63453 SumON=-.62358 SumO= .01094 Statistics for output cube

COMax= .49089 COMin=-.39885

DipAE= -.8245357658 .7624198057 .1127178115

DipAN= -.0000060000 -.0000060000 .0000000000
DipA= -.8245417658 .7624138057 .1127178115

DipBE= -.8306292172 .5490287046 .1243830393

DipBN= -.0000060000 -.0000060000 .0000000000
DipB= -.8306352172 .5490227046 .1243830393

DipOE= .0060934514 .2133911011 -.0116652278

DipON= -.0000060000 -.0000060000 .0000000000
DipO= .0060874514 .2133851011 -.0116652278

In the output, the input cubes are denoted as A and B, and the output cube is designated by O. Other code
letters are N for “negative values” or for “nuclear”, depending on the context, P for “positive values”, E for
“electronic”, C for “charge”, Dip for “dipole”, Sum for “summarization”, Max for “maximum”, and Min for
“minimum.” Thus, SumAN is the sum over the first input cube, taking the negative values only, and DipON is
the nuclear contribution to the dipole moment for the output cube. Similarly, CBMax is the maximum charge
for the second input cube, and SumO is the sum of the values in the output cube, including both positive and
negative values.

6.6 formchk
 6.6 formchk 343

formchk converts the data in a Gaussian checkpoint file into formatted forms that are suitable for input
into a variety of visualization software. By default, formchk creates a text version of the checkpoint file known
as the “formatted checkpoint file.” formchk can also generate “matrix element files” via various options. (see
Options)
formchk has the following syntax:
formchk [options] chkpt-file [formatted-file]
where chkpt-file is the name of the binary checkpoint file to be formatted and formatted-file is the name for the
resultant output file. If the name of the formatted file is omitted, it defaults to the base name of the checkpoint
file with .fchk.
For example, the following command will produce the formatted checkpoint file propell.fchk from the
checkpoint file propell.chk:
$ formchk propell.chk propell.fchk
The conventional extension for formatted checkpoint files is .fchk on Unix systems and other computers
supporting variable-length extensions.
Note that formatted checkpoint files can be used as a data exchange format between computer platforms.
Use formchk on the originating computer and unfchk on the target computer to create a binary checkpoint file.
Always include the -3 option when moving files between different types of computers (see Options).

6.6.1 Options
By default formchk produces a formatted checkpoint file that is backwardly compatible with all previous
versions of Gaussian.
-3
Produce a version 3 formatted checkpoint file, including all features supported in Gaussian 16. This is
also the format used by Gaussian 09.
-2
Produce a version 2 formatted checkpoint file. This was the version used with Gaussian 03.
-c
Causes the molecular mechanics atom types to appear in the formatted checkpoint file as strings rather
than integers.
-r
Restore data for the general case in an ONIOM checkpoint file (i.e., the low-level on the real system).
This is useful if the checkpoint file is from an ONIOM job which died in the middle of an ONIOM cal-
culation but one wants to put the real system structure and other information in the formatted checkpoint
file, e.g., to read the structure into GaussView in order to modify it.

In addition to creating formatted checkpoint files, formchk can also generate matrix element files via the
following options:
-matrix
Generates a Fortran unformatted matrix element file from the specified checkpoint file. The default
extension for the output file is .dat.
-rawmatrix
Writes a raw binary matrix element file from the specified checkpoint file. The default extension for the
 344 Chapter 6. Utility Programs

output file is .dat.

-i4
Writes the Fortran unformatted matrix element file using 4-byte integers in the output file even if Gaussian
is using 8-byte integers (i.e., on a 64-bit machine). formchk -matrix -i4 is needed if the file is to be read
using the example Fortran and Python code in the gauopen directory because they are compiled with
4-byte integers. If the file is to be read by some other program, whether -i4 is needed depends on the size
of integers in that program.
-files="(list)"
When combined with the -matrix or -rawmatrix option, includes the contents of the specified internal
Gaussian file(s) within the generated matrix element file. For example, the following option:
$ formchk -files="(123,(456,offset=1,integer=27)))" -matrix fox7_dimer.chk fox7_dimer.dat
will cause the contents of internal file 123 (assumed by default to be real values), the 27 integers in
internal file 456 starting after the first (8-byte) word, and any real values following the integers, to be
included within the matrix element file.

6.7 freqchk

The freqchk utility is used to retrieve frequency and thermochemistry data from a checkpoint file, with
optional specification of an alternate temperature, pressure, scale factor, and/or isotope substitutions.
The full syntax of the freqchk command is:
$ freqchk checkpoint-file [options] [answers to prompts]
If the checkpoint file name does not include an extension, .fchk is assumed; both formatted and unformat-
ted checkpoint files are accepted.

6.7.1 Options

The following options are supported:

-o filename
Send output to the specified file. By default, output is displayed to the screen.
-nfd
Skip the diagonalization of the full (3Natoms )2 matrix (as with Freq=NoDiagFull).
-sel
Select normal modes for inclusion. The utility will prompt for required information as usual and then
pause to allow you to enter the desired modes (without prompting). You can specify mode numbers
and/or atom lists as for Freq=ReadNormalModes. See the example below.
-read
Read normal modes from the checkpoint file rather than computing them.
-save
Save normal modes; only works with binary checkpoint files. When combined with -sel, only the selected
modes will be in the checkpoint for a subsequent -read operation.
-np=N
Use N processors to compute the frequency analysis.
 6.7 freqchk 345

6.7.2 Examples

freqchk can prompt for all other information that it requires. The following annotated sessions illustrate
its use in this mode (user input is set in boldface type):

$ freqchk
Checkpoint file? solvent.chk
Write Hyperchem files? n
Temperature (K)? [0=>298.15] 0 Zero must be entered; return doesn’t work
Pressure (Atm)? [0=>1 atm] 0
Scale factor for frequencies during thermochemistry? [0=>1/1.12] 0
Do you want the principal isotope masses? [Y]: Return accepts defaults
Isotopes for each atom are printed
Full mass-weighted force constant matrix:
Low frequencies -- -948.3077 .0008 .0020 .0026
···
Normal Gaussian frequency output follows · · ·
1 2
?A ?A
Frequencies -- 1885.3939 3853.5773
Red. masses -- 1.0920 1.0366
Frc consts -- 2.2871 9.0697
IR Inten -- 17.3416 21.5997
Raman Activ -- 7.8442 67.0384
Depolar -- .7428 .2248
Atom AN X Y Z X Y Z Normal modes
1 8 .06 .00 .04 .04 .00 .02
2 1 -.70 .00 .03 .01 .00 -.71
···
-------------------
- Thermochemistry -
-------------------
Temperature 298.150 Kelvin. Pressure 1.00000 Atm.
Thermochemistry will use frequencies scaled by .8929.
···
Zero-point vibrational energy 53494.5 (Joules/Mol)
12.78550 (Kcal/Mol)
VIBRATIONAL TEMPERATURES: 2422.01 4950.36 5495.38 (KELVIN)
Zero-point and thermal corrections:
Zero-point correction= .020375 (Hartree/Particle)
Thermal corr to Energy= .023210
Thermal corr to Enthalpy= .024154
Thermal corr to Gibbs Free Energy= .045589
E=thermal energy; CV=constant volume molar heat capacity; S=entropy
E CV S
KCAL/MOL CAL/MOL-KELVIN CAL/MOL-KELVIN
TOTAL 14.564 6.001 45.114
ELECTRONIC .000 .000 .000
TRANSLATIONAL .889 2.981 34.609
ROTATIONAL .889 2.981 10.500
VIBRATIONAL 12.787 .039 .005
Partition functions
346 Chapter 6. Utility Programs

Q LOG10(Q) LN(Q)
TOTAL BOT .561443D-01 -1.250695 -2.880127
TOTAL V=0 .132155D+09 8.121085 18.699192
VIB (BOT) .424961D-09 -9.371650 -21.579023
VIB (V=0) .100030D+01 .000129 .000297
ELECTRONIC .100000D+01 .000000 .000000
TRANSLATIONAL .300436D+07 6.477751 14.915574
ROTATIONAL .439749D+02 1.643204 3.783618

$ freqchk solvent.chk Checkpoint filename can be placed on the command line

Write Hyperchem files? n
Temperature (K)? [0=>298.15] 300 Alternate temperature.
Pressure (Atm)? [0=>1 atm] 1.5 Alternate pressure.
Scale factor for freqs during thermochem? [0=>1/1.12] 1 No scaling.
Do you want to use the principal isotope masses? [Y]: n
For each atom, give the integer mass number.
In each case, the default is the principal isotope.
Atom number 1, atomic number 8: [16] Return accepts default.
Atom number 2, atomic number 1: [1] 2 Specify isotope masses as integers.
Frequency output follows · · ·

Frequency output follows, reflecting the values specified above. Note that if scaling is specified, only the
thermochemistry data reflects it; the frequencies themselves are not scaled.
An additional prompt sometimes appears in a freqchk session:
Project out gradient direction? [N]
This prompt appears when the forces are significantly non-zero. A possible reason for the forces being
non-zero is that the frequencies were done at a point along the IRC, so projecting out the gradient direction
may be useful. If the forces are non-zero in other circumstances, the structure is not a stationary point, and its
geometry should be optimized in order to obtain a meaningful vibrational analysis. However, if you want to
look at the frequencies, for example, to see if the starting point for an optimization has the correct curvature,
then the direction of the gradient should not be projected out.
As an alternative to interactive mode, you can specify all freqchk input on the command line, as in this
example, which performs the same operation as the final interactive session above:
$ freqchk solvent.chk N 300 1.5 1 N N
You will be prompted for the isotopes if the second-to-last parameter is N. The final parameter is the
answer to the gradient direction prompt should it appear; if this parameter is omitted and the prompt is relevant,
the utility will prompt you.
Selecting Modes. The following command and input selects modes 1-5 and any others involving nitrogen
atoms, sending the output to the file ala_freq.out:

$ freqchk ala.chk -sel -o ala_freq.out N 0 0 0 N N

1-5 atoms=N
Input ends with a blank line.
$ more ala_freq.out Frequency data is ready for viewing.
···
 6.8 freqmem 347

6.8 freqmem

The freqmem utility takes parameters for a frequency calculation and determines the amount of memory
required to complete all steps in one pass for maximum efficiency. All parameters must be provided on the
command line, using the following syntax:
freqmem natoms nbasis r|u function
The arguments are:
natoms
Number of atoms in the molecule.
nbasis
Number of basis functions for this system under the desired basis set.
r|u
A one-letter code indicating an RHF (closed shell) or UHF (open shell) calculation, as appropriate.
function
A letter indicating the highest angular momentum basis function in the basis set: i.e., d for d functions,
f for f functions, h for h functions, and so on. This parameter may also be a string indicating the types
of basis functions used in the chosen basis set: sp, spd or spdf (as was used in earlier versions of this
utility).

6.8.1 Example

This examples estimates the memory resources required for RHF/STO-3G frequencies on taxol (113
atoms):

$ freqmem 113 361 r p

RHF direct frequencies with sp functions:
One pass requires 44.80 megawords.

The output indicates that the program will require about 360 MB of memory to complete the frequency
calculation in a single pass.
If the amount of memory specified by freqmem is not available, a frequency calculation can still be com-
pleted using multiple passes. Use the %Mem Link 0 command to specify the amount of available memory.
Setting this parameter to one half or one third of the amount of memory recommended by freqmem is often a
good choice.
The number of basis functions used in a Gaussian calculation is printed out early in the output file. It
may also be calculated by setting up an input file for the job in question and including the %KJob=301 Link 0
command, which tells the program to terminate as soon as Link 301 is reached (which is almost immediately).
The number of basis functions used for the molecule with the specified basis set may then be retrieved from the
log file with a command like this one:

$ grep "basis func" name.log

361 basis functions 1083 primitive gaussians
 348 Chapter 6. Utility Programs

6.9 gauopt
The gauopt utility performs an optimization by repeatedly executing Gaussian. In this way, it can optimize
any parameter in the input stream, including general or massaged basis functions. It operates by repeatedly
creating subprocesses running Gaussian. The gauopt utility is typically used to optimize parameters such as
basis functions for which there is no standard optimization method implemented within Gaussian. It is invoked
by its command verb, gauopt, and takes its input from standard input.
Input for gauopt consists of a template file, in which certain fields are replaced with variables whose values
are to be optimized. The template file is used to construct an actual Gaussian input file containing the current
values of the variables for each energy evaluation. The energy is then computed at each step automatically by
running a Gaussian single point calculation. The format for the first line of the template is:
NVar, MaxIt, SaveFlag, Conv, ConvV
using a format 2I3, L2, D9.2. The fields are defined as follows:
NVar
The number of variables.
MaxIt
The maximum number of optimization cycles to perform.
T|F
A logical flag indicating whether the intermediate Gaussian output files are to be saved. These are named
fork.com, fork.log, fork.rwf, and so on. They are deleted by default, but can be saved as an aid in
debugging the template input.
Conv
Convergence on the RMS change in the variables. A fairly tight default is provided if this parameter is
set to 0.0.
ConvV
Convergence on the energy, which defaults to 1 milliHartree when the parameter is set to 0.0.
The next line of the template file has one or more pairs of values using the following syntax:
Value C|V Repeated NVar times (no internal spaces)
where Value is the value for the variable, and the second value is a one-character flag which can be set to C to
constrain the variable (i.e., not optimize it during the current run) or to V if the variable is to be optimized. This
line uses a format of F14.9, A1 for each pair of values.
The remainder of the template file contains a Gaussian input file template. Each field in the input file
where a previously-defined variable should be inserted should contain:
<n x.y>
indicating that the nth variable should be inserted at that point using format Fx.y. If n is preceded by a minus
sign, then -1 times the specified variable will be inserted there.

6.9.1 Example
An example will help make all of these concepts clearer. The following gauopt template file optimizes the
scale factors in the STO-2G expansion of a minimal basis set for water:

3 10 T 0.00 0.00
7.660000000V 2.250000000V 1.240000000V
 6.10 ghelp 349

# RHF/Gen Test

Water RHF/STO-2G basis with optimized scale factors

0,1
O
H,1,r
H,1,r,2,a

r 0.96
a 104.5

1 0
sto 1s 2 <1 12.10>
sto 2sp 2 <2 12.10>
****
2 0
sto 1s 2 <3 12.10>
****
3 0
sto 1s 2 <3 12.10>
****

The scale factors on the two hydrogens are made equal by using the same gauopt variable in more than
one place; of course, this same effect could also have been accomplished by specifying that the same basis was
to be used on every hydrogen atom.

6.10 ghelp

The ghelp utility is a hierarchical help facility for Gaussian. Typing ghelp alone will display general
information and a list of topics for which help is available. The form ghelp topics will display just the list of
topics.
Information about Gaussian keywords and options is available using the format:
ghelp route keyword [option]
Information about Gaussian utilities may be accessed using either the utility name as the primary topic or
via the topic utilities. Information about internal option m in overlay n (IOp(n/m)) may be obtained using the
following command on Unix systems (note the quotation marks):
$ ghelp "ovn iop(m)"

6.11 mm

Standalone molecular mechanics program. This program reads a Gaussian input file from standard input
and writes a new input file with the (possibly optimized) structure to standard output. The desired force field
must be selected via the -Dreiding, -UFF, -Amber or -Param option (see Options for the latter). The type of
job to run is specified with the -Force, -Freq, -Opt, and -Micro command line options; the default is an energy
 350 Chapter 6. Utility Programs

calculation. -Micro optimizes only the atoms that are in the low ONIOM layer (i.e., the real system), in order
to preoptimize the MM portion of the molecule.

6.11.1 Options
-Param N
Use force field N (same as IOp(1/64)=N within Gaussian).
-ReadParam
Read in additional parameters. Internally-stored parameters have priority over read-in parameters.
-ReplaceParam
Read in additional parameters. Read-in parameters take priority over the internally-stored parameters.
-OptCyc N
Specify the maximum number of optimization cycles to N.
-ReadCon
Read connectivity information from the input file (i.e., the input file uses Geom=Connect).
-Test N
Set the debugging flag to N (higher numbers result in more debugging output).
-TRScale num
Use scaling scheme num for rigid translations/rotation: 0=no scaling (the default); 1 says to scale the N
atoms in a rigid block by 1/N; 2 says to scale the N atoms in a rigid block by 1/SQRT(N), and a negative
value scales by |N|/1000.
-External
Read input and write output in the formats used by the External keyword.

