118
J . Phys. Chem. 1991, 95, 118-122
basis set for oxygen. While the system proved too large to optimize automatically, even when constrained to D3hsymmetry, the energy was studied as a function of the Rh-0 distance. The energies of the I A , and 3B2state were -9587.6957 au and -9587.6452 au, respectively, for a Rh-0 distance of 2.084 A, and a Rh-Rh distance of 2.612 A. The structure of this bridged state is shown in Figure 5a. Much effect was expended in a similar all-electron calculation of the O=Rh-0-Rh=O structure. Although it was not constrained to linearity, there were no forces to bend the molecule during partial optimizations and it remained linear. Changes in the Rh=O terminal bond lengths and Rh-0 did change the energy. The best energy obtained thus far was -9587.6499 au, some 28.7 kcal/mol higher than the bridged structure. This structure had bond lengths of 1.85 A for the terminal Rh=O and 1.91 A for the central Rh-0. The RECP basis set confirmed the order of stability, Le., the energy for the trigonal-bipyramid R h 2 0 3 was -268.994 au, that for the bent O=Rh-0-Rh=O structure was -268.8483 au (shown in Figure 5b). and for the linear O=Rh-O-Rh==O structure was -268.8350 au. Thus, at the U H F level, the 0-bridged bipyramidal structure is the more stable, although none of these structures have been optimized because of time constraints.
Conclusions The current basis sets, all-electron (HB, SHIM, SHIM-SU), effective core potential (LANLI MB, LANLI DZ), and relativistic effective core potential (RECP), for the Rh atom are not able to describe the atomic excitation nor atomic ionization very accurately. These basis sets had varying degrees of success in representing the rhodium compounds studied, doing an adequate
job of describing RhH, RhH3, RhC, R h o , and Rh203. The ECP potentials, built into the G88 program, and relatively easy to use but gave unpredictable results, sometimes collapsing bonds, e.g., CO in Rh(CO),. The RECP basis sets usually gave reliable results but often did not achieve S C F even when more sophisticated convergence schemes were employed. The all-electron calculations gave reasonable vibrational frequencies for "adsorbed" CO, and Rh-0. Rh,, Rh3, and Rh4 were not well described by any of the basis sets. The donation of electrons from the d-like orbitals of these clusters into the antibonding orbitals of nearby H,, CO, and O2offers a reasonable explanation for the variation of catalytic activity with cluster size and shape. The calculations suggest that adsorbed 0, has properties much like 0,- ions on the surface.
Acknowledgment. Partial support of this work by the U S . Deparment of Energy, Office of Basic Energy Sciences (J.M.W.), is gratefully acknowledged. A large grant of computer time from the University of Texas (to J.M.W.) made initiation of this research possible. Subsequent work was partially supported by NCSA Grant CHE890003N (to G.J.M.) and utilized the Cray XMP/48 and CRAY-2 systems at the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign. A large grant of computer time to explore the capabilities of the IBM 3090 was provided (to G.J.M.) by the Oklahoma State University Computer Center. We are grateful to these institutions for their generous support. G.J.M. would like to thank Mr. Keith Lovelace, formerly of the OSU Computer Center, for help with computational problems and Prof. M. McKee for preprints of his publications and general encouragement to continue the all-electron calculations.
An ab Initio Study of Nitrous Acid: Geometries, Force Constants, Fundamental Frequencies, and Potential Surface for Cis-Trans Isomerization J. M. Coffint and Peter Pulay* Department of Chemistry and Biochemistry, University of Arkansas, Fayetteuille, Arkansas 72701 (Received: April 10. 1990: In Final Form: July 2, 1990)
The geometries, quadratic force fields, and fundamental vibrational frequencies of cis- and trans-nitrous acid have been determined by using local fourth-order Moller-Plesset perturbation theory, and also two-pair generalized valence bond wave functions. The Hartree-Fock approximation is inadequate for this molecule, due to strong electron correlation. The theoretical force field for the trans isomer agrees, after scaling, very well with the experimental values of Deeley and Mills. The experimental force field of the cis isomer is less accurately known and the present results are probably the most reliable date available. The energies and force constants along the cis-trans isomerization path have been determined for future studies of the dynamics of the isomerization reaction.
