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Quantum Chemical Study of the

Interaction of Nitrate Anion with Water

CHRISTOPH EBNER, ROLAND SANSONE, MICHAEL PROBST

Institute of General and Inorganic Chemistry, Innsbruck University, Innrain 52a,
A-6020 Innsbruck, Austria

Received 29 March 1998; revised 29 June 1998; accepted 10 July 1998

ABSTRACT: The interaction between nitrate anion and water has been investigated
by Hartree᎐Fock calculations with the 6-311 q GŽd, p. basis set and by B3LYP density
functional calculations with the aug-cc-pVTZ basis set. It is found that the global energy
minimum is a planar configuration where both hydrogen atoms of water are coordinated
to two oxygen atoms of NOy 3 by distorted hydrogen bonds. In contrast to former studies
on NOy 3 rH 2 O this configuration is found to be asymmetric at the highest theoretical
level employed. The corresponding structure with C2 v symmetry is a saddle point at
slightly higher energy. A singly hydrogen-bonded configuration is still about 2.4 kcalrmol
higher in energy. The shifts in the vibrational frequencies of water and nitrate upon
complexation were calculated. A compact analytical potential function of NOy 3 rH 2 O for
use in statistical thermodynamic simulations was obtained from 390 points of the energy
surface and an intramolecular force field for the nitrate anion is presented. 䊚 1998 John
Wiley & Sons, Inc. Int J Quant Chem 70: 877᎐886, 1998

Key words: potential functions; nitrate anion; nitrate-water interaction; nitrate-water

cluster geometries; vibrational frequencies

in the third section its vibrational behavior. An

Introduction analytical function representing the energy surface
of NOy 3 rH 2 O as well as an intramolecular poten-
tial function for NOy 3 are derived in the fourth

T his work is organized as follows: First, we

discuss relevant previous works. In the sec-
ond section we present the energetic and confor-
section.
Because of their great chemical, biological, and
technical importance, many experimental studies
mational properties of the system NOy
3 rH 2 O and have focused on elucidating the properties of
aqueous nitrate solutions. Specifically, articles in-
Correspondence to: M. Probst.
Contract grant sponsor: Austrian FWF. vestigating the structure of nitrate solutions by
Contract grant number: P10106-MOB. various spectroscopic techniques under a variety

International Journal of Quantum Chemistry, Vol. 70, 877᎐886 (1998)

䊚 1998 John Wiley & Sons, Inc. CCC 0020-7608 / 98 / 040877-10
EBNER, SANSONE, AND PROBST