6.12 newzmat
The newzmat utility was designed primarily for converting molecule specifications between a variety of
standard formats. It can also perform many related functions, such as extracting molecule specifications from
Gaussian checkpoint files. Its full set of capabilities includes the following:
♢ newzmat can convert molecule specifications between a variety of data file formats. This includes gen-
erating a Z-matrix (and hence input for Gaussian) from the files produced by other programs and also
converting between the file formats of any of these programs. The newzmat keyword can thus be used to
produce Gaussian input from the data files of many popular graphics and mechanics packages, allowing
them to act as graphical input front-ends to Gaussian. The resulting data files have the proper symmetry
constraints for efficient computation (if applicable).
♢ newzmat can also generate Gaussian 16 checkpoint files from other data files, and (more importantly)
generate the data files from checkpoint files. This capability can be used to extract data for display with
a visualization package.
♢ newzmat can retrieve intermediate structures from a checkpoint file from (or during) a geometry opti-
mization, for reuse or display.

Known Difficulties with newzmat

♢ The symmetry averaging process, which guesses the intended symmetry given coordinates which are
only approximately symmetric, does not always achieve the intended symmetry. It will take coordinates
 6.12 newzmat 351

printed in a Gaussian output file to 6 digits and restore symmetry, and it will usually work given coor-
dinates from molecular mechanics provided that the mechanics optimization was converged reasonably
far. In generating coordinates with MacroModel, for example, it is sometimes necessary to do a final full
Newton-Raphson step after the normal minimization.
♢ newzmat computes the nuclear repulsion energy of the initial read-in structure and of the final structure as
a consistency check. If these disagree, a warning is printed. Substantial disagreement indicates a failure
of the program.

6.12.1 Syntax
newzmat has the following general syntax:
newzmat option(s) input-file output-file
where option(s) is one or more options, specifying the desired operations, input-file is the file containing the
structure to be converted (or retrieved), and output-file is the file in which to place the new molecule speci-
fication (or Gaussian input). A slightly variant syntax is used when merging information from two files (see
below).
If the output filename is omitted, it is given the same base name as the input file, along with a conventional
extension denoting its file type. In general, extensions can be omitted from file specifications provided that
extension conventions are followed. The default extensions are listed in the following table:

Extension Description Option Form

.bgf Biograf internal data file bgf
.cac CaChe molecule file cache
.chk Gaussian 09 checkpoint file chk
.com Gaussian input file (Z-matrix mol. spec.) zmat
.com Gaussian input file (Cart. coords. mol. spec.) cart
.con QUIPU system data file con
.dat Model/XModel/MM2 data file model
.dat MacroModel data file (may be formatted or unformatted) mmodel, ummodel
.ent Brookhaven data file (≡PDB) ent
.com Fractional coords. for crystal structures (requires exactly 3 trans. ops.) fract
.inp MOPAC input file mopac
.pdb Protein Data Bank format (≡Brookhaven) pdb
.ppp Some PPP program (output only) ppp
.xyz Unadorned Cartesian coordinates xyz
.zin Ancient version of ZIndo zindo

6.12.2 Options
The options specifying the formats of the input and output molecule specifications are formed from the
string -i or -o (respectively), followed immediately by the appropriate option form string from the preceding
table corresponding to the desired molecule specification format (no spaces intervene). For example, -ipdb
indicates that the input molecule specification is in PDB format and that the extension .pdb should be applied
to the input filename if no extension is specified. Similarly, -oxyz specifies an output format of Cartesian
352 Chapter 6. Utility Programs

coordinates along with a default extension of .xyz for the output filename. The default input and output options
are -izmat and -ozmat. Note that -izmat and -icart are synonyms, and either one of them can read a Gaussian
input file containing any molecule specification format: Z-matrix, Cartesian coordinates, or mixed internal and
Cartesian coordinates.

Selecting An Output Format

In order to communicate with a non-supported visualization system, the first choice of format to try is the
PDB file. This format includes the connectivity information and is widely supported. Note that some software
packages use the .ent extension, rather than .pdb; the -ient and -oent options select the former, while -ipdb and
-opdb select the latter. Another commonly used alternative is the Mopac file format.
The following options further specify the input for newzmat:
-ngeom N
Use geometry from N th structure on the checkpoint file. This functions in the same manner as Geom=(NGeom=N).
-ot list
Use geometries from the listed structures on the checkpoint file. Lists can include multiple structure
numbers (separated by commas) and ranges of structure numbers. For example, -ot 3,7 extracts structures
from steps 3 and 7, and -ot 2-5 extracts all structures ranging from steps 2 through 5.
-step N
Use the structure from step N of the geometry optimization data in a Gaussian 16 checkpoint file (valid
only for the -ichk input option).
This option is not available for optimizations in redundant internal coordinates (the default coordinate
system). Instead, retrieve the structure from the checkpoint file in a subsequent job by using a route
section containing Geom=(Check,Step=N).
-ubohr
Input distances in input file are specified in Bohr (the default is Angstroms).
-urad
Input angles in input stream are specified in radians (the default is degrees).

The following options retrieve changes from the checkpoint file and apply them as the MM charges for
both regular atoms and link atoms. These options specify which kind of charges to retrieve:
-qmul
Mulliken charges.
-qesp
ESP-fit charges.
-qaim
AIM charges.
-qnpa
NPA charges.
-qapt
APT charges.

The following options further specify the output file format:

 6.12 newzmat 353

-mof1
Use macromodel format 1 (only valid with -ommodel).
-mof2
Use macromodel format 2 (this is default if -ommodel is specified).
-optprompt
Prompt for which parameters should be optimized; used when setting up a molecule specification des-
tined for a geometry optimization and -ozmat is specified (or no output option is included). By default,
all parameters not fixed by symmetry are optimized.
-prompt
Prompt for route section and title section lines and for the charge and multiplicity when using -ozmat
(or no output option is specified). Gaussian input files produced by newzmat set up HF/6-31G(d) single
point energy calculations by default.

6.12.3 Examples
The following command reads the molecule specification from the PDB file water.pdb and writes a Gaus-
sian input file, including the equivalent Z-matrix, to the file h2o.com:

$ newzmat -ipdb water h2o -ozmat is the default, so it can be omitted.

Charge and multiplicity [0,1]? A return accepts the default values shown.

newzmat prompts for the charge and multiplicity for the Z-matrix since these items cannot be determined
from the PDB file.
The following command reads the molecule specification from the Gaussian 09 checkpoint file job-11234.chk
and writes the PDB file propell.pdb:
$ newzmat -ichk -opdb job-11234 propell
The following command reads the molecule specification from step 5 of the optimization from the check-
point file newopt.chk and produces the Mopac file step5.inp:
$ newzmat -ichk -omopac -step 5 newopt step5
The following command reads the molecule specification from the Mopac file newsalt.inp and writes a
Gaussian input file including the equivalent Z-matrix to the file newsalt.com, prompting for the route and title
sections and the charge and spin multiplicity for the molecule:

$ newzmat -imopac -prompt newsalt

Percent or Route card? # B3LYP/6-31G(d,p) Opt
Route card? End route section with a blank line.
Titles? Optimization of caffeine at B3LYP/6-31G**
Titles? End title section with a blank line.
Charge and Multiplicity? 0,1

Merging Information From Two Files Using Newzmat

newzmat can create an input file where data from two different files have been combined. This feature is
helpful for setting up ONIOM calcuations in which one wants to apply a custom setup (ONIOM layers, MM
atom types, MM atom charges, etc.) from one file to another structure on a different file. It allows you to
specify the custom setup only once, and then later apply that information to other structures.
354 Chapter 6. Utility Programs

The -t and -s options request and control the creation of the merged input file. A merge command has the
following general form:
$ newzmat -itype [-otype] -tformat -sitemn files
The command requires that you specify the locations of the existing input file (input), the new input file
you are creating (output), and the template file (template). The order of the input, output and template files on
the command line varies depending on whether the input and/or template file(s) are Gaussian checkpoint files:

Is checkpoint file:
input? template? files arguments
n n input output ignore template
n y input output template
y n ignore output input template
y y input output template

In the preceding table, “ignore” is a placeholder.

-t requires a file type argument like -i and -o, and it accepts the same values.
The -s option, which can be specified multiple times, indicates the various information for the new input
file. It accepts the following keywords, each of which is followed by either 1 or 2, which indicates that the item
should be taken from the input or template file (respectively):

XYZn Geometry (coordinates, nuclear charges, etc.).

MMTn MM types.
MMCn MM charges. If copied, also copied to link atoms if there is ONIOM data present.
PDBn PDB information (including secondary structure).
Conn Connectivity.
Onin ONIOM layer and link atom data.
Micn MicOpt (freezing/optimizing atoms and rigid block info).

The default for all items is the input file (i.e., file 1).
Here is an example. We have a Gaussian input file, allsetup.gjf, containing the MM atom type, MM
charges, PDB information, connectivity, ONIOM layers, and so on. We can apply all of these settings to the
structure in the PDB file new.pdb with the following command:
$ newzmat -icart -tpdb -sXYZ2 -sCon2 allsetup.gjf newinput.gjf ignore new.pdb
This command takes only the geometry and connectivity from file 2 – the template file new.pdb – and
everything else (MM atom types, MM charges, PDB information ONIOM data and optimize/freeze atom data)
from file 1, the input file allsetup.gjf. The output file, newinput.gjf, will be the result of this merge.
The other options to newzmat are concerned with generating connectivity information, with the use of
standard geometrical parameters, and with the determination and use of molecular symmetry. A complete con-
nectivity table can be used to generate Z-matrix specifications suitable for inclusion of symmetry constraints.
Such a table is also required for output of the data files for the molecular mechanics programs. If one of the
input formats which includes full connectivity is used (e.g., MacroModel data files), the connectivity that it
provides is used.
However, when Z-matrix or MOPAC format input is provided, only the connectivity information which
6.12 newzmat 355

is implied by the internal coordinate specification is available. Thus if a new Z-matrix which incorporates
the molecular symmetry is to be generated, the remaining connectivity information must be generated. When
Cartesian coordinates are read in, naturally, no connectivity information is provided, so the default is to generate
the table using the internally stored atomic radii. In addition, when used to generate input structures, the
mechanics programs may not generate suitable bond distances and often produce coordinates which are close
to but not exactly symmetric. Options control how each of these cases is handled.

-allbonded
In generating new connectivity information, assume all atoms are bonded.
-bmodel
Use standard model B bond lengths along with internal values in determining bond distances.
-density N
Generate natural orbitals for density number N. This option is only useful if you are generating a CaChe
file. N should be set to 0 for HF, to 2 for MP2, to 6 for CI, and to 7 for QCISD or CCD.
-fudge
Fudge bond distances to make sure they are reasonable, using internal values. This is the default for
model input and is not applicable elsewhere.
-gencon
Generate connectivity information using internal radii.
-getfile
Insist on filename specifications for all arguments, making standard input and output unacceptable.
-lsymm
Use loose cutoffs for determining symmetry. This option implies -symav.
-mdensity M
Subtract generalized density M from that specified with -density to make a difference density, which is
then converted to natural orbitals.
-nofudge
Do not fudge bond distances. This is the default and only choice for all cases except model input.
-nogetfile
Cancels -getfile.
-noround
Turns off rounding of Z-matrix parameters.
-nosymav
Turns off averaging of input coordinates.
-nosymm
Turns off all use of symmetry.
-round
Rounds Z-matrix parameters to 0.01 Åand 1 degree.
-symav
Average input coordinates using approximate symmetry operations to achieve exact symmetry.
-symm
Assign molecular symmetry.
 356 Chapter 6. Utility Programs

-tsymm
Use tight cutoffs for determining symmetry. The option is the default.
-rebuildzmat
Build a new Z-matrix rather than using the read-in one (as would be the default for Z-matrix or MOPAC
input). This option implies -gencon, and the option may be abbreviated as -redoz.

6.13 testrt
testrt is a utility which takes a standard Gaussian route as input and produces the equivalent non-standard
route. The route is usually specified on the command line (enclosed in quotation marks):
$ testrt "# rhf/sto-3g"
If it is not included on the command line, testrt will prompt for the route to be tested.
If the specified route is valid, testrt will print out the non-standard route corresponding to it. If syntax errors
are present, then error messages will be displayed. Thus, testrt can be used to verify the syntactic correctness
of route sections even by users who understanding nothing of non-standard routes.

6.13.1 Example
Here are some example runs of testrt:

$ testrt "# ccsd(modredun)/6-31G* scf=driect"

----------------------------------
# ccsd(modredun)/6-31G* scf=driect
----------------------------------
QPErr — - A syntax error was detected in the input line.
# ccsd(modredundant) ModRedundant is a valid option, but not for CCSD.
’

$ testrt "mp4 nmr" NMR is not available for MP4.

-------
mp4 nmr
-------
NMR only for HF, DFT, and MP2.

$ testrt
Please type in the route specification, terminated with a blank line:
# HF/6-31G(d) Opt=QST2
End of testrt input.
----------------------
# HF/6-31G(d) Opt=QST2
----------------------
1/5=1,18=20,27=202,38=1/1,3;
2/9=110,12=2,17=6,18=5,40=1/2;
···
 6.14 unfchk 357

As the first example indicates, only the first error within the route section is flagged. The second example
illustrates the error message from an invalid combination of keywords. The final example shows the output
from a successful route test.
Note that testrt cannot detect keyword usage errors; it checks only the syntax of the given route section.
Thus, it will not warn you that including the MP2 keyword twice within the route section will have unexpected
results (running an MP4 job).
testrt’s output can be redirected to a file by standard UNIX output redirection:
$ testrt "# rhf/sto-3g" >output-file

6.14 unfchk

This utility is the opposite number to formchk. It converts a formatted checkpoint file to a binary check-
point file, in a format appropriate to the local computer system:

$ unfchk
Formatted Checkpoint file? water
Read formatted file water.fchk
Write checkpoint file water.chk

The utility applies the extension .fch to the specified filename on Windows systems and the extensions
.fchk on other computer systems.
The formatted checkpoint filename can also be given on the command line:

$ unfchk job222.chk
Read formatted file "job222.fchk"
Write checkpoint file "job222.chk"
LenFI= 2580 MDV= 104857600 DoIMCk=T

Note that formatted checkpoint files can be used as a data exchange format between computer platforms.
Use formchk on the originating computer and unfchk on the target computer to create a binary checkpoint file.
unfchk can also convert a matrix element file to a binary checkpoint file (see Options)

6.14.1 Options
In addition to formatted checkpoint files, unfchk can work with matrix element files and create binary
checkpoint files containing their data.
-matrix file1 file2
Reads (fortran unformatted) matrix element file file1.dat and writes checkpoint file file2.chk
-rawmatrix file1 file2
Reads (raw binary) matrix element file file1.dat and writes checkpoint file file2.chk

The following options specify the format of the matrix element file. They may be needed, depending on
how the file was written by formchk, Gaussian, or whatever program created it.
-i4
Use this option when the Fortran unformatted matrix element file uses 4-byte integers.
358 Chapter 6. Utility Programs

-i2
Use this option when the Fortran unformatted matrix element file was written using 2-byte integers, for
the two electron integral labels (and 4-bytes for most other integers).
III
Part Three: Appendix

A Program Development Keywords . . . . 361

B Obsolete Keywords and Deprecated Fea-

tures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

C Gaussian 16 Release Notes . . . . . . . . . 385

D Gaussian 16W Reference . . . . . . . . . . . 393

E Interfacing to Gaussian 16 (v2) . . . . . . 395

F Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

G Gaussian 16 FAQs . . . . . . . . . . . . . . . . . . 415

Bibliography . . . . . . . . . . . . . . . . . . . . . . . 417
 A. Program Development Keywords

This section documents keywords and options useful for developers who are extending and/or interfacing
to Gaussian 16. It also discusses non-standard routes and the determination of the standard orientation.

A.1 Keywords
The keywords and options described here are useful for developing new methods and other debugging
purposes, but are not recommended for production level calculations.

A.1.1 General Job Restart

We discuss here the general use of Restart, designed for debugging. See the Restart section for production
use. This keyword restarts a calculation by reusing the read-write file. The form Restart L1 reuses the read-write
file but generates a new route.
Restarts using the original route can specify the occurrence of a particular link and whether to clean up or
retain overlay and link-volatile files using the following syntax:
#P Restart [Ln[(m)]] [Clean|KeepOverlay|KeepAll]
When all parameters are specified, the job restarts at the mth occurrence of Link n. Clean requests that
all routine and overlay volatile files be removed by Link1, KeepOverlay requests that overlay-volatile files be
retained but not link-volatile ones, and KeepAll retains everything. The default is to KeepAll if the read-write
file is set up for an intra-link restart and Clean otherwise.

A.1.2 IOp Setting Keywords

IOp1=keyword
This keyword controls various details of the operating system interface. The options are standard, but not all
are implemented (or even relevant!) in every version.