Introduction Nitrous acid (HONO) plays an important role in atmospheric chemistry. It is one of the smallest molecules which exhibits a cis-trans conformational equilibrium and which has been studied extensively to obtain molecular geometries and force fields by infrared and microwave spectroscopic methods.'-9 For these reasons, it has been of significant interest both theoretically'wlx and e~perimentally.'-~ Microwave studiesS have shown that the trans form of the molecule is more stable by about 1.6 kJ/mol with an estimated barrier of interconversion of approximately 40 kJ/moL5 These results are fairly consistent with earlier experimental results,'-4 and with ab initio calculations,lp18 although the latter have some difficulty in reproducing such small energy differences. Molecules 'Present address: IBM Corporation, 2707 Butterfield Road, Oak Brooks,
IL 60521.
0022-3654/91/2095-0l18$02.50/0
containing bonds between the very electronegative first-row elements N, 0, and F usually have strong electron correlation and ( 1 ) McGraw, G. E.; Bernitt, D. L.; Hisatsune, I. C. J . Chem. Phys. 1966, 45, 1932. (2) McGraw, G. E.; Bernitt, D. L.; Hisatsune, I. C. J . Am. Chem. SOC. 1970, 92, 775. (3) Cox, P. A.; Brittain, A. H.; Finnigan, D. J. Trans. Faraday SOC.1971, 67, 2179. (4) Finnigan, D. J.; Cox, A. P.; Brittain, A. H. J . Chem. SOC.,Furaday Trans. 2 1972, 68, 548. ( 5 ) Varma, R.; Curl, R. F. J . Phys. Chem. 1976, 80, 402. (6) Allegrini, M.; Johns, J. W. C.; McKellar, A. R. W.; Pinson, P. J . Mol. Struct. 1980, 79, 446. (7) Maki, A. G.; S a m , R. L. J. Mol. Struct. 1983, 100, 215. (8) Deeley, C. M.; Mills, I. M. J. Mol. Struct. 1983, 100, 199. (9) Deeley, C. M.; Mills, 1. M. Mol. Phys. 1985, 45, 23. (IO) Schwartz, M. E.; Hayes, E. F.; Rothenberg, S. Theor. Chim. Acta 1970, 19, 98. ( 1 I ) Skaarup, S.; Boggs, J. E.J . Mol. Struct. 1976, 30, 389.
0 1991 American Chemical Society
Ab Initio Study of Nitrous Acid are therefore difficult to stud theoretically (a particularly interesting case being FOOF).
11
Calculations Unless mentioned otherwise, the calculations were performed using the 6-31 1G** basis of Pople.20 The S C F and perturbation calculations were performed using the program TEXAS,^^ while the two-pair GVB calculations were done using the program GAMESS.~~
As pointed out in the Introduction, it is important to include electron correlation in the wave function for nitrous acid; the S C F wave function is a much poorer approximation than in the usual case. In the first set of calculations, we have used fourth-order Moller-Plesset perturbation theory with single, double, and quadruple substitutions (MP4-SDQ). The Is cores were not correlated. In addition, we used the local approximation of Saebo and P ~ l a which y ~ ~ offers significant savings even in a molecule this small. In this method, first the localizedz4S C F orbitals are determined. For each localized S C F orbital, a local basis is specified, consisting of the atomic orbitals in the spatial vicinity of the molecular orbital. With a large basis set like 6-31 1G**, the loss of correlation energy because of the local restriction is usually not more than 1%. Unpublished calculations show that the effect of the local approximation is negligible for geometries and force constants. A disadvantage of MP4 is that analytical gradients are not yet available for this type of wave function. The geometries of both conformers were optimized at the local MP4(SDQ) level. These geometries were used as the reference geometries for the remainder of this set of calculations. The quadratic force constants were calculated by second-order