of conditions have been published Ž vide infra.. In

contrast, rather few quantum chemical studies The NO 3y / H 2 O Complex
dealing with the properties of NOy 3 were reported.
It has been found that NOy 3 can serve as a Geometry optimizations of the nitrate᎐water
sensitive probe of the molecular environment, es- complex with all degrees of freedom included have
pecially via vibrational spectroscopy. The experi- been performed at the HFr6-311G q Žd, p. w 15, 16x
mental evidences are, for example, reviewed in and B3LYPraug-cc-pVTZ w 17x levels. Different
great detail in w 1x . Other important reviews include starting geometries always resulted in one of two
w 2x and w 3x . The rotational behavior of NOy 3 was minima on the potential hypersurface. While this
also investigated by nuclear magnetic resonance is no proof of the nonexistence of other minima,
ŽNMR. spectroscopy w 4, 5x . The easy distortion of
the symmetric structure of NOy 3 makes it plausi-
the D 3 h symmetry of the anion causes shifts and ble that no other minima exist. Our investigations
splitting of the vibrational bands as well as changes included, for example, a nonplanar configuration
in their intensity. This topic is discussed together
with C2 v symmetry which is a saddle point, bifur-
with the results of our frequency calculations in
cated structures with two hydrogen atoms adja-
the following section.
cent to one oxygen of NOy 3 , and structures with
One of the first theoretical studies on the system
water on top or below the plane of the anion. All
NOy 3 rH 2 O was performed by Howell et al. 6 .
w x
of them do not constitute local minima as well.
With Hartree᎐Fock calculations and the 6-31G ba-
However, as discussed below, generally only small
sis set, a cyclic structure with two distorted hydro-
energy differences between various configurations
gen bonds was found to be most stable with a
are found and point to the fact that parts of the
binding energy of y18.49 kcalrmol versus y17.23
potential surface are very shallow.
kcalrmol for a singly hydrogen-bonded one.
The global minimum is a cyclic structure with
In Ref. w 7x the system NOy 3 rH 2 O was studied
two hydrogen bonds. The exact structure of this
by Hartree᎐Fock calculations and compared with
the isomeric form ONOOyrH 2 O Žas well as with configuration, however, differs between HFr6-
H 2 NO4y in a subsequent study w 8x. . The largest 311G q Žd, p. and B3LYPraug-cc-pVTZ calcula-
basis set used by them was a double zeta basis set tions. The former method leads to a structure with
with polarization functions w 9x . The authors find, C2 v symmetry similar as in w 7x and w 6x with a
similar to w 6x , the global minimum in a planar binding energy of y14.0 kcalrmol, while at the
conformation with C2 v symmetry and two strongly B3LYPraug-cc-pVTZ level the corresponding pla-
bent hydrogen bonds with a binding energy of nar configuration with C2 v symmetry exhibits one
y14.9 kcalrmol. imaginary frequency. If optimized without sym-
Velders and Feil w 10x studied changes in elec- metry constraints, the B3LYPraug-cc-pVTZ dimer
tronic density and geometry of nitrate anion in the is asymmetric and y0.1 kcalrmol lower in energy
presence of a proton and could correlate them with Žy14.5 and y14.4 kcalrmol, respectively.. Figure
experimental crystal geometries. In a related study, 1Ža. shows that despite the small energy difference
Probst w 11x calculated properties of various NOy 3 r
the deviation from C2 v symmetry is not negligible
M nq ion pairs and the intramolecular vibrational and the structure can even be viewed as an inter-
frequency shifts caused by the counterions. The mediate between a cyclic structure and a singly
binding sites and the frequency shifts were found hydrogen-bonded one. The singly hydrogen-
to depend on the size of the cation. bonded structure shown in Figure 1Žb. is q1.9
A computer simulation involving an aqueous kcalrmol higher in energy Žy12.6 kcalrmol. and
silver nitrate solution was performed by Laakso- is found to be a local minimum on the potential
nen and Kovacs w 12x . They used a rigid model with energy surface. The distance between the oxygen
a Lennard-Jones force field for the nitrate and the atom of water and the nitrogen is more than 0.3 A ˚
rigid SPC water model. Another molecular dynam- larger for the singly bonded configuration Ž3.355
ics simulation was performed by Kataoka w 13x with and 3.703 A ˚ ..
the Carravetta᎐Clementi water model and an em- A comparison between optimized monomers
pirical potential for the nitrate interactions. A se- ˚ rO — H : 0.962 A,
Ž r N — O : 1.258 A, ˚ and ⬔ H — O — H :
ries of molecular dynamics simulations investigat- 105.1⬚. and the dimers Žvalues given in Fig. 1.
ing the dynamics of NOy 3 in molten salts has been exhibits only small geometric changes with the
published by Kato et al. w 14x . exception of ⬔ H — O — H for the global minimum

878 VOL. 70, NO. 4 / 5

 INTERACTION OF NITRATE ANION WITH WATER

FIGURE 1. Geometries optimized at the B3LYPraug-cc-pVTZ level. (a) Global minimum and (b) second energy
minimum.

configuration which decreases by 6.2⬚. The largest ing mode Ž ␯s s ␯ 1 ., two degenerate asymmetric
change in one of the ⬔ O — N — O angles is less than stretching modes Ž ␯as s ␯ 3 ., two degenerate bend-
1⬚ and the largest changes in r N — O and rO — H ing modes Ž ␦as s ␯4 ., and one out-of-plane mode
bond lengths are q0.013 and q0.025 A, ˚ respec- Ž ␯oop s ␯ 2 .. While the occurrence of the splitting of
tively. It can be seen that the values of rO — H the ␦as and ␯as vibrations in an asymmetric envi-
correspond to the ability of the corresponding ronment is therefore easy to understand in princi-
atoms to participate in hydrogen bonding. ple, there is yet no concise explanation why this
symmetry lowering can even readily be observed
in dilute aqueous solutions w 1, 2x . Ion pair forma-
Vibrations of Nitrate Anion
tion can be ruled out experimentally because the
and NO 3y/ H 2 O splitting is largely independent of concentration
As already mentioned above, nitrate anion is an and cation. An explanation by assuming specific
extremely useful molecule for probing the molecu- hydrogen bonding between the anion and its hy-
lar environment, especially via its vibrational be- dration shell has the drawback that the splitting is
havior. This stems partially from the fact that NOy neither found in deuterated H 2 O nor in other
3 ,
due to its high symmetry, is a ‘‘ vibrationally defi- solvents with strong hydrogen bonding to NOy 3 .

