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NORTH LAKHIMPUR COLLEGE (AUTONOMOUS)
A Project Report On-
THEORETICAL STUDIES OF FEW MOLECULES
Submitted to:-
Department of Chemistry
For Partial Fulfilment of the requirement of Certificate Course in-
“Analytical & Computational Chemistry”
Submitted By:-
ANKUR BISWAKARMA
B.Sc. 6Th Semester
Roll No: 15BS160
NORTH LAKHIMPUR COLLEGE (AUTONOMOUS)
DEPARTMENT OF CHEMISTRY
Dr. Raghab Parajuli
M.Sc. (Ph.D.)
Assistant Professor
Assam
CERTIFICATE
This is to certify that the Project Report entitled “THEORETICAL STUDIES
OF FEW MOLECULES” submitted by “ANKUR BISWAKARMA, 6th Semester,
Department of Chemistry”, North Lakhimpur College (Autonomous) has been
completed under my supervision at the Department of Chemistry, North
Lakhimpur College (Autonomous) for partial fulfillment of the Bachelor of
Science in Chemistry under Dibrugarh University.
(Mr. Diganta Kalita) (Dr. Raghab Parajuli)
Head Supervisor
Department of Chemistry
North Lakhimpur College (Autonomous)
Date:
ACKNOWLEDGEMENT
I would like to warmly acknowledge and express my deep sense of
gratitude and indebtedness to the supervisor of the project work Dr. Raghab
Parajuli Sir, who helped us a lot and guided properly to complete this dissertation.
I would like to thank the faculty members of Department of Chemistry,
North Lakhimpur College (Autonomous) for allowing me to complete this project
work in the computer laboratory and for their cooperation.
Date:……/……../………… DEPARTMENT OF CHEMISTRY
NORTH LAKHIMPUR COLLEGE (AUTONOMOUS)
CONTENTS:
1. Introduction
1.1. Introduction to Computational Chemistry
1.2. The necessity of Computational Chemistry
1.3. Different Methods of Theoretical Calculations
1.4. Basis Set:
1.5. History
2. Present Work
2.1. Study of BF3
2.2. Study of C2H2
2.3. Study of c2H4
2.4. Study of C6H6
2.5 Study of CH3 Free Radical
2.6. Study of CH3-
2.7. Study of CH3+
2.8. Study of CH4
2.9. Study of H2O
2.10. Study of NH3
3. Discussions
4. Conclusion
5. References
Theoretical studies of few important molecules using Ab-initio Hartree Fock
(HF) and Density function Theory (DFT) methods.
1. INTRODUCTION:
1.1. INTRODUCTION TO COMPUTATIONAL CHEMISTRY:
Chemistry is the science dealing with construction, transformation, and
properties of molecules. The term theoretical chemistry may be defined as the
mathematical description of chemistry where mathematical methods are
combined with fundamental laws of physics to study processes of chemical
relevance.
Currently, there are two ways to approach theoretical chemistry problems.
Computational theoretical chemistry and non-computational theoretical
chemistry.
The term computational chemistry is usually used when a mathematical
method is sufficiently well developed that it can be automated for
implementation on a computer. Computational chemistry is the application of
chemical, mathematical and computing skills to the solution of interesting
chemical problems. It uses computers to generate information such as properties
of molecules or simulated experimental results. Very few aspects of chemistry can
be computed exactly, but almost every aspect of chemistry has been described in
a qualitative or approximate quantitative computational scheme. The biggest
mistake that computational chemists can make is to assume that any computed
number is exact. However, just as not all spectra are perfectly resolved, often a
qualitative are approximate computation can give useful insight into chemistry if
we understand what it tells us and what it doesn’t.
Computational chemistry has become a useful way to investigate material
that is too difficult to find or too expensive to purchase. It also helps chemists to
make predictions before running the actual experiments so that they can be
better prepared for making observations.
1.2. THE NECESSITY OF COMPUTATIONAL CHEMISTRY:
Computational chemistry has become very useful to investigate for those
materials which are too expensive to buy or difficult to obtain. It helps chemists
to predict before running the actual experiments so that they can be better
prepared for making observations.
Using the chemistry software following particulars can be performed –
• Electronic structure determinations,
• Geometry optimizations,
• Frequency calculations,
• Definition of transition structures and reaction paths,
• Protein calculations, i.e. docking,
• Electron and charge distributions calculations,
• Calculations of potential energy surfaces (PES),
• Calculations of rate constants for chemical reactions (kinetics)
• Thermodynamic calculations- the heat of reactions, the energy of activation, etc.
• Calculation of many other molecular and balk physical and chemical properties.