numerical differentiation of the energy, using central difference formulas. In addition to calculating the frequencies using the raw ab initio results, the force constant matrices were scaled by using the scaled quantum mechanical (SQM) method.2s While the SQM method is not purely a b initio, the inclusion of empirical scale factors takes into account the remaining deficiencies of the wave function, as well as anharmonicity effects. For molecular dynamics studies of the cis-trans isomerization process, a quadratic force field along the approximate reaction coordinate is needed. Mainly because of the lack of the gradients, the local MP4-SDQ method is too expensive for this purpose. We have therefore used a two-pair perfect-pairing generalized valence bond (GVB) wave function.26 This type of wave function readily allows the evaluation of analytical gradients. The starting GVB orbitals have been selected by using occupation numbers of the natural orbitals of a prior unrestricted Hartree-Fock (UHF) c a l c u l a t i ~ n . ~This ~ procedure yields two orbital pairs with significant (between 0.02 and 1.98) fractional occupancy: the N = O
(12) Larrieu, C.; Dargelos, A.; Chaillet, M. Chem. Pfiys. Lett. 1982, 91, 465. (13) Kleier, D. A.; Lipton, M. A. THEOCHEM 1984, 109, 39. (14) Contreras, J. G.; Seguel, G.V. THEOCHEM 1985, 121, 137. (15) Murto, J.; Markku, R.; Aspiala, A.; Lotta, T. THEOCHEM 1985, 122. 213. (16) Turner, A. G. J. Phys. Chem. 1985, 89, 4480. (17) Darsey, J. A.; Thompson, D. L. J . Phys. Chem. 1987, 91, 3168. ( 1 8) Nakamura, S.; Takahasi, M.; Okazaki, R.; Morokuma, K. J . Am. Chem. SOC.1987, 109, 142. (19) Clabo, D. A.; Schaefer, H. F. Ill. Int. J . Quantum Chem. 1987,31, 429. (20) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Pfiys. 1980, 72, 650. (21) Pulay, P. Theor. Cfiim.Acta 1979, 50, 599. (22) Dupuis, M.; Spangler, D.; Wendoloski, J. J. Not/. Res. Comput. Cfiem. Software Cur. 1980, I , 4601. (23) Saebo, S.; Pulay, P. J . Cfiem. Phys. 1987, 86, 914. (24) Boys, S . F.; Foster, J. J. Rev. Mod. Phys. 1960, 32, 305. (25) Pulay, P.; Fogarasi, G.; Pongor, G.; Boggs, J. E.; Vargha, A. J . Am. Chem. SOC.1983, 105, 7037. (26) Hunt, W. J.; Hay, P. J.; Goddard, W. A. 111. J . Cfiem.Pfiys. 1972, 57, 738. (27) Pulay, P.; Hamilton, T. P. J. Cfiem. Pfiys. 1988, 88, 4926.
The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 119 TABLE I: Geometries of cis- and tmns-HONW (Bond Lenptbs - in A. Angles in deg) SCF MP4 GVB calcd calcd 2-pair exptl coordinate value correln reP value value valueb 1.309 1.3817 (487) 1.376 1.391 1.392 1. N-0 2. 0-H 0.951 0.9730 (956) 0.973 0.950 0.982 1.169 1.185 1.1863 (109) 1.186 3. N=O 1.148 104.754 (647) 104.99 106.35 104.0 4. HON 108.3 5. ON0 114.1 113.196 (057) 113.11 112.60 113.6 0.0 0.0 0.0 0.0 0.0 6. torsion 1. N-O 2. 0-H 3. N=O 4. HON 5. O N 0 6. torsion
1.322 1.411 (6810) 0.942 0.963 (3837) 1.175 (2436) 1.141 105.8 101.86 (0391) 110.79 (0769) 11 1.9 180.0 180.0
1.432 1.405 1.412 0.944 0.958 0.963 1.175 1.162 1.170 102.11 103.49 102.1 110.63 109.99 110.7 180.00 180.00 180.0
"This is the geometry used in the Moller-Plesset force constant calculations (values in parentheses are not physically significant). Reference 3. Experimental geometries are obtained through isotopic substitution. T bonding and antibonding pair, and the N-0 u and cr* orbitals. This wave function was used to determine the approximate reaction path, by fixing the torsional angle at 30' increments, and optimizing all other parameters. The quadratic force field was then determined at these geometries, using numerical central differentiation of the gradient in internal coordinates.