cient’’ molecule. Symmetry lowering from D 3 h to Table I gives a comparison of various theoreti-
C2 v can occur easily, leading to infrared ŽIR. and cal methods with experiments. The experimental
Raman band splitting and intensity changes. Also values were derived from measurements in solu-
IR, Raman, and the ultraviolet ŽUV. intensities of tion. It can be seen that a high theoretical level and
its electronic transitions depend much on the envi- large basis set is needed and that the B3LYP val-
ronment, but this shall not be studied further here. ues are closer to the experiment than the more
As a tetraatomic molecule, nitrate anion exhibits expensive MP4 results. Keeping in mind that ex-
six vibrational modes: A total symmetric stretch- perimentally the typical half-height linewidth of

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 879

EBNER, SANSONE, AND PROBST

TABLE I
Vibrational frequencies of nitrate anion (cm y1).

Method E X ( ␦as ) A2Y ( ␯oop ) A1X ( ␯s ) E X ( ␯as )

NO 3y
MP4raug-cc-pVTZ 689 816 996 1379
B3LYPraug-cc-pVTZ 707 844 1062 1364
BLYPraug-cc-pVTZ 663 783 978 1240
MP4(SDQ)rMIDI + ** 705 842 1056 1369
HFrMIDI + ** 781 959 1200 1516
NO 3yrK +
HFrMIDI + ** 785, 796 945 1183 1453, 1688
MP4(SDQ)rMIDI + ** 713, 720 832 1029 1263, 1518
NO 3yrH 2 O
B3LYPraug-cc-pVTZ 712, 718 841 1062 1341, 1402
Solution
IR, Raman [19] 719 825 1049 1348, 1404
IR, Raman [18] 720 825 1050 1345, 1400

the peaks is 50 cmy1 , the B3LYPraug-cc-pVTZ a rather weak cation like Kq causes a larger split-
values seem very reasonable. The largest deviation ting in the ␯as band. In accordance with experi-
from the experimental values is 19 cmy1 for ␯oop ment, the splitting of the other degenerate band,
Žthe experimental value for the unperturbed ␯as is ␦as , is much smaller.
about 1380 cmy1 w 18x. .
In the optimized NOy 3 rH 2 O complex global
Ž
minimum., the coordination of water leads to a Potential Energy Functions
splitting of the degenerate asymmetric stretching
modes at 1364 cmy1 into 1341 and 1402 cmy1 and A calculation of the energy surface of NOy 3 r
of the two degenerate asymmetric bending modes H 2 O was performed at the Hartree᎐Fock level
at 707 cmy1 into 712 and 718 cmy1 ŽB3LYPraug- with the 6-311 q GŽd, p. basis set. This method
cc-pVTZ values.. The out-of-plane and the sym- was chosen in view of the large computational
metric stretching modes remain Žnearly. un- effort involved in the more accurate B3LYPr aug-
changed at 844 and 1062 cmy1 . These splittings are cc-pVTZ calculations. Despite the fact that, as dis-
very similar to the experimental values from cussed above, a symmetric global minimum struc-
Table I. ture results at the 6-311 q GŽd, p. level, the actual
In order to be able to compare these frequency binding energies of both methods are very close
splittings from hydrogen bonding with the split- and, for example, comparable to the approxima-
tings caused by symmetry lowering from ion pair tions introduced by assuming rigid monomers.
formation, corresponding calculations were per- w The HFr6-311G q Žd, p. binding energy at the
formed on an NOy 3 rK
q
contact ion pair. The fre- global minimum obtained with rigid monomers is
quencies obtained with the MP4ŽSDQ. method and y13.67 kcalrmol versus y13.97 kcalrmol for a
the MIDI basis set augmented with diffuse and full optimization.x The intramolecular geometries
polarization functions each w 20x Žno aug-cc-pVTZ of water and nitrate anion were kept rigid at the
basis set for K has yet been published. are in- experimental values w 21x with r N — O s 1.220 A, ˚
cluded in Table I. With 255 cmy1 , a considerably ⬔ O — N — O s 120⬚, rO — H s 0.957 and ⬔ H — O — H s
larger splitting than for H 2 O was found for the ␯as 104.5⬚. No counterpoise correction has been ap-
mode. It is not unlikely that for a hydrated potas- plied since test calculations showed that for this
sium cation ion pair the spitting comes down to a basis set the superposition error at the global mini-
similar range than for H 2 O. mum is less than 4% of the binding energy.
It can be concluded that the magnitude of the Fifteen sets of configurations were chosen and
band splitting found in NOy 3 rH 2 O is comparable for each set 26 energy points were calculated by
to the experimental value in solution and that even moving the water molecule along a line. Due to