FileIODump Dump FileIO tables at the end of each link. FDump is a synonym for this keyword.
 362 Chapter A. Program Development Keywords

TimeStamp Turn on time stamping. TStamp is a synonym for this keyword.

FileIOPrint Turn on additional debug print in FileIO.
Synch Currently a no-op (appears in a few test jobs).
NoDFTJ Turn off use of the pure Coulomb term for non-hybrid DFT (seldom useful in pro-
duction jobs).
AbelianOnly Force the use of only abelian symmetry (seldom useful in production jobs).
NoPackSort Turn off packing addresses into 32-bits during sorts, even if the address space being
sorted is < 231 (seldom useful in production jobs).

IOp2
This option sets the maximum amount of memory which will be dynamically allocated. MDV and Core are
synonyms for IOp2.
IOp33
This sets the standard debug print option as specified.For example, the following sets IOp(33) to 3 in all invo-
cations of overlay 2, and IOp(33) to 1 in all invocations of overlay 7:
IOp33(2=3,7=1)

The Gaussian 16 IOps Reference also documents all internal options (IOps).

A.2 Options
CPHF
The following options are used for debugging:

KeepMicro Keep all EE centers in CPHF, even for Opt=CalcFC or Opt=CalcAll with non-
quadratic microiterations, where atoms that are not used in internal coordinates
need not be included in the CPHF.
NoReuse Do not reuse the electric field CPHF solution in the 2nd (nuclear) CPHF during
frequency calculations. The default is ReUse.
XY Treat real and imaginary perturbations together. The opposite is NoXY, which does
them separately. The default is to treat them separately if nuclear perturbations
are also being done, but to treat them together if there are only electromagnetic
perturbations.
ZVector Use the Z-Vector method [225–227] for post-SCF gradients. Allowed and the de-
fault if Hartree-Fock 2nd derivatives are not also requested. The NoZVector key-
word says to use the full 3 × NAtoms CPHF for post-SCF gradients.

FMM
The following options are available for debugging:

LMax=N Specifies the maximum order multipole. The default is 25.

Levels=N Specifies the number of levels to use in the FMM. The default is 8 for molecules
and is adjusted dynamically for PBC.
A.2 Options 363

Tolerance=N Specifies the accuracy level as 10−N . The default values for N are 11 except for
pass 0 of the SCF where it is 7.
JBoxLen=N Sets the minimum box length (size) to N/1000 Bohrs when doing J. By default, N
is 2.5. The maximum of JBoxLen and KBoxLen is used if J and K are done at the
same time. BoxLen is a synonym for JBoxLen.
KBoxLen=N Sets the minimum box length (size) to N/1000 Bohrs when doing K. By default, N
is 0.75. The maximum of KBoxLen and JBoxLen is used if K and J are done at the
same time.
AllNearField Turn on all near-field in FMM.
NoParallelCPHF Forbid parallel execution in FMM during the CPHF phase. NoParCPHF is a syn-
onym for this option.

Integral
The following options are used for debugging:

CNDO Do calculation in main code using CNDO/2 integrals.

INDO Do calculation in main code using INDO/2 integrals.
ZIndo1 Do calculation in main code using ZIndo/1 integrals.
ZIndoS Do calculation in main code using ZIndo/S integrals.
DPRISM Use the PRISM algorithm [782] for spdf integral derivatives. This is the default.
Rys1E Evaluate one-electron integrals using the Rys method [783–785], instead of the
default method. This is necessary on machines with very limited memory.
Rys2E If writing two-electron integrals, use Rys method (L314) [783–786]. This is slower
than the default method, but may be needed for small memory machines and is
chosen by default if regular (non-Raffenetti) integrals are requested (by the NoRaff
option).
DSRys Use scalar Rys integral derivative code. Can combine with Berny for df only using
Rys.
Berny Use Berny sp integral derivative and second derivative code (L702).
Pass Pass specifies that the integrals be stored in memory via disk, and NoPass disables
this. Synonymous with SCF=[No]Pass, which is the recommended usage.
NoJEngine Forbid use of special Coulomb code.
NoSP Do not use the special sp integral program (L311) when writing integrals to disk.
RevDagSam Reverse choice of diagonal sampling in Prism.
NoSchwartz Do not use Schwartz integral estimates (only use the heuristic set). Schwartz says
to use the Schwartz integral estimates in addition to the heuristic set. The default is
to use both.
RevRepFock Reverse choice of Scat20 vs. replicated Fock matrices.
NoDFTCut Turn off extra DFT cutoffs.
SplitSP Split AO S=P shells into separate S and P shells. NoSplitSP is the default.
SplitSPDF Split AO S=P=D and S=P=D=F shells into S=P, D, and F. NoSplitSPDF is the
default.
 364 Chapter A. Program Development Keywords

SplitDBFSPDF Split density S=P=D and S=P=D=F into S=P, D, and F. NoSplitDBFSPDF is the
default.
NoGather Forbid use of gather/scatter digestion, even when processing small numbers of den-
sity matrices. Splatter is a synonym for this option.
ForceNuc Do nuclear-electron Coulomb with electron-electron.
SepJK Do J and K in HF/hybrid DFT separately for testing.
Seq2E Set up for parallel 2 electron integral evaluation but then do not run in parallel (for
debugging).
SeqXC Set up for parallel 2 electron integral evaluation but then do not run in parallel (for
debugging).
SeqLinda Cause Linda workers to run sequentially. Currently just makes the Linda workers
other than the master run simultaneously but before the master.
BigAtoms Make all atom sizes large in XC quadrature.
BigShells Make all shell sizes large in XC quadrature.
NoSymAtGrid Do not use (Abelian) symmetry to reduce grid points on symmetry-unique atoms.
LinMIO Convert to linear storage in FoFCou for testing.
RevDistanceMatrix Reverse choice of whether to precompute distance matrix during numerical quadra-
ture. The default is to precompute for molecules but not for PBC.
NoDynParallel Turn off dynamic work allocation.

Sparse
The following options are used for debugging:

Loose Sets the cutoff to 5 * 10−5 .

Medium Sets the cutoff to 5 * 10−7 . This is the default for semi-empirical methods.
Tight Sets the cutoff to 1 * 10−10 . This is the default for DFT methods.
N Sets the cutoff to 1 * 10−N .

A.2.1 Changing Link Invocation and Ordering

ExtraLinks
This requests that additional links be executed. They are added to all instances of their overlay after the regular
links. For example, ExtraLinks=L9997 will cause each instance of overlay 99 to include links 9999 (by default)
and 9997, in that order.
ExtraOverlays
This command requests that extra overlay cards be read in non-standard route format and inserted into the
standard route immediately before the final (overlay 99) card.
Skip
Skip initial overlay cards in the route. Skip=OvNNN skip until first occurrence of overlay NNN. Skip=M skip
first M cards.
Use=Lnnn
This specifies alternate routes through the program. The following options are available:
 A.3 The Standard Orientation 365

L123 Use L123 instead of L115 for IRC. This is the default for IRC, except for IRCMax
jobs.
L402 Use old link 402 code for semi-empirical.
L503 Use link 503 for SCF.
L506 Use link 506 for ROHF.

A.3 The Standard Orientation

Before a calculation is performed, a molecule can be reoriented to a different coordinate system, called the
standard orientation, with the use of molecular symmetry. In geometry optimizations, reorientation occurs at
every step; the program then checks if the standard orientation of a molecule has flipped by 180 degrees during
an optimization and avoids the flip. This avoids jumps when animating optimizations, IRCs, etc. in GaussView
and improves SCF convergence.
This section describes the goals, factors to consider, and various rules for positioning axes for the standard
orientation of molecules.

A.3.1 Selection Goals

The goals for selecting conventions for standard orientation are:
♢ To simplify the 3×3 transformation matrices by reorienting the molecule.
♢ Two Z-matrices differing in values of internal coordinates but identical in integer quantities (such as
occurs on subsequent points of a geometry optimization) should produce the same standard orientation.
♢ Two different Z-matrices for the same molecule should produce the same coordinates, except for a possi-
ble renumbering of atoms.
♢ Maximizing the number of molecular orbital coefficients which are zero by symmetry.

A.3.2 General Considerations

The factors that should be considered for standard orientation are:
♢ A right-handed coordinate system is used throughout the calculation.
♢ The molecule is translated so that its center of charge is at the origin.
♢ Atoms are not reordered relative to their order upon input.
♢ The Cartesian axes are considered to increase in priority in the order X < Y < Z.

A.3.3 Rules for Positioning an Axis

Criteria for rotating and aligning an axis are listed below. If rotation is required to meet one of these
criteria, it should be a 180 degree rotation about the X, Y, or Z axis, defined as follows:
X Rotate about X
Y Rotate about Y
Z Rotate about Z
An axis of rotation or a principal axis of charge can be aligned with a Cartesian axis in one of two ways
– either parallel or antiparallel, depending on the successive application of the following tests until a definite
result is achieved:
♢ The sum of the coordinates of the atoms of the highest atomic number on the axis must be positive.
 366 Chapter A. Program Development Keywords

♢ The third moment of charge must be positive.

♢ The sum of the projections of the atomic coordinates onto the reference axis must be positive.
♢ The first atom with a non-zero projection on the reference axis must have a positive projection on that
axis.

A.3.4 Rules for Positioning Principal Axes of Charge

In the absence of any other rules, the principal axis corresponding to the largest principal moment of
charge must be aligned with the highest priority Cartesian axis available. Individual point groups have specific
considerations:

Cs The molecular plane must be made coincident with the XY plane. Note that al-
though this convention conflicts with Mulliken’s suggestion, it is consistent with
the character tables of Cotton and Herzberg. The molecule is then rotated about the
Z axis according to the rules given below for Cn molecules.
C2v The molecular plane is placed in the YZ plane, following Mulliken’s recommen-
dation for planar C2v molecules. The following tests are successively applied for
non-planar molecules: (1) The mirror plane with the most atoms is put in the YZ
plane; (2) The mirror plane with the most non-hydrogen atoms is put in the YZ
plane; (3) The mirror plane with the lowest numbered atom is made coincident with
YZ. Finally, the axes of charge rules are applied (as described above).
Planar, D2h Following Mulliken’s recommendation, the molecular plane is placed in the YZ
plane. The molecule is rotated about the X axis so that the Z axis can pass through
either the greater number of atoms, or, if this is not decisive, the greater number of
bonds.
Cn Follow the rules for general symmetric top molecules.
Ci Translate but do not reorient.
C1 Translate but do not reorient.

A.3.5 Special Rules for Symmetric Top Molecules

Symmetric top molecules are distinguished by having two of three moments of inertia equal. The third
moment can thus be uniquely identified as the reference axis and the point group is analyzed by considering
circular sets of atoms.
The following rules are applied for symmetric top molecules:
♢ The unique axis is aligned with the Z axis.
♢ A circular-set of atoms is composed of atoms lying in a plane which have the same atomic number, and
are equidistant from a reference axis perpendicular to the plane. Atoms on the reference axis are not
included in any circular-set. A circular-set of atoms is generated by a proper rotation axis.
♢ The key atom in a symmetric top molecule is the atom with the lowest number in the key circular-set.
The following tests are carried out successively to find the key circular-set:
• Which set is nearest the XY plane?
• Which set has a positive projection on the Z axis?
• Which set is nearest the Z axis?
 A.4 Non-Standard Routes 367

• Which set is comprised of atoms with the lowest atomic number?

♢ The orientation is then chosen for the specific point group:
• Cn , Cnh , Sn : The molecule is rotated about the Z axis to maximize the number of pairs of heavy
atoms parallel to the Y axis. If no such arrangement is satisfactory, then the key atom is placed in
the YZ plane to give it a positive Y coordinate.
• Dn , Dnh : One of the C2 axes is made coincident with the Y Cartesian axis. The tests described
below are used to decide which C2 axis is so positioned.
• Dnd , Cnv : One of the vertical planes is made coincident with the YZ Cartesian plane. The tests
below are used to decide which plane is so positioned.
♢ The following are tests for selecting among axes for the Dn , Dnh , Dnd , and Cnv molecules:
• Maximize the projection of the key atom on the Y axis.
• If two orientations give the maximum projection on the Y axis, select one with the maximum
projection on the X axis.
• For molecules contained in the XY plane, the standard axis orientation rules (see above) are applied
to the X axis to complete the orientation specification.

A.3.6 Special Rules for Spherical Top Molecules

Spherical top molecules are distinguished by having their equal moments of inertia and can be character-
ized by identifying spherical sets of atoms.
A spherical-set of atoms is composed of atoms which are equidistant from the origin and have the same
atomic number. Spherical-sets should be ordered in terms of increasing distance from the origin and of increas-
ing atomic number at any one distance. The key atom is the lowest numbered atom in the first spherical-set.
Although not generally the case, it is possible, with appropriate geometric constraints, to have D2d , D2h , or
D2 molecules that are symmetric tops. Such molecules have three perpendicular two-fold axes that are aligned
with the X, Y, and Z axes in accordance with the rules given above.

A.4 Non-Standard Routes

If a combination of options or links is required which is drastically different than a standard route, then
a complete sequence of overlays and links with associated options can be read in. The job-type input section
begins with the line:
# NonStd
This is followed by one line for each desired overlay, in execution order, giving the overlay number, a
slash, the desired options, another slash, the list of links to be executed, and finally a semicolon:
Ov/Opt=val,Opt=val,· · · /Link,Link,· · · ;
For example:
7/5=3,7=4/2,3,16;
specifies a run through the links 702, 703, and 716 (in this order), with option 5 set equal to 3 and option 7
equal to 4 in each of the links. If all options have their default value, the line would be
7//2,3,16;
A further feature of the route specification is the jump number. This is given in parentheses at the end
of the link list, just before the semicolon. It indicates which overlay line is executed after completion of the
 368 Chapter A. Program Development Keywords

current overlay. If it is omitted, the default value is +0, indicating that the program will proceed to the next line
in the list (skipping no lines). If the jump number is set to -4, on the other hand, as in
7//2,3,16(-4);
then execution will continue with the overlay specified four route lines back (not counting the current line).
This feature permits loops to be built into the route and is useful for optimization runs. An argument to
the program chaining routine can override the jump. This is used during geometry optimizations to loop over a
sequence of overlay lines until the optimization has been completed, at which point the line following the end
of the loop is executed.
Note that non-standard routes are not generally created from scratch but rather are built by printing out and
modifying the sequence produced by the standard route most similar to that desired. This can be accomplished
most easily with the testrt utility.
A Simple Route Example. The standard route:
# RHF/STO-3G
causes the following non-standard route to be generated:

1 1/38=1/1;
2 2/12=2,17=6,18=5,40=1/2;
3 3/6=3,11=1,16=1,25=1,30=1,116=1/1,2,3;
4 4//1;
5 5/5=2,38=5/2;
6 6/7=2,8=2,9=2,10=2,28=1/1;
7 99/5=1,9=1/99;

The resulting sequence of programs is illustrated in Figure A.1.

Figure A.1: A Simple Route Sequence

 A.4 Non-Standard Routes 369

The basic sequence of program execution is identical to that found in any ab initio program, except that
Link 1 (reading and interpreting the route section) precedes the actual calculation, and that Link 9999 (writing
to the checkpoint file) follows it. Similarly, an MP4 single point has integral transformation (links 801 and 804)
and the MP calculation (link 913) inserted before the population analysis (Link 601) and Link 9999. Link 9999
automatically terminates the job step when it completes.
A Route Involving Loops. The standard route:
# RHF/STO-3G Opt produces the following on-standard route:
1 1/18=20,19=15,38=1/1,3;
2 2/9=110,12=2,17=6,18=5,40=1/2
3 3/6=3,11=1,16=1,25=1,30=1,71=1,116=1/1,2,3;
4 4//1;
5 5/5=2,38=5/2;
6 6/7=2,8=2,9=2,10=2,28=1/1;
7 7//1,2,3,16;
8 1/18=20,19=15/3(2);
9 2/9=110/2;
10 99//99;
11 2/9=110/2;
12 3/6=3,11=1,16=1,25=1,30=1,71=1,116=1/1,2,3;
13 4/5=5,16=3/1;
14 5/5=2,38=5/2;
15 7//1,2,3,16;
16 1/18=20,19=15/3(-5);
17 2/9=110/2;
18 6/7=2,8=2,9=2,10=2,19=2,28=1/1;
19 99/9=1/99;

The resulting sequence of program execution is illustrated in Figure A.2.