Results and Discussion Table I compares the theoretical geometries of the two conformers with the most recent experimental substitution (rs)values.' The accuracy of the latter may be influenced by the large-amplitude vibrations. As expected, the S C F geometry is very poor. The agreement is significantly better at the MP4(SDQ) level but there is still a significant (0.02-0.03 A) deviation for the N-0 single bond. This is very likely due to the strong correlation in the K space, which makes triple substitutions (not included here) more important than usual. Probably for this reason, the two-pair GVB value is somewhat better than the MP4 one for this parameter. Although both calculations show that the N-0 bond lengthens significantly on going from the cis to the trans isomer, the magnitude of this effect is significantly smaller than in the experimental geometry of Cox et aL3 We determined the energy difference between the cis and trans conformers using various geometries, basis sets, and levels of theory. This difference was calculated at three different geometries as seen in Table 11. According to the recent microwave intensity measurements by Varma and Curl? the trans isomer is more stable by about 1.6 kJ/mol. Previous theoretical calculation^^^^'^^'^^'^ do not have such high level of correlation taken into account. Hartree-Fock calculations with 6-3 1 1G** basis set predict that the cis form is lower in energy than the trans form by about 4 kJ/mol. Addition of diffuse functions to the basis set leads to a stabilization of the trans form of the molecule, but not enough to lower it below the cis form (only about 3 kJ/mol). The addition of electron correlation leads to a further stabilization of the trans form, which causes an overestimation of the energy splitting between the two isomers (about 4.8 kJ/mol). The addition of two other orbital pairs in the GVB type description led to an overall stabilization in the trans isomer which caused the trans isomer to be lower than the cis form by 4.7 kJ/mol. The force constants were calculated through the MP4(SDQ) level numerically and the values are reported in Tables 111 and IV, along with Deeley and Mills' experimentally derived values for c~mparison.~ For reproducibility, we quote the exact reference geometry used in the force field calculations. This geometry has been optimized until the gradients were all below 0.005 aJ/A. Most of our unscaled values are in reasonably good agreement, both in sign and order of magnitude (particularly for the trans isomer), with those obtained by Deeley and Mills9 (within *20%). They are also in qualitative agreement with previous ab initio calculations.",'6 The SQMZ5scaled force fields, using the same scale factors for both isomers, are also shown. The scale factor
120 The Journal of Physical Chemistry, Vol. 95, No. 1, 1991
Coffin and Pulay
TABLE 11: Ab Initio Calculated Energies for HONO on Different Levels of Theory at Three Different Reference Geometries (in hartrees) and Values for Enerev Difference between the Cis and Trans Conformer (in kJ/mol) at Each Level reference level cis trans AE (cis-trans) exptl' SCF -204.694414 356 -204.693 252 347 -3.05 1 (6131 IG**) MP2 -0.575 338 98 -0.576 007 41 1.755 MP3 0.010921 81 0.010 409 48 1.345 MP4(SDQ) -0.016488 33 -0.016 13645 -0.924 total -205.275 3 19 85 -205.274 986 73 -0.875 ref I b SCF -204.695 758 104 -204.694 085 999 -4.390 (6-31 lG**) MP2 -0.57401802 -0.575 323 83 3.428 0.010 17947 0.927 MP3 0.01053263 -0.01 3 41 8 6 I -0.01323752 -0.475 MP4(SDQ) -205.272 467 88 -0.510 total -205.272 662 I 1 rcf 2c S CF -204.696 294 999 -204.694 603 6 15 -4.441 (6-31 IG**) M P2 -0.573 422 35 -0.574 726 48 3.424 MP3 0.010341 62 0.009 959 91 1.002 MP4(ADQ) -0.01 3 305 64 -0.013 11891 -0.490 total -205.272 68 1 37 -205.272 489 909 -0.505 ref 2 SCF -204.701 583 070 -204.701 306 856 -0.725 (6-3 I I ++G**) MP2 -0.578 441 79 -0.58063581 5.760 MP3 0.01 1 788 26 0.01 1 808 89 -0.054 -0.014 143 57 -0.190 M P4 (SDQ) -0.014 2 15 92 -205.282455 52 -205.284 277 34 4.791 total 'Cox, A. P.; Brittain, A. H.; Finnigan, D. J. Trans., Furuduy SOC.1971, 67, 2179. Experimental geometries are obtained through isotopic substitution. bThis is the geometry used in the force constant calculations (values in parentheses are not physically significant). CThis is the theoretically obtained MP4 relaxed geometry (see text).