880 VOL. 70, NO. 4 / 5

 INTERACTION OF NITRATE ANION WITH WATER

the high symmetry of nitrate anion the resulting 13 both hydrogen atoms point away from it. Con-
390 energy points should sufficiently cover the figurations 14 Žlike 13 but the hydrogen atoms
representative regions of interaction. point toward N. and 15 Žlike 13 but with water
Figures 2Ža. and 2Žb. visualize some of the 15 below one oxygen atom of NOy 3
. are not shown.
configurations. The configurations which result by The binding energies corresponding to the vari-
water being rotated out of the nitrate plane by 90⬚ ous sets of configurations are shown in Figure 3
are not shown in order to avoid overcrowding the Žcircles. as a function of the N—O distance. As can
picture: In Figure 2Ža., configuration 2 is derived be expected from electrostatic considerations, con-
from configuration 1 Žnitrate anion and water are figurations 5, 6, 7, 11, and 15 are always repulsive.
in one plane and the atoms N—O ⭈⭈⭈ H—O are In 12, a hydrogen atom approaches NOy 3 from the
collinear. with water rotated around the N—O ⭈⭈⭈ top. The attraction from the oxygen atoms predom-
H—O axis by 90⬚. Configurations 4, 7, and 9 Žnot inates in this case and a shallow minimum is
shown. are derived in the same way from configu- found.
rations 3, 6, and 8, respectively. Configuration 5 is The 390 energy points were used to fit a polyno-
derived from configuration 9 but has the hydrogen mial with 4 adjustable parameters for each site᎐site
atoms pointing away from the nitrate anion. Con- interaction:
figurations in which the oxygen atom of water is
located out of the nitrate plane are shown in Fig- qk qi Ak i Bk i Ck i Dk i
Vfitnyw s Ý q q q q ,
ure 2Žb.. In configurations 10 and 11, the O ⭈⭈⭈ N k, i rk i r k4i r k6i r k8i r k9i
axis is inclined by 45⬚ out of the nitrate plane Ž1.
whereas in configurations 12 and 13 it is perpen-
dicular to it. In 10 and 12, one hydrogen atom where A to D are the parameters to be fitted, qk
points toward the nitrogen atom while in 11 and and qi are the partial charges at the centers of

FIGURE 2. Configurations considered in the scan of the potential energy surface. (a) Shows the configurations where
water oxygen atom is in the nitrate plane and (b) shows the out-of-plane configurations. See text for further
explanations.

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 881

EBNER, SANSONE, AND PROBST

FIGURE 3. Calculated energy points (symbols) and fitted energies (solid lines) for the 15 configurations plotted
˚
against the N ⭈⭈⭈ O interatomic distance. The energies are given in kcalrmol and the distances in Angstrøm.

interaction k and i in the two molecules, and r k, i and q0.717, respectively. The charges were kept
is their distance. A calculation of the q’s by constant in the fitting process. Their values, some-
CHELPG w 22x population analysis gave charges of what arbitrary as any charge partition scheme, are
q1.298 and y0.766 electrons for nitrogen and oxy- larger than the corresponding ones from CHELPG
gen, respectively. Since the potential function is Žy0.808 and q0.404, respectively. and are in-
intended to be used in computer simulations of tended to be effective charges for liquid water. The
aqueous nitrate solutions, for reasons of electro- values of the optimized parameters A to D are
static consistency the partial charges of the well- given in Table II.
known MCYL water potential w 23x were taken. For The overall standard deviation of the fit Žinclud-
O and H atoms of water the charges are y1.434 ing the electrostatic terms. was 1.17 kcalrmol.