Several considerations complicate this route:
♢ The first point of the optimization must be handled separately from later steps, since several actions must
be performed only once. These include reading the initial molecule specification and generating the
initial orbitals.
♢ There must be a loop over geometries, with the optimization program (in this case the Berny optimizer,
Link 103) deciding whether another geometry was required or the structure has been optimized.
♢ If a converged geometry is supplied, the program should calculate the gradients once, recognize that the
structure is optimized, and quit.
♢ Population analysis and orbital printing are done by default only at the first and last points, not at the
relatively uninteresting intermediate geometries.
The first point has been dealt with by having two basic sequences of integrals, guess, SCF, and integral
derivatives in the route. The first sequence includes Link 101 (to read the initial geometry), Link 103 (which
does its own initialization), and has options set to tell Link 401 to generate an initial guess. The second sequence
uses geometries produced in Link 103 in the course of the optimization, and has options set to tell Link 401 to
retrieve the wavefunction from the previous geometry as the initial guess for the next.
The forward jump on the eighth line has the effect that if Link 103 exits normally (without taking any spe-
370 Chapter A. Program Development Keywords

Figure A.2: A Route Involving Loops

cial action), the following lines (invoking Links 202 and 9999) are skipped. Normally, in this second invocation
of Link 103, the initial gradient will be examined and a new structure chosen. The next link to be executed will
be Link 202, which processes the new geometry, followed by the rest of the second energy+gradient sequence,
which constitutes the main optimization loop. If the second invocation of Link 103 finds that the geometry is
converged, it exits with a flag which suppresses the jump, causing Links 202, 601 and 9999 to be invoked by
the following lines and the job to complete.

Lines 11-16 form the main optimization loop. This evaluates the integrals, wavefunction, and gradient for
 A.5 RWF Numbers 371

the second and subsequent points in the optimization. It concludes with Link 103. If the geometry is still not
converged, Link 103 chooses a new geometry and exits normally, causing the backward jump on line 16 to be
executed, and the next line processed to be line 11, beginning a new cycle. If Link 103 finds that the geometry
has converged, it exits and suppresses the jump, causing the concluding lines (17-19) to be processed.
The final instance of Link 601 prints the final multipole moments as well as the orbitals and population
analysis if so requested. Finally, Link 9999 generates the archive entry and terminates the job step.
MP and CI optimizations have the transformation and correlation overlays (8 and 9) and the post-SCF
gradient overlays (11 and 10, in that order) inserted before overlay 7. The same two-phase route structure is
used for numerical differentiation to produce frequencies or polarizabilities.
The route for Opt=Restart is basically just the main loop from the original optimization, with the special
lines for the first step omitted. The second invocation of Link 103 is kept and does the actual restarting.

A.5 RWF Numbers

The following is a list of read-write files. Those that are permanently on the checkpoint file are marked
with the letter P, and those that are temporarily on the checkpoint file are marked with the letter T. T files
are saved for use in restarting an optimization or numerical frequency run, but are deleted when the job step
completes successfully.

Type RWF Description

P 501 Gen array.
P 502 /LABEL/–Title and atomic orbital labels.
503 Connectivity information (MxBond,0),NBond(NAtoms),IBond(MxBond,NAtoms),RBond(MxBond,
NAtoms), where arrays are rounded to a multiple of IntPWP.
504 Dipole derivative matrices (NTT,3,NAt3).
P 505 Array of copies of /Gen/ from potential surface scan.
P 506 Saved basis set information before massage, uncontraction, etc.
P 507 ZMAT/ and /ZSUBST/.
P 508 /IBF/ Integral Bugger Format.
509 Incomplete integral buffer.
T 510 /FPINFO/ Fletcher-Powell optimization program data.
P 511 /GRDNT/ energy, First and second derivatives over variables, NVAR.
P 512 Pseudo-potential information.
P 513 /DIBF/ integral derivative buffer format.
514 Overlap matrix, optionally followed by absolute overlap and absolute overlap over primitives.
515 Core-Hamiltonian. There are four matrices here: H(α ), the α core Hamiltonian; H(β ), the β core
Hamiltonian; G’(α ), the α G’ contribution to Fock matrix; G’(β ), the β G’ contribution to Fock
matrix. H(α ) and H(β ) differ only if Fermi contact integrals have been added. The G’ matrices are
for perturbations which are really quadratic in the density (and hence have a factor of 1/2 in their
contribution to the energy as compared to the true one-electron terms) but which are computed
externally to the SCF.
372 Chapter A. Program Development Keywords

516 Kinetic energy and modifications to the α and β core Hamiltonian. These include ECP terms,
Douglas-Kroll-Hess corrections, multipole perturbations and Fermi contact perturbations. The
latter are used for calculations in which the nuclear and electronic Coulomb terms are computed
together, such as the Harris functional and PBC calculations. For semi-empirical, holds the core
Hamiltonian without nuclear attraction terms for use in the initial guess.
517 Fermi contact integrals.
518 Multipole integrals, in the order X,Y,Z,XX,YY,ZZ,XY,XZ,YZ,XXX,YYY,ZZZ,XYY,XXY,XXZ,
XZZ,YZZ,YYZ,XYZ,XXXX,YYYY,ZZZZ, XXXY,XXXZ,YYYX,YYYZ,ZZZX,ZZZY,XXYY,
XXZZ,YYZZ,XXYZ,YYXZ,ZZXY.
T 519 Common /OptEn/–optimization control for link 109.
T 520 Electronic state: count and packed string (1+9 integers).
P 521 Electronic state: count and packed string (1+9 integers).
P 522 Eigenvalues, alpha and if necessary, beta.
523 Symmetry assignments.
P 524 MO coefficients, real alpha.
P 525 (no longer used)
P 526 MO coefficients, real beta.
P 527 (no longer used)
T 528 SCF density matrix, real alpha.
T 529 (no longer used)
T 530 SCF density matrix, real beta.
T 531 (no longer used)
T 532 SCF density matrix, real total.
T 533 (no longer used)
T 534 SCF density matrix, real spin.
535 (no longer used)
536 Fock matrix, real alpha.
537 Fock matrix, imaginary alpha.
538 Fock matrix, real beta.
539 Fock matrix, imaginary beta.
540 Molecular alpha-beta overlap (U), real.
541 Molecular alpha-beta overlap (U), imaginary.
T 542 Pseudo-potential information.
T 543 Pseudo-potential information.
T 544 Pseudo-potential information.
P 545 /ORB/ – window information.
546 Bucket entry points.
547 Eigenvalues (double precision with window: always alpha and beta, even in RHF case).
P 548 MO coefficients (double precision with window, alpha and if necessary beta). Complex if neces-
sary.
549 Molecular orbital alpha-beta overlap, double precision with window.
A.5 RWF Numbers 373

T 550 Potential surface scan common block.

T 551 Symmetry operaiton info (permutations, transformation matrices, etc.)
P 552 Character strings containing the stoichiometric formula and framework group designation.
T 553 Temporary storage of common/gen/ during FP optimizations.
T 554 Alternate starting MO coefficients, from L918 to L503, real alpha. Also MO coefficients in S-1/2
basis for L509 and rotation angles from L914 to L508.
555 Alternate starting MO coefficients, from L918 to L503, imaginary alpha.
T 556 Alternate starting MO coefficients, from L918 to L503, real beta. Also MO coefficients in S-1/2
basis for L509 and rotation angles from L914 to L508.
557 Alternate starting MO coefficients, from L918 to L503, imaginary beta.
558 Saved HF 2nd derivative information for G1, G2, etc.
559 Common /MAP/.
560 Core-Hamiltonian (a. o. basis) with 2 j – k part of deleted orbitals added in. (i.e. frozen core).
P 561 External point charges or SCIPCM informations.
P 562 Symmetry operations and character table in full point group.
T 563 Integer symmetry assignments (α ).
T 564 Integer symmetry assignments (β ).
T 565 Lists of symmetry equivqlent shells and basis functions.
T 566 Unused in G16.
T 567 GVB pair information (currently dimensioned for 100 paired orbitals).
P 568 Saved hamiltonian information from L504 and L506.
P 569 Saved read-in window.
P 570 Saved amplitudes (IAS1,IAS2,IAD1,IAD2,IAD3; only IAS1 and IAD2 for closed-shell).
571 Energy weighted density matrix.
572 Dipole-velocity integrals <Phi|Del|Phi’>, X, Y, and Z, followed by R × Del integrals (R × X, R
× Y, R × Z).
573 More SCIPCM information.
T 574 /MSINFO/ Murtaugh-Sargent program data.
T 575 /OPTGRD/ Gradient optimization program data for L103, L115, and L509.
T 576 /TESTS/ Control constants in L105.
T 577 Symmetry adapted basis function data.
T 578 A logical vector indicating which MO’s are occupied.
T 579 NEQATM (NATOMS*NOP2) for symmetry.
T 580 NEQBAS (NBASIS*NOP2+NBas6D*NOp2) for symmetry.
T 581 NSABF (NBASIS*NOP2) for symmetry. Followed by matching integer character table, always
(8,8).
T 582 MAPROT (3*NBASIS) for symmetry.
T 583 MAPPER (NATOMS) for symmetry.
P 584 FXYZ (3*NATOMS) cartesian forces. During PSCF gradient runs, there will be two arrays here:
first the PSCF gradient, then the HF only component (needed for PSCF with HF 2nd deriv).
P 585 FFXYZ (NAT3TT) cartesian force constants (lower triangle).
374 Chapter A. Program Development Keywords

T 586 Info for L106, L110, and L111.

T 587 L107 (LST) data.
588 Sx over cartesians in the ao basis.
589 Hx over cartesians in the ao basis.
590 F(x) over cartesians in the ao basis (all α , followed by all β for UHF) (without CPHF terms).
591 U1(A,I) – MO coefficient derivatives with respect to electric field and nuclear coordinates.
592 Electric field and nuclear P1 (AO basis).
593 Electric field and nuclear W1 (AO basis).
594 Electric field and nuclear S1 (MO basis).
595 Magnetic field U1(A,I) – Del(X,Y,Z) then R × (X,Y,Z), 6 α followed by 6 β .
596 Full MO Fock derivatives in the MO basis, including CPHF terms.
P 597 Configuration changes for Guess=Alter.
598 User Name.
599 Density basis set info: NDBFn, NVar, U0, DenBfn(4,NDBfn), ITypDB(NDBfn), Var(NVar),
IJAnDB(NDBfn), IVar(4,NDBfn).
600 Saved data for intra-link restart.
P 601 Saved structures, and possibly forces and force constants along reaction path. All structures, then
all forces, then all force constants.
602 Post-SCF two-particle density matrix.
P 603 Density Matrices at various levels of theory.
T 604 common /drt1/ from drt program · · · misc integer ci stuff, followed by variable dimension drt
arrays.
P 605 Atomic charges from Mulliken Populations, ESP fits, etc. Bitmap followed by 0 or more NAtoms
arrays. Bits 0/1/2/3/4 Mulliken/ESP-fit/Bader/NPA/APT.
606 SCF orbital symmetries in Abelian point group. Alpha and, if necessary, beta, full set followed by
windowed set.
607 Window’d orbital symmetries like rw 606 (always alpha and beta).
608 IBF for sorted integrals (normally on SAO unit).
609 Bit map for sorted integrals (normally on SAO unit).
610 Sorted AO integrals (normally on SAO unit).
611 NTT maps for sorted integrals (normally on SAO unit).
612 Some 1E generators for direct CI matrix element generation.
613 Some more 1E generators for direct CI matrix element generation.
614 Configuration information for CAS-MP2.
615 - Used for CAS-MP2.
616
617 Spin-orbit integrals.
P 618 Nuclear coordinate third derivatives.
P 619 Electric field derivatives: 1 WP word bit map, dipole, dipole derivative, polarizability, dipole 2nd
derivatives, polarizability derivatives, hyperpolarizability.
620 Magnetic field derivatives for GIAOs.
A.5 RWF Numbers 375

621 Susceptiblity and chemical shift tensors.

622 Partial overlap derivatives (<Mu|dNu/da>, NBasis*NBasis*NAt3).
P 623 Born-Oppenheimer wavefunction derivatives (<Phi|d2Phi/dadb> for electronic Phi and a,b nu-
clear, NAt3TT).
624 Unused in G16.
625 Expansion vectors and AY products from CPHF, in the order Y α , AY α , Y β , AY β .
626 MCSCF MO 1PDM (NTT).
627 MCSCF MO Lagrangian (NTT).
628 MCSCF MO 2PDM (NTT,NTT) or NVTTTT.
629 AO 2PDM (shell order).
T 630 MCSCF information.
631 Post-SCF Lagrangian (TA, then TB if UHF).
632 O*V*3*NAtoms, followed by O*V*NVar d2E/d(V,O)d(XYZ,Atom).
P 633 Excited-state CI densities.
T 634 SCF Restart information (alpha, then possibly beta MOs).
P 635 CIS and CASSCF CI coefficients and restart information.
636 NBO analysis information.
637 Natural orbitals generated by link 601.
640 MCSCF data or CIS AO Tx’s for 2nd derivatives.
641 MCSCF data for 2nd derivatives.
642 MCSCF data for 2nd derivatives.
643 MCSCF data for 2nd derivatives.
644 MCSCF data for 2nd derivatives.
645 MCSCF data for 2nd derivatives.
646 MCSCF data for 2nd derivatives.
647 MCSCF data for 2nd derivatives.
648 MCSCF data for 2nd derivatives.
649 Eigenvalue derivatives (non-canonical form even if done canonically).
650 2PDM derivatives, (LenTQ,NDeriv,ShellQuartet) order.
651 Full U’s, canonical or non-canonical as requested.
652 Generalized density derivatives for the current method (NTT,NDeriv,IOpCl+1).
653 Lagrangian derivatives for the current method (NTT,NDeriv,IOpCl+1).
654 Gx(Gamma).
655 G(Gamma).
656 Non-symmetric S1 and S2 parts of Lagrangian for MP2 or CIS second derivatives.
657 t*Ix and t*Ix/D matrices from L811 for L1112.
658 L(x) from L1111.
659 MO correlated W for correlated frequencies.
660 2nd order CPHF results: Pia,xy, Sxy, Fxy (complete) all in MO basis, PSF α then PSF β if UHF.
661 Computed electric field from L602.
662 Points for electrostatic evaluation.
376 Chapter A. Program Development Keywords

T 663 Saved information for L117 and L124.