1.3. DIFFERENT METHODS OF THEORETICAL CALCULATIONS:
The most important numerical techniques are Ab-initio, semi-empirical
and molecular mechanics.
a) Ab initio Method:
The term “Ab initio” is a Latin word which means “From the beginning“. This
name is given to computations which are derived directly from theoretical
principles, with no inclusions of experimental data.
The most common and simplest type of Ab initio electronic structure
calculations is calle3d Hartree Fock scheme, an extension of molecular orbital
theory in which the correlated electron-electron repulsion is not especially taken
into account, only its average effect is included in the calculations.
The energy calculated are usually in units called Hartree (1H=27.2114 eV)
and approximate energies calculated are all equal and greater than the exact
energy.
b) Density Functional Theory (DFT) Method:
According to DFT, the electronic energy (E) is expressed as a function
of electron density and is denoted as E[p]. As against a function in which a basic
variable is a number, for example, f(x) = sin x is a function of x, in the functional,
the basic variable is a function and there is a one to one correspondence between
the variable and the functional:
The expectation value of energy
E[] ( H d ) /( d )
The advantage with the DFT method is that the central quantity of interest
in it is electron density which is a 3D quantity, in place of wave function which is
3N dimensional, N being the number of electrons.
c) Semi-Empirical and Empirical Method:
Semi-empirical calculations are set up with the same general structures as
HF calculations. Within this framework, certain pieces of information, such as two-
electron integrals are approximately or completely omitted.
In order to correct for the errors introduced by omitting part of the
calculation, the parameterized, by curve fitting in a few parameters or numbers, in
order to give best possible agreement with experimental data.
The good side of semi-empirical calculations is that they are much faster
than the Ab-initio calculations. The bad side of semi-empirical calculations is that
the results can be erratic. If the molecule under study is similar to molecules in
the database used to parameterize the method, then the results may be very
good. If this molecule is significantly different from anything in the
parameterization set, the answers may be poor. Semi-empirical calculations have
been very successful in computational organic chemistry, where there are only a
few elements used extensively and the molecules are of moderate size. However,
semi-empirical methods have been devised specifically for the description of
inorganic chemistry as well. Molecular mechanic approach: If a molecule is too
big to effectively use a semi-empirical treatment, it is still possible to model its
behavior by avoiding quantum mechanics. This is done by constructing a simple
expression for “molecular force field”, i.e. the potential energy as a function of all
atomic positions, and using it study molecular properties without the need to
compute a wave function or total electron density. The energy expression
consists of simple classical
Equations, such as the harmonic oscillator equation in order to describe
the energy associated with bond stretching, bending, rotation and
intermolecular forces, such as Van
1.4. BASIS SET:
A basis set in theoretical and computational chemistry is a set of functions (called
basis functions) that is used to represent the electronic wave function in the
Hartree–Fock method or density-functional theory in order to turn the partial
differential equations of the model into algebraic equations suitable for efficient
implementation on a computer. In principle, a complete (infinite) basis set should
be used for high accuracy. But in practice, the finite basis set is used.
Several types of atomic orbitals can be used: Gaussian-type orbitals, Slater-type
orbitals, or numerical atomic orbitals. Out of the three, Gaussian-type orbitals are
by far the most often used, as they allow efficient implementations of Post-
Hartree–Fock methods.
1. Slater Type Orbitals (STO) basis set
2. Gaussian Basis set
1. STO:
Atomic orbital to be used for high accuracy in calculations should be
a linear combination of several Slater Type Functions. However, at the
minimum, one may choose a set of STOs, one for each occupied orbital.
Such a basis set is called “Minimal Basis Set”. For example, in H2O molecule,
the minimal basis set consists of five STOs for 1s, 2s, 2px, 2py, 2pz of oxygen
and two 1s STOs for two hydrogen atoms.
2. GAUSSIAN BASIS:
Boys (1950) proposed the use of Gaussian type function in place of
STO. A Gaussian function at a point centered around atom A is defined as
q
X G N xA y e Aar2
p r
A z A
Where N is normalized constant; x, y, z are Cartesian coordinates of the
point (p, q, r) are small positive integers including zero, ‘a’ is a variable
parameter, ‘r’ is the radial distance of the point from the nucleus A.