TABLE II
˚ ) of the analytical pair potential for the nitrate – water interaction in
Values of the parameters (kcal / mol, A
formula (1).

On ᎐O w On ᎐H w N n ᎐O w N n ᎐H w

A 456.230953 y9.267009 y141.352593 y286.238598

B y14346.495583 509.57219 8378.086698 1710.782613
C 135881.693843 y1063.771480 y52972.399360 y4740.608610
D y163716.597217 654.054407 60790.249131 3454.023536

882 VOL. 70, NO. 4 / 5

 INTERACTION OF NITRATE ANION WITH WATER

ear hydrogen bonds and bifurcated ones. Finally,

the contour diagram at the bottom shows a set of
typical repulsive configurations.
The agreement between the calculated points
and the fitted potential as discussed above indi-
cates that our potential function is no worse than
comparable ion᎐water potentials published so far.
It can be assumed to be more reliable than poten-
tials constructed from standard molecular mechan-
ics parameters or combination rules. Since for our
system it describes a shallow energy surface with
subtle hydrogen bonding features, it should be
mentioned that its parameters are certainly not
transferable and that only subsequent computer
simulations can demonstrate its accuracy.
No intramolecular potential for NOy 3 seems to
have been described in the literature yet. In order
to be able to perform future simulation studies
with flexible nitrate anion, we prepared a simple
FIGURE 4. Correlation of all fitted energy points versus intramolecular potential function compatible with
Hartree᎐Fock energies (kcalrmol). the NOy 3 rH 2 O potential described above. A com-
parison of the quantum chemically calculated har-
monic spectrum with a force-field-based one was
Figure 4 shows a reasonably good correlation be- performed. The matrix of the second derivative of
tween ab initio and fitted energies. The solid curves the energy with respect to the Cartesian coordi-
in Figure 3 show the analytical potential. It can be nates was obtained by quantum chemical calcula-
seen that the important characteristics of the ab tions and was converted into a function of the six
initio potential curves can be found in the calcu- internal coordinates ⌬ r N — O , ⌬ ⬔ O — N — O and
lated potential. Configuration 8 includes the global ⬔ OOP where the ⌬ r and ⌬ ⬔ values are the devia-
minimum and shows that within the method used tions of the bond length and bond angles from the
and under the restriction of rigid monomers, a equilibrium values and ⬔ OOP is the out-of-plane
cyclic structure is somewhat more stable than angle describing the pyramidal distortion of NOy 3 .
a single hydrogen bonded one. Structures with It can be defined as 90⬚ minus the angle between
linear O—H ⭈⭈⭈ O—N hydrogen bonds Žconfigura- the vector perpendicular to the O1 —N—O 2 plane
tions 1 and 2. are about as stable as the corre- and the vector from N to O 3 :
sponding configurations where the nitrate mole-
cule is turned by 60⬚ and O—H points to the 6 6
bisector of O—N—O Žconfigurations 3 and 4.. If Vintra s 1
2 Ý f i i Di Di q Ý f i j Di Dj . Ž2.
is1 i/js1
the nitrogen atom is directly involved, the bonding
is much weaker Žconfiguration 12..
Figure 5 shows two-dimensional cuts of the Here the three distances ⌬ r, the two independent
potential energy surface in the plane of NOy 3 for angular internal coordinates ⌬ ⬔, and the out-of-
three typical cases. In the left part the orientations plane angle Ž⬔ OOP . are abbreviated D1 ᎐D6 . This
of the water molecules are shown and in the right function was used in molecular dynamics calcula-
part the corresponding energy surface as contour tions, and the vibrational spectrum was subse-
plot. From the picture on top which includes the quently extracted from the trajectories of the atoms
configurations with two hydrogen bonds Žy13 by the usual Fourier-transform methods. The re-
kcalrmol contour., it can be seen that Žif water is sults showed that for NOy 3 even modest accuracy
thought to move around the anion. bifurcated hy- in reproducing intramolecular vibrational frequen-
drogen bonds are about 4᎐5 kcalrmol less stable. cies requires the inclusion of the terms in the
For the singly hydrogen-bonded structures ŽFig. 5 second sum in formula Ž2., the harmonic cross
middle., there is even less difference between lin- terms. On the other hand, the inclusion of anhar-