664 Spin projection data.
P 665 Redundant coordinate information.
666 (no longer used)
667 CIS AO Fock matrix.
668 CIS Gx(T) matrices.
669 Saved /ZMat/ and /ZSubst/ during redundant optimzations.
P 670 New format basis set data (compressed /B/).
P 671 New optimization (L103/L104) data.
P 672 Unused in G16.
673 Global optimization data.
674 ONIOM internal data.
675 Saved files for LS during ONIOM.
676 Saved files for MS during ONIOM.
677 Saved files for LM during ONIOM.
678 Saved files for HS during ONIOM.
679 Saved files for MM during ONIOM.
680 Saved files for LL during ONIOM.
681 Saved files for HM during ONIOM.
682 Saved files for ML during ONIOM.
683 Saved files for HL during ONIOM.
684 SABF information for DBFS: equivalent to files 577 and 581 for AOs.
685 Cholesky U, or transformation to surviving basis functions.
686 Cholesky U-1.
687 Molecular mechanics parameters.
688 Density in orthogonal basis (α spin) for ADMP or sparse SCF.
691 Saved initial files during ONIOM (gridpoint 17, hence 674+17=691).
694 Permutation applied to MOs for post-SCF symmetry.
695 Magnetic properties.
696 Saved magnetic field density derivatives.
698 Saved initial structure during geometry optimization, in standard orientation, also used for con-
straints with the force constants following the structure.
699 Density in orthogonal basis (β spin) for ADMP or sparse SCF.
700 Saved /Mol/ for ONIOM.
701 Saved Trajectory/IRC/Optimization history.
702 Fit density for Coulomb.
703 Fit density for Coulomb.
704 Saved XC contribution to electric field F(xa) for polar derivatives.
P 710 Basic PCM information.
P 711 Other PCM data.
P 712 Non equilibrium data for PCM.
A.5 RWF Numbers 377

713 Saved information for RFO with ONIOM microiterations.

714 Saved model system information for ONIOM microiterations.
715 Saved rigid fragment information for ONIOM microiterations.
T 716 Saved copy of basis set data for counterpoise.
T 717 Saved copy of ECP data for counterpoise.
T 718 Saved copy of fitting basis for counterpoise.
719 Saved DiNa information.
P 720 Saved DiNa information.
721 Frequency-dependent properties.
722 Derivatives of frequency-dependent properties.
723 Density fitting matrices (metrics).
724 Density fitting basis (same format as /B/).
725 DBF symmetry information (NEqDBF(NDBF,NOp2),NEqDB6(NDBF6D,NOp2)).
726 DBF shell symmetry information (NEqDBS(NDBShl,NOpAll)).
727 F(x)(P-Pfit) for density fitting second derivatives.
728 PBC cell replication information.
729 Alternate new guess during optimizations.
730 Counterpoise input specification.
731 Counterpoise intermediate data.
732 Basis set for finite nuclei.
733 PBC Cell scalars and integer cell indices.
734 State-specific input parameters for SAC-CI.
735 Excitation lables of SAC and SAC-CI.
736 Eigenvalues and eigenvectors of SAC and SAC-CI.
737 H matrices and their indices of non-zero elements used for SAC/SAC-CI.
738 Saved atomic parameters for DFTB/EHTSC.
739 Temporary storage for imaginary core Hamiltonian perturbations.
740 Orbital information for SAC/SAC-CI gradients and PES by GSUM.
741 MOD Orbital information for SAC gradients.
742 Saved quadrature grid.
743 Alpha Fock matrices in orthonormal basis for ADMP, also alpha HF Fock matrix for non-HF
post-SCF.
744 Beta Fock matrices in orthonormal basis for ADMP, also beta HF Fock matrix for non-HF post-
SCF.
745 K-integration mesh information.
746 Eigenvalues and orbitals at all k-points.
747 Information for external low-level calculations for ONIOM.
748 TS vector information for ONIOM TS optimizations.
749 Conical intersection information for ONIOM.
750 Not used in G16.
751 Temporary storage for SO ECP integrals.
378 Chapter A. Program Development Keywords

752 Pseudo-canonical MO Fock matrix for ROMP and ROCC.

753 Data for FD polar derivatives.
754 Saved PCM charge derivatives.
755 PCM inverse matrices.
756 Charge information for ONIOM.
757 MO:MO embedding charge data for L924.
758 Derivatives of embedding charges, when computed explicitly.
759 Basis set info for density embedding.
P 760 Full set of pseudocanonical orbitals for RO.
761 Charges from external PCM iterations (both L117 and L124).
762 Saved weights for non-symmetric Mulliken analysis.
763 File for FC/HT integrals.
764 File for FC/HT integrals.
P 765 Saved normal modes.
766 Saved QuadMac vectors (temporary).
767 CIS coefficients reordered by symmetry.
768 Semi-empirical parameters.
769 Saved MOs during numerical differentiation.
P 770 Saved ground-to-excited state energies and transition moments.
771 EOM iteration information.
772 Symmetry operations and character table in Abelian point group.
989 Multi-step job information (1000 reals and 2000 integers).
990 KJob info in some implementations.
991 Holds file names, ID’s and save flags.
992 Used for link substitution information in some implementations.
993 COMMON /INFO/
994 COMMON /PHYCON/
995 COMMON /MUNIT/
996 COMMON /IOP/
P 997 COMMON /MOL/
P 998 COMMON /ILSW/
999 Overlay data.
 B. Obsolete Keywords and Deprecated Features

B.1 Obsolete
The following table lists obsolete keywords used by previous versions of Gaussian.

Obsolete Keyword Replacement Keyword & Option

Alter Guess=Alter
BD-T BD(T)
BeckeHalfandHalf BHandH
Camp-King SCF=Camp-King
CCSD-T CCSD(T)
CubeDensity cubegen utility
GridDensity cubegen utility
Cube cubegen utility
DIIS SCF=Fermi
Direct SCF=Direct (the default)
Formchk formchk utility
Guess=Restart SCF=Restart
MP2=Stingy and VeryStingy none (options are a no-op)
NoDIIS SCF=NoDIIS
NoExtrap SCF=NoExtrap
NoRaff Int=NoRaff
OldConstants Constants=1979
Opt=AddRedundant Opt=ModRedundant
OptCyc=n Opt(MaxCyc=n)
PlotDensity cubegen utility
Prop=Grid cubegen utility
 380 Chapter B. Obsolete Keywords and Deprecated Features

QCID CCD
QCISD-T QCISD(T)
QCSCF SCF=QC
Raff Int=NoRaff
Save none (Save is a no-op)
SCFCon=n SCF(Conver=n)
SCFCyc=n SCF(MaxCyc=n)
SCFDM SCF=QC
SCFQC SCF=QC
SCRF=Checkpoint Field=EChk
VShift[=n] SCF(VShift[=n])
%NProcLinda %LindaWorkers
-L- -W-
%NProc %CPU
-N- -C-
chkmove utility formchk and unfchk

B.2 Deprecated
NoFMM
This keyword prevents the FMM facility from being used even when it would improve performance. It
was required in some circumstances when running in parallel on a cluster or LAN with Linda in Gaussian
03. The associated problems have been fixed, and it is no longer needed.
CCD+STCCD
Specifies a coupled cluster calculation using double substitutions and evaluation of the contribution of
single and triple excitations through fourth order using the CCD wavefunction. It is superseded by
CCSD(T).
CBS-Q, CBS-Lq
Request the CBS-Q [180] and CBS-q [178] methods (i.e., Lq for “little q”). These are superceded by
CBS-QB3.
CBS-QB3O
Uses the original parametrization [110] of CBS-QB3. It is obsolete and is included for backward com-
patibility only.
CBS-4O
Requests the original parametrization [180] of CBS-4. It is obsolete and is included for backward com-
patibility only.
Geom=Coord
Indicates that the geometry specification is in Cartesian coordinates. Cartesian coordinates can be in-
cluded in molecule specifications without any special options being necessary.
Geom=OldRedundant
Use the Gaussian 94 redundant internal coordinate generator.
Geom=ModLargeRedundant
B.2 Deprecated 381

Uses the minimal setup for Opt=Big. It may not be used for periodic boundary calculations.
Int=Raff
Applies only to SCF=Conventional. Raff requests that the Raffenetti format [787] for the two-electron
integrals be used. NoRaff demands that the regular integral format be used. It also suppresses the use of
Raffenetti integrals during direct CPHF. This affects conventional SCF and both conventional and direct
frequency calculations.
Int=BWeights
Use the weighting scheme of Becke for numerical integration.
ReUse
Use an existing integral file. Both the integral file and checkpoint file must have been preserved from a
previous calculation. Only allowed for single point calculations and Polar=Restart.
WriteD2E
Forces the integral derivative file to be written in HF frequency calculations. Useful only in debugging
new derivative code.
LST, LSTCyc
Requests that an initial guess for a transition structure be generated using Linear Synchronous Transit
[788]. The LST procedure locates a maximum along a path connecting two structures and thus provides
a guess for the transition structure connecting them.
Note that an LST calculation does not actually locate a proper transition state. The LST method has
been superseded by Opt=QST2.
Massage
The Massage keyword requests that the molecule specification and basis set data be modified after it is
generated. This keyword is deprecated in favor of ExtraBasis, Charge, Counterpoise and other keywords.
Opt=EnOnly
Requests an optimization using a pseudo-Newton-Raphson method with a fixed Hessian and numerical
differentiation of energies to produce gradients. This option requires that the Hessian be read in via
ReadFC or RCFC. It can be used to locate transition structures and higher saddle points. Requires the
molecule be specified as a Z-matrix. The default for energy-only methods is Opt=(EnOnly,EF).
Opt=FP
Requests the Fletcher-Powell optimization algorithm [789], which does not require analytic gradients.
The maximum number of variables allowed for a Fletcher-Powell optimization is 30. Requires the
molecule be specified as a Z-matrix.
Opt=Grad
Requests a gradient optimization, using the default method unless another option is specified. This is the
default whenever analytic gradients are available and is invalid otherwise.
Opt=MNDOFC
Requests that the MNDO (or AM1, if possible) force constants be computed and used to start the (pre-
sumably ab initio) optimization. We recommend performing a PM6 Freq calculation followed by
Opt=RCFC instead of this option.
Opt=MS
Specifies the Murtaugh-Sargent optimization algorithm [790]. The Murtaugh-Sargent optimization method
382 Chapter B. Obsolete Keywords and Deprecated Features

is an obsolete alternative, and is retained in Gaussian only for backwards compatibility. The maximum
number of variables allowed for a Murtaugh-Sargent optimization is 50. Requires the molecule be speci-
fied as a Z-matrix.
Opt=UnitFC
Requests that a unit matrix be used instead of the usual valence force field guess for the Hessian.
Opt=GDIIS
Specifies the use of the modified GDIIS algorithm [791–793]. The default GEDIIS algorithm is always
better.
Opt=Big
Requests the optimization to be done using the fast equation solving methods [794] for the coordinate
transformations and the Newton-Raphson or RFO step. This method avoids the matrix diagonalizations.
Consequently, the eigenvector following methods (Opt=TS) cannot be used in conjunction with it. This
option is unreliable and not recommended.
Output=PolyAtom
This requests output of an integral file in one variant of the format originated for the PolyAtom integrals
program. The format produced by default is that used by the Caltech MQM programs, but the code in
Link 9999 is easily modified to produce other variations on the same theme.
Output=Trans
Write an MO coefficient file in Caltech (Tran2P5) format. This is only of interest to users of the Caltech
programs.
SCF=Sleazy
Requested the loose SCF convergence criteria appropriate for single points; equivalent to SCF=(Conver=4,VarInt,
NoFinal,Direct). SinglePoint is a synonym for Sleazy. It is never recommended for production quality
calculations.
SCF=VerySleazy
Reduced cutoffs even further; uses Int=CoarseGrid and single-point integral accuracy during iterations,
followed by a single iteration with the usual single point grid (MediumGrid). Not recommended for
production quality calculations.
SCRF=DPCM
Uses the polarizable dielectric model [685, 686, 688], which corresponds to the Gaussian 98 SCRF=PCM
option except for some minor implementation details [700]. This model is no longer recommended for
general use. The default SCRF method is IEFPCM.
SCRF=Numer
Force numerical SCRF rather than analytic. This keyword is required for multipole orders beyond Dipole.
This option implies the use of spherical cavities, which are not recommended. No gradients are available
for this option.
SCRF=Dipole
The options Dipole, Quadrupole, Octopole, and Hexadecapole specify the order of multipole to use in
the SCRF calculation. All but Dipole require that the Numer option be specified as well.
SCRF=Cards
Begin the SCRF=Numer calculation with a previously computed reaction field read from the input stream,
B.2 Deprecated 383

immediately after the line specifying the dielectric constant and radius (three free-format reals).
%SCR
Used to specify the location of the .SCR scratch file.
Stable=Symm
Retain symmetry restrictions. NoSymm relaxes symmetry restrictions and is the default.
Transformation=Old2PDM
Forces the old-fashioned process of the 2PDM in post-SCF gradients (sorted in L1111 and then processed
in L702 and L703). This is slow, but it reduces memory requirements. This option cannot be used for
frozen core calculations.
Transformation=New2PDM
Causes the 2PDM to be generated, used, and discarded by L1111 in post-SCF gradient calculations.
Transformation=Conventional
Requests that the original transformation method based on externally stored integrals be used.
 C. Gaussian 16 Release Notes

Features and changes introduced in Rev. B.01 are indicated by [REV B].

C.1 New Features

C.1.1 New Modeling Capabilities
♢ [REV B] Static Raman intensities can be computed for excited states at the CIS and TD levels of theory.
TD Freq=Raman computes the polarizability by numerical differentiation with respect to an electric field,
so the cost of Freq=Raman for these methods is 7x that of the frequencies without Raman intensities.
♢ TD-DFT analytic second derivatives for predicting vibrational frequencies/IR and Raman spectra and
performing transition state optimizations and IRC calculations for excited states.
♢ EOMCC analytic gradients for performing geometry optimizations.
♢ Anharmonic vibrational analysis for VCD and ROA spectra: see Freq=Anharmonic.
♢ Vibronic spectra and intensities: see Freq=FCHT and related options.
♢ Resonance Raman spectra: see Freq=ReadFCHT.
♢ New DFT functionals: M08HX, MN15, MN15L.
♢ New double-hybrid methods: DSDPBEP86, PBE0DH and PBEQIDH.
♢ PM7 semi-empirical method.
♢ Ciofini excited state charge transfer diagnostic: see Pop=DCT.
♢ The EOMCC solvation interaction models of Caricato: see SCRF=PTED.
♢ Generalized internal coordinates, a facility which allows arbitrary redundant internal coordinates to be
defined and used for optimization constraints and other purposes. See Geom=GIC and GIC Info.

C.1.2 Performance Enhancements

♢ NVIDIA K40, K80 and P100 (Pascal) GPUs are supported under Linux for Hartree-Fock and DFT calcu-
lations; P100 support is new with [REV B] which also provides performance improvements for all GPU
types. See Using GPUs for details on GPU support and usage.
 386 Chapter C. Gaussian 16 Release Notes

♢ Parallel performance on larger numbers of processors has been improved. See the Parallel Performance
tab for information about how to get optimal performance on multiple CPUs and clusters.
♢ [REV B] Dynamic allocation of tasks among Linda workers is now the default, improving parallel effi-
ciency.
♢ Gaussian 16 uses an optimized memory algorithm to avoid I/O during CCSD iterations.
♢ There are several enhancements to the GEDIIS optimization algorithm.
♢ CASSCF improvements for active spaces ≥ (10,10) increase performance and make active spaces of up
to 16 orbitals feasible (depending on the molecular system).
♢ Significant speedup of the core correlation energies for W1 compound model.
♢ Gaussian 16 incorporates algorithmic improvements for significant speedup of the diagonal, second-
order self-energy approximation (D2) component of composite electron propagator (CEP) methods as
described in [385]. See EPT.

C.1.3 Usage Enhancements

♢ [REV B] The ChkChk utility now reports the job status (whether the job completed normally, failed, is
in progress, etc.)
♢ [REV B] The optional parameters in the input line for an atom can now specify the radius to use when
finite (non-point) nuclei are used. The radius is specified as a floating point value in atomic units using
the RadNuclear=val item. For example:
C(RadNucl=0.001) 0.0 0.0 3.0
♢ Tools for interfacing Gaussian with other programs, both in compiled languages such as Fortran and C
and with interpreted languages such as Python and Perl. Refer to Interfacing to Gaussian 16 for details.
[REV B] adds many additional quantities have been added to the matrix element file, including atomic
populations, one-electron and property operator matrices and the non-adiabatic coupling vector. The
new items are the labeled sections QUADRUPOLE INTEGRALS, OCTOPOLE INTEGRALS, HEX-
ADECAPOLE INTEGRALS, [MULLIKEN,ESP,AIM,NPA,MBS] CHARGES, DIP VEL INTEGRALS,
R X DEL INTEGRALS, OVERLAP DERIVATIVES, CORE HAMILTONIAN DERIVATIVES, F(X),
DENSITY DERIVATIVES, FOCK DERIVATIVES, ALPHA UX, BETA UX, ALPHA MO DERIVA-
TIVES, BETA MO DERIVATIVES, [Alpha,Beta] [SCF,MP2,MP3,MP4,CI Rho(1),CI,CC] DENSITY
and TRANS MO COEFFICIENTS and the scalars 63-64.
♢ Parameters specified in Link 0 (%) input lines and/or in a Default.Route file can now also be specified via
either command-line arguments or environment variables. [REV B] introduces command-line options to
specify input and/or data using a checkpoint or matrix element file (the equivalent of the %OldChk or
%OldMatrix Link 0 commands for input). See the Equivalencies tab for details.
♢ You can now compute the force constants at every nth step of a geometry optimization: see Opt=Recalc.
♢ [REV B] DFTB parameters are now read in Link 301 before the basis set is constructed, so that the
presence or absence of d functions for an element can be taken from the parameter file.
♢ [REV B] There are now command-line options to specify input and/or data to/from checkpoint or matrix
element files. See the Equivalencies tab or the command line options page for details.
 C.2 Functional Changes 387

C.2 Functional Changes

C.2.1 Changes from Gaussian 16 Rev. A.03
♢ There have been minor modifications to the procedure for building from source code, which is docu-
mented at http://gaussian.com/g16/g16src_install.pdf.