* Pople basis sets:
The notation for the split-valence basis sets arising from the group of John Pople
is typically X-YZg. In this case, X represents the number of primitive Gaussians
comprising each core atomic orbital basis function. The Y and Z indicate that the
valence orbitals are composed of two basis functions each, the first one
composed of a linear combination of Y primitive Gaussian functions, the other
composed of a linear combination of Z primitive Gaussian functions. In this case,
the presence of two numbers after the hyphens implies that this basis set is a split-
valence double-zeta basis set. Split-valence triple- and quadruple-zeta basis sets
are also used, denoted as X-YZWg, X-YZWVg, etc. Here is a list of commonly used
split-valence basis sets of this type:
3-21G
3-21G* - Polarization functions on heavy atoms
3-21G** - Polarization functions on heavy atoms and hydrogen
3-21+G - Diffuse functions on heavy atoms
3-21++G - Diffuse functions on heavy atoms and hydrogen
3-21+G* - Polarization and diffuse functions on heavy atoms
3-21+G** - Polarization functions on heavy atoms and hydrogen, as well
as diffuse functions on heavy atoms
4-21G
4-31G
6-21G
6-31G
6-31G*
6-31+G*
6-311G
6-311G*
The 6-31G* basis set (defined for the atoms H through Zn) is a valence double-
zeta polarized basis set that adds to the 6-31G set six d-type Cartesian-Gaussian
polarization functions on each of the atoms Li through Ca and ten f-type
Cartesian Gaussian polarization functions on each of the atoms Sc through Zn.
Pople basis sets are somewhat outdated, as correlation-consistent or
polarization-consistent basis sets typically yield better results with similar
resources. Also note that some Pople basis sets have grave deficiencies that may
lead to incorrect results.
1.5 HISTORY:
Building on the founding discoveries in the history of quantum
mechanics, the first theoretical calculation in the chemistry were those of Walter
Heitler and Fritz London in 1927.
With the development of computer technology in 1940, the solution of
the elaborate wave equation for complex atomic system began to the realizable
objective.
In the early 1950s, the first empirical atomic orbital calculations were
carried out. The first Ab initio Hartree Fock calculations on diatomic molecules
were carried out in 1556s at MIT using a basis set of Slater orbitals. For diatomic
molecules, a systematic study using a minimum basis set and first calculation with
a larger basis set were published by Rancil and Nesbet respectively in 1950.
In the early 1970s, efficient Ab initio computer programs such as ATMOL,
Gaussian, IBMOL, and POLYAYTOM, began to be used to speed up Ab initio
calculation of molecular orbitals. Of these four programs, only Gaussian is now
widely expanded.
The journal of computational chemistry was first published in 1980.
DISCUSSIONS:
By observing the above data (those obtained from computational methods) and
comparing with the values that provided by Literature, the following conclusions can be
drawn-
1. DFT always gives the lowest energy for all the molecules. So we may conclude that
structure of molecule obtained from DFT is more stable than those obtained from other
methods.
2. It is found that in case of most of the molecules (studied for this Project Work), values
of bond length obtained from all four methods are close to the standard one. In case
of C2H4, all the methods give quite good results for the C=C bond. However, DFT gives
the closest value to the standard value. It is also found that in case of C2H2, H2O
molecules, DFT gives highest accurate values of bond lengths than other methods.
But in case of NH3, it is not same i.e. DFT does not give the most appropriate value
of bond length, but HF method using 6-31G** basis set calculate the closest value to
standard one.
3. In case of C6H6, CH3 [Free Radical], C2H4, C2H2, CH4 molecules, the dipole moment is
found 0.0000 Debye which is consistent with Literature Value.
In case of H2O, the values of dipole moment that obtained from the four methods HF/6-
31G**, HF/6-31G, HF/STO-3G, B3LYP/6-31G** are 2.1481 Debye, 2.5005 Debye, 1.7092
Debye, 2.0424 Debye respectively. And literature provides that the dipole moment of
H2O is 1.8546 Debye; so in case of HF method using STO-3G basis set, the value of dipole
moment is closest to the standard one.
In case of NH3, HF method using 6-31G basis set gives the closest value to the
standard one. It may indicate that in case of polar molecules HF method using suitable
basis sets give more accurate value.
3. CONCLUSION:
From the study of the given molecules following conclusions can be drawn
–
The structure of a molecule from 631-G** is the most stable.
The bond angles of a molecule in the three basic sets are almost
equal, but those in case of 631-G** and 631-G are more close to each
other. Similar in the case of bond length too.
Dipole moment values are equal in all the three basic sets.
4. REFERENCES:
Computational Chemistry- Wikipedia
Introduction to Computational Chemistry- CCL.net
Computational Chemistry using PC, 3rd Edition, Donald W. Rogers,
Published by John Wiley & Sons, Inc., 2003.
Essentials of Computational Chemistry: Theories and Models, 2nd
edition Christopher J Cramer, Published by John Wiley & Sons, Inc.,
2004.
Introduction to Computational Chemistry, Second Edition, Frank
Jensen, Published by John Wiley & Sons, Inc., 2007.
Theory and Applications in Computational Chemistry: The First Decade
of the Second Millennium, Pavia, Italy.
Published by: American Institute of Physics, 2012.
Quantum Chemistry, (5th Edition), Ira N Levine, Published by Prentice
Hall (1999).
Fundamentals of Computational Chemistry: A Guide for Organic
Chemists, Hui-Wen Shih, MacMillan Group Meeting, June 17, 2009.
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