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 883

EBNER, SANSONE, AND PROBST

FIGURE 5. Contour plots of the nitrate ᎐water energy surface (right side) together with pictures of the respective water
orientations (left side) for three typical orientations. The water molecule is located in the plane of the nitrate anion. The
contour map on top contains the global energy minimum at the HFr6-311G + (d, p) level of theory.

884 VOL. 70, NO. 4 / 5

 INTERACTION OF NITRATE ANION WITH WATER

monicity has a much smaller effect as was found NOy 3 r H 2 O were calculated and are in good
by augmenting formula Ž2. by correction terms agreement with experimental results. The magni-
incorporating the first anharmonicities along the tude of the splitting of the asymmetric stretching
normal modes. The largest anharmonic contribu- mode due to symmetry lowering is similar to the
tion to the energy is contributed by the cubic force experimental values found for aqueous nitrate so-
constant f 444 of the total symmetric mode. Its in- lutions. It is therefore—at least in principle—pos-
clusion gives our final expression for the in- sible that asymmetric anionic hydration causes the
tramolecular force field: observed behavior. However, in view of the rather
low binding energies of about 14 kcalrmol the
6 6 absence of dynamic averaging remains to be un-
Vintra s 1
2 Ý f i i Di Di q Ý f i Dj Di j derstood.
is1 i/js1 Interaction potentials for NOy 3 rH 2 O were ob-
q 16 f 444 S4 S4 S4 , Ž3. tained from high-level ab initio calculations. Dia-
grams of the potential energy surface show that
little energetic differences between linear, cyclic, or
where S4 is the coordinate Ž ⌬ r N — O1 q ⌬ r N — O2 q
bifurcated hydrogen bonding exist. Configurations
⌬ r N — O3 .r '3 .
with hydrogen bonding from above or below the
The values of the force constants are given in
nitrogen atom are somewhat less favorable but
Table III. The numerical values of the harmonic
still result in attractive interactions. An intramolec-
force constants were determined by calculations
ular force field for nitrate anion that includes the
on the MP4raug-cc-pVTZ level of theory. The cu-
most important anharmonic terms was developed.
bic force constant f 444 was obtained from five
Work on molecular dynamics simulations of
energy points at displacements of 0, "0.05 and
aqueous nitrate solutions incorporating the inter-
"0.1 A ˚ along the total symmetric normal mode S4
action potentials is in progress.
by minimizing the least-square difference between
their ab initio energies and the energies obtained
from formula Ž3.. ACKNOWLEDGMENTS
Financial support from the Austrian FWF Žpro-
Summary ject P10106-MOB. is gratefully acknowledged. The
ab initio calculations were performed with the
The system NOy computer programs Gaussian 92 and 94 w 24x .
3 rH 2 O at the B3LYPraug-cc-
pVTZ level forms a planar complex with C s sym-
metry and two distorted hydrogen bonds. The
binding energy is y14.5 kcalrmol. The symmetric References
complex which is found to be stable at a lower
theoretical level w HFr6-311G q Žd, p.x is a saddle 1. D. E. Irish, M. H. Brooker, in Advances in Infrared and Raman
point about q0.1 kcalrmol higher in energy. A Spektroscopy, R. J. Clark and R. E. Hester, Eds. ŽHeyden,
singly hydrogen-bonded complex is still q2.4 London᎐New York, 1976., Vol. 2, Chapter 6.
kcalr mol higher in energy. The vibrational fre- 2. B. E. Conway, Studies in Physical and Theoretical Chemistry
quencies of nitrate anion and of the complex 12, ŽElsevier, Amsterdam᎐Oxford᎐New York, 1981., Chap-
ter 8.
3. R. E. Verall, in Water: A Comprehensive Treatise, F. Franks,
Ed. ŽPlenum, New York, 1973., Vol. 31, Chapter 5.
TABLE III
Force constants of the intramolecular potential of 4. A. M. de P. Nicholas and R. Wasylishen, Can. J. Chem. 65,
NO3 (atomic units). 951 Ž1987. and J. Phys. Chem. 89, 5446 Ž1985..
5. M. Nakahara, A. Adachi, H. Kiyoyama, A. Shimizu, Y.
f r 1y r 1 0.4840 Taniguchi, and Y. Masuda, J. Phys. Chem. 94, 6179 Ž1990..
f ␣1y ␣1 0.7130 6. J. M. Howell, A. M. Sapse, E. Singman, and G. Snyder,
foop 0.1748 J. Phys. Chem. 86, 2345 Ž1982..
f r 1y r 2 0.0583
7. M. Shen, Y. Xie, H. F. Schaefer, and C. A. Deakyne, J. Chem.
f ␣1y ␣ 2 0.3565
Phys. 93, 3379 Ž1990..
f ␣1y r 1 0.0886
f444 y1.3759 8. M. Shen, Y. Xie, H. F. Schaefer, and C. A. Deakyne, Chem.
Phys. 151, 187 Ž1991..