C.2.2 Changes from Gaussian 09

Calculation Defaults

The following calculation defaults are different in Gaussian 16:

♢ Integral accuracy is 10−12 rather than 10−10 in Gaussian 09.
♢ The default DFT grid for general use is UltraFine rather than FineGrid in G09; the default grid for CPHF
is SG1 rather than CoarseGrid. See the discussion of the Integral keyword for details.
♢ SCRF defaults to the symmetric form of IEFPCM [702] (not present in Gaussian 09) rather than the
non-symmetric version.
♢ Physical constants use the 2010 values rather than the 2006 values in Gaussian 09.
The first two items were changed to ensure accuracy in several new calculation types (e.g., TD-DFT fre-
quencies, anharmonic ROA). For these reasons, Integral=(UltraFine,Acc2E=12) was made the default. Using
these settings generally improve the reliability of calculations involving numerical integration, e.g., DFT opti-
mizations in solution. There is a modest increase in the CPU requirements for these options compared to the
Gaussian 09 defaults of Integral=(FineGrid,Acc2E=10).
The G09Defaults keyword sets all four of these defaults back to the Gaussian 09 values. It is provided for
compatibility with previous calculations, but the new defaults are strongly recommended for new studies.

Default Memory Use

Gaussian 16 defaults memory usage to %Mem=100MW (800MB). Even larger values are appropriate for
calculations on larger molecules and when using many processors; refer to the Parallel Jobs tab for details.

TD-DFT Frequencies

TDDFT frequency calculations compute second derivatives analytically by default, since these are much
faster than the numerical derivatives (the only choice in Gaussian 09).

C.3 Using GPUs

See Sec. 4.6.

C.4 Parallel Usage and Performance Notes

C.4.1 Shared-memory parallelism
Memory allocation. Calculations involving larger molecules and basis sets benefit from larger memory
allocations. 4 GB or more per processor is recommended for calculations involving 50 or more atoms and/or
500 or more basis functions. The freqmem utility estimates the optimal memory size per thread for ground-
state frequency calculations, and the same value is reasonable for excited-state frequencies and is more than
sufficient for ground and excited state optimizations.
388 Chapter C. Gaussian 16 Release Notes

The amount of memory allowed should rise with the number of processors: if 4 GB is reasonable for one
processor, then the same job using 8 CPUs would run well in 32 GB. Of course, there may be limitations to
smaller values imposed by the particular hardware, but scaling memory linearly with number of CPUs should
be the goal. In particular, increasing only the number of CPUs with fixed memory size is unlikely to lead to
good performance when using large numbers of processors.
For large frequency calculations and for large CCSD and EOM-CCSD energies, it is also desirable to leave
enough memory to buffer the large disk files involved. Therefore, a Gaussian job should only be given 50-70%
of the total memory on the system. For example, on a machine with a total of 128 GB, one should typically give
64-80 GB to a job which was using all the CPUs, and leave the remaining memory for the operating system to
use as disk cache.
Pinning threads to CPUs under Linux. Efficiency is lost when threads are moved from one CPU to
another, thereby invalidating the cache and causing other overhead. On most machines, Gaussian can tie threads
to specific CPUs, and this is the recommended mode of operation, especially when using larger numbers of
processors. The %CPU Link 0 line specifies the numbers of specific CPUs to be used. Thus, on a machine with
one 8-core chip, one should use %CPU=07 rather than %NProc=8 because the former ties the first thread to
CPU 0, the next to CPU 1, etc.
On some older Intel processors (Nehalem and before), there is not enough memory bandwidth to keep all
the CPUs on a chip busy, and it is often preferable to use half the CPUs, each with twice as much memory as
if all were used. For example, on such a machine with four 12-core chips and 128 GB of memory, with CPUs
0-11 on the first chip, 12-23 on the second, and so on, it is better to run using 24 processors (6 on each chip)
and give them 72 GB/24 procs = 3 GB memory each, rather than use all 48 with only 1.5 GB of memory each.
The required input directives would be:

%Mem=72GB
%CPU=0-47/2

where the /2 means to use every other core: i.e., cores 0, 2, 4, 6, 8, and 10 (on chip 0), 12, 14, 16, 18, 20, and
22 (on chip 1), etc.
With the most recent generations of Intel processors (Haswell and later), the memory bandwidth is better
and using all the cores on each chip works well.
As long as sufficient memory is available and threads are tied to specific cores, then parallel efficiency on
large molecules is good up to 64 or more cores.
Disable hyperthreading. Hyperthreading is not useful for Gaussian since it effectively divides resources
such as memory bandwidth among threads on the same physical CPU. If hyperthreading cannot be turned off,
Gaussian jobs should use only one hyperthread on each physical CPU. Under Linux, hyperthreads on different
processors are grouped together. That is, if a machine has 2 chips each with 8 cores and 3-way hyperthreading,
then “CPUs” 0-7 are across the 8 cores on chip 0, 8-15 are across the 8 cores on chip 1, and 16-23 are the
second hyperthreads on the 8 cores of chip 0, and so on. So a job would run best with %CPU=015.
Under AIX, hyperthreads are grouped together with up 8 hyperthread numbers for each CPU even if fewer
hyperthreads are in use, so with two 8 core chips and 4-way hyperthreading, “CPUs” 0-3 are all on core 0 of
chip 0, 8-11 are on core 1 of chip 0, etc. Thus, one would want to use %CPU=0127/8 to select “CPUs” 0, 8,
16, · · · which are each using a distinct core.
 C.5 CCSD Performance 389

C.4.2 Cluster (Linda) parallelism

Availability. Hartree-Fock and DFT energies, gradients and frequencies run in parallel across clusters,
as do MP2 energies and gradients. MP2 frequencies, CCSD, and EOM-CCSD energies and optimizations
are SMP parallel but not cluster parallel. Numerical derivatives, such as DFT anharmonic frequencies and
CCSD frequencies, are parallelized across nodes of a cluster by doing a complete gradient or second derivative
calculation on each node, splitting the directions of differentiation across workers in the cluster.
Combining with MP parallelism. Shared-memory and cluster parallelism can be combined. Generally,
one uses shared-memory parallelism across all CPUs in each node of the cluster. Note that %CPU and %Mem
apply to each node of the cluster. Thus, if one has 3 nodes names apple, banana and cherry, each with two
chips which have 8 CPUs each, then one might specify:

%Mem=64GB
%CPU=0-15
%LindaWorkers=apple,banana,cherry
# B3LYP/6-311+G(2d,p) Freq ···

This would run 16 threads, each pinned to a CPU, on each of the 3 nodes, giving 4 GB to each of the 48 threads.
For the special case of numerical differentiation only – e.g., Freq=Anharm, CCSD Freq, etc. – one extra
worker is used to collect the results. So these jobs should be run with two workers on the master node (where
Gaussian 16 is started). For the above example if the job was computing anharmonic frequencies, then one
would use:

%Mem=64GB
%CPU=0-15
%LindaWorkers=apple:2,banana,cherry
# B3LYP/6-311+G(2d,p) Freq=Anharm ···

where Gaussian 16 is assumed to be started on node apple. This will start 2 workers on node apple, one of
which just collects results, and will do the computational work using the other worker on apple and those on
banana and cherry.

C.5 CCSD Performance

C.5.1 Memory requirements for CCSD, CCSD(T) and EOM-CCSD calculations
These calculations can use memory to avoid I/O and will run much more efficiently if they are allowed
enough memory to store the amplitudes and product vectors in memory. If there are NO active occupied
orbitals (NOA in the output) and NV virtual orbitals (NVB in the output) then approximately 9NO2 NV 2 words
of memory are required. This does not depend on the number of processors used.

C.6 Equivalencies
Most options that control how Gaussian 16 operates can be specified in any of 4 ways. From highest to
lowest precedence these are:
1. As Link 0 input (%-lines): This is the usual method to control a specific job and the only way to control
a specific step within a multi-step input file. Example: %CPU=1,2,3,4
390 Chapter C. Gaussian 16 Release Notes

2. As options on the command line: Command line options are useful when you want to define aliases or
other shortcuts for different common ways of running the program. Example: g16 -c="1,2,3,4" · · ·
3. As environment variables: This is most useful in standard scripts, for example for generating and
submitting jobs to batch queuing systems. Example: export GAUSS_CDEF="1,2,3,4"
4. As directives in the Default.Route file: This is most useful when one wants to change the program
defaults for all jobs. Example: -C- 1,2,3,4
When searching for a Default.Route file the current default directory is checked first, followed by the
directories in the path for Gaussian 16 executables: environment variable GAUSS_EXEDIR, which normally
points to $g16root/g16.
The following table lists the equivalences among Link 0 commands, command line options, Default.Route
items and environment variables. The -h, -o options and the -i and -o option classes were introduced in [REV
B], as were their corresponding environment variables.

Default.Route Link 0 Option Env. Var. Description

Gaussian 16 execution defaults
-R- -r GAUSS_RDEF Route section keyword list.
-M- %Mem -m GAUSS_MDEF Memory amount for Gaussian jobs.
-C- %CPU -c GAUSS_CDEF Processor/core list for multiprocessor
parallel jobs.
-G- %GPUCPU -g GAUSS_GDEF GPUs=Cores list for GPU parallel
jobs.
-S- %UseSSH, %UseRSH -s GAUSS_SDEF Program to start workers for network
parallel jobs: rsh or ssh.
-W- %LindaWorkers -w GAUSS_WDEF List of hostnames for network parallel
jobs.
-P- %NProcShared -p GAUSS_PDEF #processors/cores for multiprocessor
parallel jobs. Deprecated; use -C-.
-L- %NProcLinda -l GAUSS_LDEF #nodes for network parallel jobs.
Deprecated; use -W-.
Archive entry data
-H- -h GAUSS_HDEF Computer hostname.
-O- -o GAUSS_ODEF Organization (site) name.
Utility program defaults
-F- GAUSS_FDEF Options for the formchk utility.
-U- GAUSS_UDEF Memory amount for utilities.
Parameters for scripts and external programs
# section -x GAUSS_XDEF Complete route for the job (route not
read from input file).
%Chk -y GAUSS_YDEF Checkpoint file for job.
%RWF -z GAUSS_ZDEF Read-write file for job.
%OldChk -ic GAUSS_ICDEF Existing checkpoint file from which
to read input.
 C.7 Bugs Fixed 391

%OldMatrix -im GAUSS_IMDEF Matrix element file from which to

read input.
%OldMatrix=(file,i4lab) -im4 GAUSS_IM4DEF Matrix element file using 4-byte inte-
gers from which to read input.
%OldRaw -ir GAUSS_IRDEF Raw matrix element file from which
to read input.
%OldRaw=(file,i4lab) -im4 GAUSS_IR4DEF Raw matrix element file using 4-byte
integers from which to read input.
-oc GAUSS_OCDEF Output checkpoint file. Generally re-
dundant with -y/GAUSS_YDEF.
-om GAUSS_OMDEF Output matrix element file.
-om4 GAUSS_OM4DEFOutput matrix element file using 4-
byte integers.
-or GAUSS_IRDEF Output raw matrix element file.
-or4 GAUSS_IR4DEF Output raw matrix element file using
4-byte integers.

Note that the quotation marks are normally required around the specified value for the command line and
environment variables to avoid modification of the parameter string by the shell.

C.7 Bugs Fixed

The following bugs are fixed in Rev. B.01:
♢ A problem with restarting in the middle of a job step (from the RWF) when using SCF=QC was fixed.
♢ When doing the regular SCF part of SCF=XQC or SCF=YQC, the orbitals and density are only saved
when a new lowest energy wavefunction is found. If L502 fails to converge and the calculation moves
on to L508 (QC or steepest descent SCF) then the best wavefunction from the regular SCF iterations is
used.
♢ Problems with restarting from the RWF in the middle of EOM-CC calculations were fixed.
♢ Problems with ROMP4 and with EOM-CC when there was an empty beta spin-space or a full alpha
spin-space were fixed.
♢ The erroneous labels in the summary table for G4 and G4MP2 jobs were corrected.
♢ Problems with naming scratch files for NBO when the RWF was split across physical files were fixed.
♢ An allocation problem which caused CIS and TD frequency jobs on large molecules using very small
amounts of memory to fail was fixed. These jobs now complete, but they would run much more efficiently
if given more memory (i.e., a larger value to %Mem).
♢ A bug which caused jobs which used the FormCheck keyword to fail was fixed. This keyword is depre-
cated, and the -fchk command line option, which is more flexible, is the preferred alternative.
♢ Unnecessary warnings which were printed by formchk when operating on a checkpoint file from a calcu-
lation which included PCM solvation were removed.
♢ The route for Opt=(TS,ReCalcFC=N) was corrected.
♢ Molecular mechanics parameters are now stored correctly in formatted checkpoint files.
392 Chapter C. Gaussian 16 Release Notes

♢ The route for doing interaction deletions using NBO6 (Pop=NBO6Del) was corrected.
♢ A bug which prevented GPUs from being enabled in later steps of a compound job was fixed.
♢ A problem with parsing the obsolete keywords QMom and Magneton in atomic property lists was cor-
rected.
D. Gaussian 16W Reference

Not included in this document. See http://gaussian.com/g16w/.

 E. Interfacing to Gaussian 16 (v2)

E.1 Introduction
This documentation covers version 2 of the interfacing files. See “Release History” for information about
changes from earlier versions.
There are a variety of circumstances where it is useful to run one or more calculations in Gaussian as part
of a larger task, with data passed between Gaussian and the other part(s) of the task:
♢ Scripting to automate running multiple, related Gaussian jobs. This is typically done with the shell
scripts or programs in scripting languages such as Python and Perl. Some of the tools provided here for
more closely integrated computations are also useful for this purpose.
♢ Post-processing of Gaussian calculation results. In the past, the formatted checkpoint file (.fchk) has
been the standard method to communicate results for this purpose. It is well suited to analysis tasks such
as visualization, but is less suitable for numerically intensive follow-on calculations for reasons discussed
below. Wavefunction (.wfn) files provide some additional information for these purposes but share some
of the limitations of .fchk files.
♢ Computations in other programs using intermediate data generated by Gaussian. This strategy avoids the
need to program features in the other program which would duplicate functionality already in Gaussian.
Typical uses fall in three main categories:
• Running production calculations combining Gaussian results with those of an independent program.
These programs would typically be implemented in a compiled language such as Fortran or C.
For example, SCF methods such as Valence Bond methods or unusual MCSCF methods can use
one- and two-electron integrals computed by Gaussian. Similarly, post-SCF methods can use the
required integrals over molecular orbitals produced by Gaussian.
• Gaussian’s infrastructure can also incorporate results from external programs. For example, ge-
ometry optimizations and ONIOM calculations can be done in Gaussian using energies and forces
provided by an external program (e.g., computed using a theoretical method not available in Gaus-
sian).
 396 Chapter E. Interfacing to Gaussian 16 (v2)

• Prototyping new models or methods, implemented in either a compiled language or an interpreted

one such as Python. It can be convenient to have all the quantities computed by Gaussian available
so that only the unique aspects of the new model need to be implemented and debugged.
• Classroom exercises, which created using interpreted languages such as Python or MatLab, so that
the exercise can focus on a specific issue without having to provide code for unrelated parts (e.g.,
coding a simple SCF algorithm without having to evaluate integrals).
There are several methods available to facilitate this type of communication, with data flowing to Gaussian
from anther source, from Gaussian to another program, or both. The process can be controlled with Gaussian,
by a script or by another program. In general, data interchange happens via a text file known as the matrix
element file. Its structure is designed to be very general. Some interface routines are provided; they are
implemented with open source software and hence are useful for communication between user programs and
other quantum chemistry packages as well.
The matrix element file is the recommended tool for communicating intermediate results with external
programs since all quantities are included to full precision. The formatted checkpoint file remains a simpler
and machine-independent option for visualization, post-processing and other cases where a moderate number
of significant figures is adequate or having a plain text file is desirable.

E.2 Description
In the past, some people have used functionality from Gaussian by linking the executables for their pro-
grams with Gaussian’s libraries, or by having their code called within a Gaussian link. However, this is prob-
lematic in many ways. It requires having Gaussian source code, that the user compile their own code with
the same compiler and options as Gaussian, and that the user understand the internal data structures and call-
ing conventions within Gaussian. It made the resulting code fragile in that internal changes in future versions
of Gaussian, transparent to ordinary users, could break the user’s code. In addition, it created unnecessary
complications with respect to code ownership and intellectual property.

E.2.1 Goals for a General Interface

Our goals for a general interface are to facilitate all of the above uses in clean and maintainable ways. It
should:
♢ Allow communication between other programs or scripts and standard Gaussian binaries without requir-
ing recompilation, modification of Gaussian, or access to Gaussian source code.
♢ Be as simple for the user as possible, in particular by providing an interface which does not require
knowledge of Gaussian’s internal data structures or algorithms, and requiring as little knowledge of the
internal structure of interface files as possible.
♢ Be self-defining and upward compatible, so that new types of data and new functionality can be added
without breaking user code which worked with a previous version of the interface.
♢ Facilitate the use of Gaussian as either the controlling or the subordinate program.
♢ Be as non-Gaussian-centric as possible, to allow code that uses the Gaussian interface to also use other
quantum chemistry codes which provide the same interface.
Previously, we have provided the formatted checkpoint file as an interface mechanism, particularly for post-
processing of results from Gaussian. This file is still supported and available. It is self-defining and extensible.
 E.2 Description 397

Being an ordinary text file gives it a relatively simple format to process. However, while this design is suitable
for post-processing results from Gaussian, especially for visualization, it is not adequate as a general interface
for two reasons. First, the limited precision with which values are stored is not sufficient for intermediate data
such as integrals. Second, reading and writing the file is expensive when large amounts of data are involved
because of the conversion to and from text form. In addition, since the file was intended for post-processing
and for moving data between Gaussian running on different types of hardware, it mirrors many of the internal
Gaussian data structures.

E.2.2 Structure of the General Interface

There are three basic components of the new interface:
♢ A binary data file which is self-defining but reasonably compact, and which attempts to store standard
data in simple forms rather than using Gaussian’s internal data structures. These forms are supported in
either Fortran unformatted form, which is useful for interfacing to programs in Fortran or Python, and as
raw binary data, which is suitable for use in C, C++, and Perl programs. Data is organized in the same
way in either type of file. Details of the file structure can be found in Matrix Element File. The formchk
and unfchk utilities can convert between Gaussian checkpoint files and either type of binary interface file.
♢ Functionality within Gaussian to use such binary data files as input or output for complete Gaussian
jobs and as input/output between Gaussian and external programs being run from within Gaussian. A
subordinate program is connected to Gaussian via the External interface. Such a program can be used:
• In lieu of a Gaussian SCF link.
• As a post-SCF step using orbitals generated within Gaussian.
• To compute derivatives for use in optimizations and frequency calculations controlled by Gaussian.
• To perform one or more of the sub-calculations within an ONIOM model.
Gaussian can also be run as a subordinate program, taking most or all of its input from a data file provided
by the controlling program, and producing a new data file containing the results from Gaussian.
♢ Libraries and scripts which provide easy-to-use interfaces for reading and writing these file. They are
open source and hence can be easily incorporated in user programs.
The interface will continue to evolve as additional capabilities are required. The quantities which are
currently available in the data file include the most common quantities used in SCF and post-SCF calculations,
such as the location and identities of atoms, basis set, one and two electron integrals over atomic orbitals,
molecular orbital coefficients, and two electron integrals over molecular orbitals.

E.2.3 About the Interface Libraries and Scripts

The open source interface libraries and scripts have reached varying degrees of maturity depending on
their extent of use so far:
♢ The Fortran interface routines (in qcmatrix.F and qcmatrixio.F) provide for convenient reading and writ-
ing data from the files with minimal knowledge of their structure. The Fortran interfaces have been tested
with the PGI, Gnu and Intel Fortran compilers.
♢ The Python modules import the Fortran interface via f2py but add higher-level functionality, including
object interfaces for both the individual items in the file (atomic coordinates, operator matrices, etc. in
QCOpMat.py) and for the entire file as an object (in QCMatEl.py). In addition to reading and writing the
file, the file object also provides methods to transparently run Gaussian to generate additional data, so a
 398 Chapter E. Interfacing to Gaussian 16 (v2)

Python user can request and consume results from Gaussian without any knowledge of Gaussian’s input
or any knowledge of the structure of the interface file on disk. The actual data from the file are stored as
NumPy arrays and hence are useful directly in NumPy and SciPy routines. The Python interface uses
many features of Python3 and is not supported with Python2.
♢ The Perl modules (OpMat.pm and MatEl.pm) provide transparent object interfaces to the data items and
entire file in the same style as the Python modules, but do not include all of the higher level functionality.
Details of all the interfaces are in the comments in the source files.
The interface routines assume 4 byte integers in the data file. For the raw form of the file, a fixed integer
size must be assumed because there is no reliable way to determine this when the file is read. Since both Perl
and Python currently use 32-bit addressing and cannot handle arrays larger than 2 GB, this is not a limitation
for these languages. Versions of the Fortran interface routines are built for both 4-byte and 8-byte integers (the
latter have 8 appended to their filename).
There is not currently a separate C interface library; depending on the circumstances, C code can either
read the raw binary files using the same logic as in the Perl modules, or can call the Fortran interface routines.
Since the details of calling Fortran from C or C++ depend on the particular operating system and compilers, we
have not attempted to standardize this.

E.2.4 Generating Interface Data Files in Gaussian

The binary matrix element file can be produced in three ways:

♢ Using the formchk utility to convert the binary checkpoint file left after a Gaussian job.
♢ Using an external script or program is to be run as part of the calculation in Gaussian via the External
keyword.
♢ Using the Output=MatrixElement or Output=RawMatrixElement keywords to cause a file to be generated
at the end of the current Gaussian job step.
A formatted checkpoint file can similarly be produced in three ways:
♢ Using the formchk utility to convert the binary checkpoint file left after a Gaussian job.
♢ Generating it when an external script or program is to be run as part of the calculation in Gaussian (see
External).
♢ By using the -fchk switch on the g16 command line, which causes a formatted checkpoint file to be
written or rewritten at each “interesting” point of a job step: for a new geometry during an optimization,
the end of the job step, and the like.

E.2.5 Using Data Files as Input to Gaussian

Either the formatted checkpoint file or the binary matrix element file can be used as input to Gaussian by
converting it to a binary checkpoint file. This is done using the unfchk utility. You then specify the name of
the generated binary checkpoint file with the %Chk or %OldChk Link 0 command to provide the file to the
Gaussian job step.
In addition, a matrix element file can be specified as input using the %OldMatrixElement or %OldRawMa-
trixElement Link 0 commands. These take the data from the matrix element file and move it to the checkpoint
file for the current job step, where it can be used to provide the geometry, initial wavefunction, etc.
 E.3 Matrix Element File 399

E.2.6 Running Gaussian from within other programs

There are at least two ways this can be accomplished:
♢ The other program can generate an Gaussian input file. This input filspecifies that Gaussian take input
from a data file and/or generate a data file containing its results. The controlling program can then
run Gaussian in a subprocess using the UNIX system command, the fork/exec facility, or equivalent
functionality.
♢ The Python interface (QCMatEl.py) provides a matrix element class which includes methods which auto-
matically run Gaussian and update a matrix element object with additonal data. This can be used directly
by a Python program, or by a program in another language can create a subprocess running a simple
Python script which in turn runs Gaussian.

E.3 Matrix Element File

The matrix element file is a simple unformatted file designed to exchange data, such as the overlap and
core Hamiltonian matrix and two-electron integrals, in an extensible format. It can be written either as a Fortran
unformatted file, suitable for processing by other Fortran programs, or as a raw binary fine without any flags
or lengths for records, suitable for processing in C/C++/Perl/Python. This file format can be used as input to
and/or output from a program run via the external interface (using the External keyword), or written as file by
Gaussian for separate use by another program (using the Output=MatrixElement or Output=RawMatrixElement
keywords). Various options to Output in combination with one of these will select various additional data within
the file (e.g., the two-electron integrals over MOs). Finally, the data within any internal Gaussian file can be
included within the matrix element file via the Output=Files option.
The structure of the unformatted matrix element is as follows. The initial section contains records relating
to the molecular structure and other general job characteristics:

Record Format and Description

1 Character*64 LabFil, Integer IVers, Integer NLab, Character*64 GVers
A label for the file type, version number for the file format, the number of general data records which
precede the matrix element data (including this record), and the version of Gaussian which wrote the
file.
2 Character*64 Title, Integer NAtoms, Integer NBasis, NBsUse, ICharg, Multip,
NE, Len12L, Len4L, IOpCl, ICGU
The first 64 characters of the title section from the run which created the file, and the number of
atoms and basis functions. NBsUse is the number of linearly independent basis functions. ICharg is
the molecular charge, Multip the spin multiplicity (1=singlet, etc.), and NE is the number of electrons.
Len12L is the number of bytes used for the integer labels for sparse 1D and 2D matrices, and Len4L
is the number of bytes used for 4D matrices (2 electron integrals). Len12L and Len4L will be 4 if the
file is written in raw mode (i.e., all integers will be I*4), for compatibility with other languages.
400 Chapter E. Interfacing to Gaussian 16 (v2)

IOpCl is the closed/open-shell flag, which set if the matrix element file is written after an initial guess
or the SCF has completed (otherwise it is -1, meaning unspecified). ICGU encodes whether the
calculation is complex and/or GHF in a simpler way than IOpCl. Its three-digit value is interpreted
as klm, where k is 1 for the spin-aligned case and 2 for GHF; l is 1 for real and 2 for complex;
and m is 1 for RHF/GHF and 2 for UHF (i.e., 1 vs. 2 spin blocks). When k=2, then NBasis is the
number of spatial basis functions, but the operator matrices are over the spin orbital basis and hence
have dimension k*NBasis. When the file is read back into Gaussian, IOpCl can be -1 to indicate that
ICGU should be used to specify these parameters. If IOpCl≥0 and ICGU≥0, then they are checked
for consistency.
3 Integer IAn(NAtoms)
Atomic numbers, padded to an even number of integers if using I*4.
4 Integer IAtTyp(NAtoms)
Atom type information. The main aspect of interest to other programs is that negative values indicate
inactive atoms during an ONIOM model system calculation. By default, the file is written with
inactive atoms omitted from all arrays and NAtoms set to the number of active atoms, but all atoms
can optionally be included. It is padded to an even number of integers if using I*4.
5 Real*8 AtmChg(NAtoms)
Nuclear charges; may be different from atomic numbers if ECPs were used.
6 Real*8 C(3,NAtoms)
Cartesian nuclear coordinates in Bohr.
7 Integer IBfAtm(NBasis), IBfTyp(NBasis)
IBfAtm is the map from basis functions to atoms. IBfTyp is a type flag for each basis function. Each is
of the form lllmmm, where lll is the angular momentum and mmm is the component number. Negative
values indicate pure functions, and positive values indicate Cartesian functions. Thus, Cartesian d
functions are numbered 2001 through 2006, and pure d functions are -2001 through -2005.
8 Real*8 AtmWgt(NAtoms)
Atomic weights.
9 NFC, NFV, ITran, IDum
Window information for MO 2 electron integrals. The MOs include NFC frozen core orbitals and
NFV frozen virtuals, so the MO 2 electron integrals will be over NBsUse-NFC-NFV orbitals. ITran=0
if no MO integrals were stored, ITran=4 if only MOs involving at least one occupied orbital were
stored, or ITran=5 if a full transformation was done.
10 to Other scalar data about the calculation (if applicable).
NLab Record 10 is only present when NLab>9. It contains NLab-10 integers, each of which specifies the
number of 32-bit words in the corresponding initial record (allowing programs to skip them when the
file is stored without record marks/lengths). E.g., if NLab were to be 13, record 10 will contain 3
integers, specifying the lengths of the eleventh through thirteenth initial records. Currently, NLab’s
maximum value is 11, and record 10 contains the single integer 16.
11 16 additional integers, of which only the first five are currently used:
NShellAO: Number of contracted shells of AO basis functions, needed if shell data is provided.
NPrimAO: Number of primitive AO shells.
 E.3 Matrix Element File 401

NShellDB: Number of contracted shells of density fitting functions, needed if fitting shell data is
provided.
NPrimDB: Number of primitive density fitting shells.
NBTot: Total Number of bonds in connectivity data, if any.

In general, programs should read (or skip) NLab records at the beginning of the file in order to reach the
matrix element data. Doing so will ensure that additional initial records added in subsequent versions of the
matrix element file are handled properly.
These NLab records are followed by zero or more matrix sections, each of which has an initial record:
Character*64 Label, Integer NI, NR, NTot, NPerRec, N1, N2, N3, N4, N5, ISym
where the fields contain a label, the number of integers and number of reals for each element, the total number
of elements, and number of elements per record. NI can be zero for dense matrices (stored with zeros included).
NR is negative to flag complex rather than real data.
N1 through N5 are dimensions for the object as a matrix, with 0 for unused dimensions and negative values
for ones which are lower triangular. For example, if NBasis=50 and NBsUse=49 then N1 · · · N5 would be -50
50 0 0 0 for the overlap matrix and 50 49 0 0 0 for the transformation to an orthogonal basis. ISym=-1 for
anti-symmetric/Hermetian matrices.
The end of the file is marked with a record whose label is END and having all 0 values for the integers.
This initial record is followed by (NTot+NPerRec-1)/NPerRec records, each of the one of the following
forms:
Integer ID(NI,NPerRec), Real*8 DX(NR,NPerRec)
or just:
Real*8 DX(NR,NPerRec)
If NI=0 or NR<0, then the format is:
Integer ID(NI,NPerRec), Complex*16 DX(-NR,NPerRec)
or
Complex*16 DX(NR,NPerRec)
with the labels (if any) in ID, and values in DX. All matrix elements are over pure or Cartesian basis functions
in accord with that specified in the Gaussian route or defaulted for the particular basis set.

E.3.1 Labeled Sections

The possible labels and sections include the following:

OVERLAP
CORE HAMILTONIAN ALPHA
CORE HAMILTONIAN BETA
KINETIC ENERGY

Each is a lower triangular matrix stored dense (all N*(N+1)/2 elements with no labels). The two core Hamilto-
nians are identical unless a Fermi contact perturbation has been applied.

ORTHOGONAL BASIS

If present, this is an (NBasis,NBsUse) matrix giving the transformation from AOs to a linearly independent
orthonormal set.
402 Chapter E. Interfacing to Gaussian 16 (v2)

DIPOLE INTEGRALS

If present, this includes three lower-triangular matrices holding the X, Y, and Z dipole matrix elements.

QUADRUPOLE INTEGRALS
OCTOPOLE INTEGRALS
HEXADECAPOLE INTEGRALS

If present, these items are the 6, 10 or 15 matrices of the Cartesian multipole integrals (respectively).

DIP VEL INTEGRALS

R X DEL INTEGRALS

If present, these are the 3 matrices of the Del and RxDel one-electron operators.

GIAO D2H/DBDM

If present, each is a 9×NAtoms lower triangular matrices holding the GIAO core Hamiltonian second deriva-
tives with respect to an external field and nuclear magnetic moments (the matrix elements required for the
diamagnetic shielding term).

GIAO L/R3

If present, this each is a 3×NAtoms lower triangular matrices holding the GIAO magnetic perturbations (the
matrices required for the paramagnetic shielding term).

ALPHA ORBITAL ENERGIES

If present, this is an NBsUse vector of initial guess or converged orbital energies.

ALPHA MO COEFFICIENTS

If present, this is an NBasis×NBsUse matrix of initial guess or converged orbitals.

BETA ORBITAL ENERGIES

If present, this is an NBsUse vector of initial guess or converged orbital energies.

BETA MO COEFFICIENTS

If present, this is an NBasis×NBsUse matrix of initial guess or converged orbitals.

ALPHA DENSITY MATRIX

If present, this is a lower-triangular matrix containing the alpha spin part of the density matrix selected by the
options for population analysis, etc. If read back into Gaussian, it is stored in place of the SCF density.

BETA DENSITY MATRIX

If present, this is a lower-triangular matrix containing the beta spin part of the density matrix selected by the
options for population analysis, etc. If read back into Gaussian, it is stored in place of the SCF density.

ALPHA SCF DENSITY MATRIX

If present, this is a lower-triangular matrix containing an initial guess or converged SCF density.

BETA SCF DENSITY MATRIX

E.3 Matrix Element File 403

If present, this is a lower-triangular matrix containing an initial guess or converged SCF density.

[ALPHA,BETA] [MP2,MP3,MP4,CI,QCI/CC] DENSITY MATRIX

If present, these are the alpha and beta densities computed including the indicated type of correlation.

[MULLIKEN,ESP,AIM,NPA,MBS] CHARGES

Atomic charges of the specific type. Multiple charge sections may be present depending on the options to
the Population keyword. Note that all types of electrostatic potential-derived charges are labeled as “ESP
CHARGES”.

GAUSSIAN SCALARS

This a vector of labeled reals. Labels between 1 and 1000 refer to elements of the Gaussian /Gen/ file (for a
table, see below). Labels higher than 1000 are reserved for specific scalars to/from the external program.

ALPHA DENSITY DERIVATIVES

BETA DENSITY DERIVATIVES

If present, these hold the lower triangular AO density derivatives with respect to whatever perturbations were
applied during the CPHF. The number of matrices is the number of perturbations, and it varies.

ALPHA MO DERIVATIVES
BETA MO DERIVATIVES

If present, these are the (NBasis,NAE,3) and (NBasis,NBE,3) MO coefficient derivatives with respect to a mag-
netic field.