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 885

EBNER, SANSONE, AND PROBST

9. T. H. Dunning, Jr., and P. J. Hay, in Modern Theoretical 18. T. J. Findlay and M. C. Symons, J. Chem. Soc. Faraday
Chemistry: Methods of Electronic Structure Theory, H. F. Trans. II 72, 820 Ž1976..
Schaefer III, Ed. ŽPlenum, New York, 1997., Vol. 3, p. 1. 19. D. E. Irish and A. R. Davis, Can. J. Chem. 46, 943 Ž1968..
10. G. Velders and D. Feil, Theor. Chim. Acta 84, 195 Ž1992.. 20. S. Huzinaga, J. Andzelm, M. Klobukowski, E. Radzio-
11. M. Probst, Int. J. Quant. Chem. 29, 559 Ž1995.. Andzelm, Y. Sakai, and H. Tatewaki, in Gaussian Basis Sets
12. A. Laaksonen and H. Kovacs, Can. J. Chem. 72, 2278 Ž1994.. for Molecular Calculations ŽElsevier, Amsterdam, 1984..
13. Y. Kataoka, Bull. Chem. Soc. Jpn. 66, 2478 Ž1993.. 21. N. Greenwood, Chemie der Elemente ŽVCh Verlag, Wein-
14. T. Kato, S. Hayashi, M. Oobatake, and K. Katsunosuke, J. heim, 1990., p. 604.
Chem. Phys. 99, 3966 Ž1993.; T. Kato, K. Machidae, M. 22. C. M. Breneman and K. B. Wiberg, J. Comp. Chem. 11, 361
Oobatake, and S. Hayashi, J. Chem. Phys. 93, 3970 Ž1990.; J. Ž1990..
Chem. Phys. 92, 5506 Ž1990.; J. Chem. Phys. 89, 7471 Ž1988.; 23. G. Lie and E. Clementi, Phys. Rev. A33, 2679 Ž1986..
J. Chem. Phys. 89, 3211 Ž1988..
24. M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill,
15. R. Krishnan, J. S. Binkley, R. Seeger, and J. A. Pople,
B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. A. Keith,
J. Chem. Phys. 72, 650 Ž1980.. G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A.
16. A. D. McLean and G. S. Chandler, J. Chem. Phys. 72, 5639 Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman,
Ž1980.. C. Y. Peng, P. Y. Ayala, M. W. Wong, J. L. Andres, E. S.
17. T. H. Dunning, Jr., J. Chem. Phys. 90, 1007 Ž1989.; R. A. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley,
Kendall, T. H. Dunning, Jr., and R. J. Harrison, J. Chem. D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C.
Phys. 96, 6796 Ž1992.; D. E. Woon and T. H. Dunning, Jr., Gonzalez, and J. A. Pople, Gaussian 94, Gaussian, Inc.,
J. Chem. Phys. 98, 1358 Ž1993.. Pittsburgh, PA, 1995.

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