ALPHA FOCK MATRIX

If present, this is the alpha-spin Fock matrix, or the only Fock matrix for closed-shell and GHF.

BETA FOCK MATRIX

If present, this is the beta-spin Fock matrix for unrestricted SCF calculations.

NUCLEAR GRADIENT

If present, there are the 3*NAtoms derivatives of the energy with respect to the nuclear coordinates. This is
more likely to be a field returned by an external program than one used as input to the external program.

NUCLEAR FORCE CONSTANTS

If present, these are the second derivatives of the energy with respect to the nuclear coordinates. This is more
likely to be a field returned by an external program than one used as input to the external program. They are
stored as a lower triangular matrix of dimension 3*NAtoms.

ELECTRIC DIPOLE MOMENT

ELECTRIC DIPOLE DERIVATIVES
ELECTRIC DIPOLE POLARIZABILITY
DIPOLE POLARIZABILITY DERIVATIVES
ELECTRIC DIPOLE HYPERPOLARIZABILITY
ATOMIC AXIAL TENSORS
404 Chapter E. Interfacing to Gaussian 16 (v2)

If present, these are derivatives with respect to static external fields. If provided back to Gaussian, only the
properties in the file are updated in the Gaussian internal data; any other properties already present in the
Gaussian internal data are unaltered.

SHELL TYPE
NUMBER OF PRIMITIVES PER SHELL
CONTRACTION COEFFICIENTS
P(S=P) CONTRACTION COEFFICIENTS
COORDINATES OF EACH SHELL

These specify the basis set and are in the same format as the same fields in the fchk file. The same field names
prefixed with DENSITY specify the density fitting set, if any.

OVERLAP DERIVATIVES
CORE HAMILTONIAN DERIVATIVES
F(X)
DENSITY DERIVATIVES
FOCK DERIVATIVES
ALPHA UX
BETA UX

These records contain the results of a derivative SCF (CPHF) calculation and are in the notation of [795]: Sx,
Hx, F(x), Px, Fx, Ux, and Cx. F(x) and Fx contain all alpha followed by all beta Fock derivatives for open-shell,
while the spin-cases of Ux and Cx are in separate records.

[Alpha,Beta] [SCF,MP2,MP3,MP4,CI Rho(1),CI,CC] DENSITY

These records hold post-SCF densities, alpha followed by beta for open-shell.

REGULAR 2E INTEGRALS or
RAFFENETTI 2E INTEGRALS

Only non-zero integrals are stored with 4 indices i ≥ j, i ≥ k, k ≥ l, j ≥ l if i = k. NR is 1 for regular integrals
and 1, 2, or 3 for Raffenetti integral combinations:

R1(i, j, k, l) = (i j|kl) − 1/4[(ik| jl) + (il| jk)]

R2(i, j, k, l) = (i j|kl) + (il| jk)
R3(i, j, k, l) = (ik| jl) − (il| jk)

The default is R1 only for closed-shell systems, R1 and R2 for UHF. The NoRaff keyword forces regular
integrals, and IOp(3/11=N) can be used for force a particular set of Raffenetti integrals.
If MO 2 electron integrals were requested, then these are stored dense (zeroes included and no inte-
ger labels). For restricted calculations there will be one set labelled AA MO 2E INTEGRALS with inte-
grals stored over the unique quartets of indices if a fill transformation (ITran=5 above) is done. That is, if
NROrb = NBsUse - NFC - NFV is the number of active orbitals (included in the transformation) then there
will NO4=(NOrbTT*(NOrbTT+1))/2 integrals, where NOrbTT=(NROrb*(NROrb+1))/2, when there was a full
transformation. For unrestricted and a full transformation, there will be 3 sets of integrals, AA, BA, and BB.
AA and BB are length NO4 and BA is NOrbTT 2 , with the beta spin indices running fastest.
 E.3 Matrix Element File 405

For a partial transformation (ITran=4) there will be one set of MO integrals for restricted, dimensioned
(NOrbTT,NROrb,NOA) where NOA=NAE-NFC is the number of active occupieds. For restricted there will be
AA, AB, BA and BB with dimensions (NOrbTT,NROrb,NOA), (NOrbTT,NROrb,NOB), (NOrbTT,NROrb,NOA),
and (NOrbTT,NROrb,NOB), respectively.

TRANS MO COEFFICIENTS

If MO two-electron integrals are included, this record holds the MO coefficients used in the transformation (i.e.,
with any frozen core or virtual orbitals omitted), alpha followed by beta spins.

E.3.2 Gaussian Scalars

1 Virial ratio
2-4 Components of applied electric field, if any
5 2e SCF energy
6 SCRF g-factor
7 SCRF a0
8 Thermal energy
9 E(CI/CC/QCI/BD)
10 E(CCD+ST4(CCD)/QCISD(T)/BD(T)/CI+Davidson)
11 E(VAR1)
12 Zero-point energy
13 Multi-step (G1, G2, etc.) energy
14 Number of imaginary frequencies
15 D(PUHF)
16 EPUHF
17 ECBS2
18 ECBSI
19 EPMP2-0
20 EPMP3-0
21 Root-mean-squared force of optimized parameters
22 E(CIS-MP2)
23 RMS error in density matrix
24 S2 after annihilation of first contaminant
25 CIS energy
26 UMP4D (=UMP4DQ - E4(R+Q))
27 Reference energy for BD
28 MP5
29 S4SD (computed in ANNIL in L502, used by PSCF spin projection routines)
30 Frozen-core part of total energy
31 “TAU” from SCFDM
32 SCF energy
33 UMP2 energy
34 UMP3 energy
 406 Chapter E. Interfacing to Gaussian 16 (v2)

35 UMP4(SDTQ) energy
36 CBS OIii
37 Total energy with RF from L116
38 MP4DQ energy
39 MP4SDQ energy
40 Used by L116
41 Nuclear repulsion energy
42 T (length of correction of reference determinant)
43 Updated energy for optimizations
44 <S2 > of SCF wave function
45 <S2 > corrected to first order (after DOUBAR)
46 <S2 > corrected for doubles (not implemented)
47 A0
48 Used to accumulate energy during Opt=Simult
49 Temperature for thermochemistry
50 Pressure for thermochemistry
51 Scale factor for frequencies in thermochemistry
52 Nuclear repulsion contribution from inactive atom pairs
53 Singles contribution to E2 in ROMP2
54 E(2) with current orbitals for extrapolation
55 Nuclear term in the reaction field energy
56 Electronic term in the reaction field energy
57 Curvature from projected frequency jobs
58 Reaction coordinate for single-points along IRCs
59 Flag for status from external programs; see RunExt.
60 SCF energy at first iteration
61 Job status: -1=in progress; 0=undefined/old chk file; 1=finished successfully;
2=step in multi-step job completed successfully; 3=error termination in Link 9999
62 Highest order of nuclear coordinate derivatives available.
63 Number of iterations in most recent SCF.
64 Nuclear repulsion energy without external field contribution.

E.4 FChk File

This file is designed to be machine independent with a structure that makes it easy for post-processors to
extract required data and ignore the remainder. The latter fact is important for extensibility as future additions
will not interfere with applications designed for previous revisions. Typically a job is run specifying a .chk file,
which is the binary file containing results from a calculation which are potentially useful in later calculations or
for post-processing, and then after Gaussian has completed, the formchk utility is run to generate the text .fchk
file from the binary .chk file. There is also a utility, unfchk, to reverse the process. For backwards compatibility,
running formchk without any options produces a subset of the full information. This document describes the
results of running formchk -3 chkfile fchkfile, which produces a version 3 formatted checkpoint file (the current
E.4 FChk File 407

and most full-featured version).

Here is a description of the data in Fortran formatted form, although there is no particular reason to use
Fortran as opposed to other languages to read the data.
The first two lines in the file contain strings describing the job:

Initial 72 characters of the title section. Complete route and title appear later.
Type, Method, Basis Format: A10,A30,A30

Type is one of the following keywords:

SP Single point
FOPT Full optimization to a minimum
POPT Partial optimization to a minimum
FTS Full optimization to a transition state
PTS Partial optimization to a transition state
FSADDLE Full optimization to a saddle point of order 2 or higher
PSADDLE Partial optimization to a saddle point of order 2 or higher
FORCE Energy+gradient calculation
FREQ Vibrational frequency (2nd derivative) calculation
SCAN Potential surface scan
GUESS=ONLY Generate molecular orbitals only, also used with localized orbital generation
LST Linear synchronous transit
STABILITY Test of SCF/KS stability
REARCHIVE/MS- Generate archive information from checkpoint file
RESTART
MIXED Mixed method model chemistry (CBS-x, G1, G2, etc.), with method and basis set
implied by model

Method is the method of computing the energy (AM1, RHF, CASSCF, MP4, etc.), and Basis is the basis
set.
All other data contained in the file is located in a labeled line/section set up in one of the following forms:
♢ Scalar values appear on the same line as their data label. This line consists of a string describing the data
item, a flag indicating the data type, and finally the value:
• Integer scalars: Name,I,IValue, using format A40,3X,A1,5X,I12.
• Real scalars: Name,R,Value, using format A40,3X,A1,5X,E22.15.
• Character string scalars: Name,C,Value, using format A40,3X,A1,5X,A12.
• Logical scalars: Name,L,Value, using format A40,3X,A1,5X,L1.
♢ Vector and array data sections begin with a line naming the data and giving the type and number of
values, followed by the data on one or more succeeding lines (as needed):
• Integer arrays: Name,I,Num, using format A40,3X,A1,3X,’N=’,I12. The N= indicates that this is
an array, and the string is followed by the number of values. The array elements then follow starting
on the next line in format 6I12.
• Real arrays: Name,R,Num, using format A40,3X,A1,3X,’N=’,I12, where the N= string again in-
408 Chapter E. Interfacing to Gaussian 16 (v2)

dicates an array and is followed by the number of elements. The elements themselves follow on
succeeding lines in format 5E16.8. Note that the Real format has been chosen to ensure that at least
one space is present between elements, to facilitate reading the data in C.
• Character string arrays (first type): Name,C,Num, using format A40,3X,A1,3X,’N=’,I12, where the
N= string indicates an array and is followed by the number of elements. The elements themselves
follow on succeeding lines in format 5A12.
• Character string arrays (second type): Name,H,Num, using format A40,3X,A1,3X,’N=’,I12, where
the N= string indicates an array and is followed by the number of elements. The elements them-
selves follow on succeeding lines in format 9A8.
• Logical arrays: Name,L,Num, using format A40,3X,A1,3X,’N=’,I12, where the N= string indicates
an array and is followed by the number of elements. The elements themselves follow on succeeding
lines in format 72L1.
All quantities are in atomic units and in the standard orientation, if that was determined by the Gaussian
run. Standard orientation is seldom an interesting visual perspective, but it is the natural orientation for the
vector fields. The field names are fairly verbose to make them informative and should not be an impediment as
only the interface program needs to use them. An example program, demofc, is distributed with Gaussian and
demonstrates how to extract a named field.

Basis Set Data

The basis set information is provided in a reasonably general way which does not assume the specific
structure of Gaussian’s Common /B/, which is rather obscure and reflects history more than clarity. The basis
set data will include scalars giving the number of shells (NShell), largest degree of contraction, highest angular
momentum present, and number of primitive shells (NPrim). There will then be arrays containing:
♢ Shell types (NShell values): 0=s, 1=p, -1=sp, 2=6d, -2=5d, 3=10f, -3=7f
♢ Number of primitives per shell (NShell values).
♢ Shell to atom map (NShell values): number of the atom on which each shell is located.
♢ Primitive exponents (NPrim values).
♢ Contraction coefficients (NPrim values): contraction coefficients of each normalized primitive shell.
Contains the S coefficient for any S=P shells.
♢ P(S=P) Contraction coefficients (NPrim values): contraction coefficients for p portions of S=P shells.
Not present if there are no S=P shells. Contains zeros for every primitive which is not part of an S=P
shell.
♢ Coordinates of each shell: (3,NShell) array of XYZ coordinates for each shell.
Other data, such as basis function indexing arrays, are easily derived from the above. The order of basis
functions within shells is the usual Gaussian order:
S,X,Y,Z,XX,YY,ZZ,XY,XZ,YZ,XXX,YYY,ZZZ,XYY,XXY,XXZ,XZZ,YZZ,YYZ,XYZ
or
3ZZ-RR,XZ,YZ,XX-YY,XY,ZZZ-ZRR,XZZ-XRR,YZZ-YRR,XXZ-YYZ,XYZ,XXX-XYY,XXY-YYY

Available Items

The following items are among those currently defined:

♢ Route
E.4 FChk File 409

♢ Full Title
♢ Number of atoms
♢ Charge
♢ Multiplicity
♢ Number of electrons
♢ Number of alpha electrons
♢ Number of beta electrons
♢ Number of basis functions
♢ Number of contracted shells
♢ Highest angular momentum
♢ Largest degree of contraction
♢ Number of primitive shells
♢ Virial Ratio
♢ Atomic numbers
♢ Nuclear charges
♢ Current Cartesian coordinates
♢ Alpha Orbital Energies
♢ Beta Orbital Energies
♢ Alpha MO coefficients
♢ Beta MO coefficients
♢ Shell types
♢ Number of primitives per shell
♢ Shell to atom map
♢ Primitive exponents
♢ Contraction coefficients
♢ P(S=P) Contraction coefficients
♢ Coordinates of each shell
♢ Total SCF Density
♢ Spin SCF Density
♢ Total MP2 Density
♢ Spin MP2 Density
♢ Total CI Density
♢ Spin CI Density
♢ Total CC Density
♢ Spin CC Density
♢ Cartesian Forces
♢ Cartesian Force Constants
♢ Dipole Moment
♢ Dipole Derivatives
♢ Polarizability
♢ Dipole 2nd Derivatives
 410 Chapter E. Interfacing to Gaussian 16 (v2)

♢ Polarizability Derivatives
♢ HyperPolarizability

E.4.1 Formatted Checkpoint File FAQ

Which energy should be used by default?
The Total Energy field has the energy at whatever level of theory the user requested. This is so other
programs don’t have to figure out where the energy is from the Method string. In particular, we can add
new methods and you won’t have to change logic to find the energy you’ll normally want.
Why does the field descriptor include the data type information?
The purpose of including the data type for each field is to facilitate skipping that field if it’s not of interest,
as illustrated in the demo program below.
How are ECP atomic charges handled?
The “Nuclear charges” will differ from the atomic numbers if ECPs are in use.
Which density matrix will be present?
The total density will always be present; the spin density will be stored only for open-shell systems. By
default this will be the SCF density. If a post-SCF density is desired, include the Density keyword in the
Gaussian input.
When will force constants be present?
The force constants may be present and zero for cases for which only first derivatives were actually
computed, or when they were computed at the first point of a geometry optimization but not at later
points. They should only be used for vibrational analysis if the job type is Freq.
Why is there no mapping array between shells and primitives?
It was pointed out that the mapping from shells to primitives is not made explicit, so that the primitive
data is stored separately for every atom, even if some have the same basis set. The information that atoms
have the same basis set is discarded early in Gaussian. The basis set is only of interest if the orbitals or
density is also used. Since the latter are quadratic in the size of the molecule, the potential savings for
large molecules from removing redundant primitives seemed modest.

E.5 Example FChk File

Here is an example formatted checkpoint file for an APFD/6-311+G(2d,p) energy calculation on HOF:
Example
SP RAPFD 6-311+G(2d,p)
Number of atoms I 3
Info1-9 I N= 9
8 8 0 0 0 111
1 18 -402
Full Title C N= 1
Example
Route C N= 4
#p apfd/6-311+g(2d,p) geom=modela test
Charge I 0
Multiplicity I 1
Number of electrons I 18
 E.6 License 411

Number of alpha electrons I 9

Number of beta electrons I 9
Number of basis functions I 60
Number of independent functions I 60
Number of point charges in /Mol/ I 0
Number of translation vectors I 0
Atomic numbers I N= 3
8 9 1
Nuclear charges R N= 3
8.00000000E+00 9.00000000E+00 1.00000000E+00
Current cartesian coordinates R N= 9
9.50213801E-02 1.30811042E+00 -4.93038066E-32 9.50213801E-02 -1.37530068E+00
4.93038066E-32 -1.61536346E+00 1.91282278E+00 -4.93038066E-32
Number of symbols in /Mol/ I 0
···
See http://gaussian.com/interfacing/ for the full content.

E.6 License
Gaussian Interface Code Open Source Public License, v. 1.0
Based on the Mozilla Public License version 2.0
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This version of the interface package:
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25 February 2018: Version 1.1 for Gaussian 16 Rev B.01
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416 Chapter G. Gaussian 16 FAQs

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