TABLE III: Force Constants for cis-HONO (in aJ kn, Where n Is the Number of Stretching Coordinates) up to Local MP4 Level of Theory Using the 6-311C** Basis Set total total total correln contribn Hartree-Fock correln unscaled scaled Deeley/Mills' con t ri bn MP2 MP3 M P4 contrbn" value value' valueb -0.293 0.28 1 -0.107 -0.120 3.848 2.814 2.947 FlJ(N-0) 3.968 0.057 -0.072 -0.103 7.664 -0.088 6.712 6.547 F2.2(0-W 7.767 13.356 0.647 -0.966 0.614 0.295 13.651 12.330 11.734 F,,,(N=O) -0.182 0.076 -0.025 -0.131 0.902 0.780 0.900 F4,4(H-0-N ) 1.033 -0.082 -0.020 0.005 -0.097 2.608 2.368 2.334 F5,5(O-N=O) 2.706 0.172 0.041 -0.029 0.009 0.021 0.160 0.167 0.193 F6.6(T) 0.038 0.020 -0.031 0.027 0.276 0.221 0.000d FI.~(N-O/O-H) 0.249 0.010 -0.156 -0.290 1.951 1.586 2.000d 2.251 -0.144 Fl,,(N-/N=O) F1,4(N-O/ H-0-N) 0.300 -0.04 1 0.03 I -0.01 3 -0.023 0.277 0.220 0.52d -0.150 0.087 -0.022 -0.085 0.407 0.332 0.353 Fi,s(N-O/O-N=O) 0.492 0.048 -0.03 1 -0.004 -0.052 0.046 0.000d -0.048 -0.02 1 F2,3(O-H/N=O) 0.003 -0.005 0.007 0.005 0.091 0.079 0.000d F2,,(O-H/H-0-N) 0.086 -0.034 0.012 -0.0 I 8 -0.040 -0.189 -0.168 0.000d F2,5(O=H/O-N=O) -0.149 0.018 -0.026 0.035 0.03 1 O.ld Fj,4(N=O/H-O-N) 0.061 -0.033 -0.01 1 F,,s(N=O/O-N=O) 0.754 0.137 -0.034 -0.031 0.072 0.826 0.748 0.247 F4,d(HON/ONO) -0.246 0.023 0.000 -0.004 0.019 -0.227 -0.201 0.19 'The correlation contribution is a total contribution through the MP4 level. bReference 9. CScalefactors used are 0.7313, 0.8758, 0.8653, 0.9033, 0.9079, and 0.8267 for N-0, 0-H, N=O, HON, ONO, and torsional force constants. dConstrained in the experimental least-squares refinement.
TABLE IV: Force Constants for trans-HONO (in aJ A-n, Where n Is the Number of Stretching Coordinates) up to Local MP4 Level of Theory Using the 6-311C** Basis Set total total total correln contribn Hart r ee- Fock correln unscaled scaled Deeley/Mills' contribn MP2 MP3 MP4 contribn' value valueC valueb 0.242 -0.065 -0.051 3.495 2.556 2.718 3.546 -0.228 FIJ(N-0) -0.110 8.264 7.237 7.285 0.052 -0.077 -0.085 F2.2(0-H) 8.374 14.260 -0.926 1.043 -0.513 -0.396 13.864 12.523 13.036 F,,,(N=O) 0.085 -0.032 -0.144 0.884 -0.197 0.765 0.757 F4.4( H-0-H) 1.028 -0.020 0.000 -0.104 2.430 2.206 2.221 2.534 -0.084 F5,5(O-N=O) F6.6(T) 0.1 19 0.065 -0.024 0.010 0.051 0.170 0.141 0.134 0.058 -0.041 0.002 0.002 0.000d -0.022 0.025 -0.039 FI,~(N-O/O--H) 1.608 2.434 -0.058 -0.003 -0.229 -0.290 1.979 FI,,(N-O/N=O) 2.269 F1,4(N-O/ H-0-N) -0.064 0.030 -0.01 1 0.352 0.280 0.267 0.397 -0.045 Fi,,(N-O/O-N=O) 0.633 -0.168 0.077 -0.047 -0.138 0.495 0.403 0.462 0.024 0.01 1 -0.006 0.029 -0.047 -0.042 0.000d F2,,(O-H /N=O) -0.076 0.006 0.022 0.072 0.063 0.000d 0.022 -0.006 F2,4(O=H/H-O-N) 0.050 F2,,(O-H/O-N=O) 0.102 0.052 -0.010 0.004 0.040 0.142 0.127 0.000d F3,4( N=O/ H 4 - N ) 0.157 0.024 -0.009 -0.009 0.006 0.163 0.144 0.132 F,,,(N=O/O-N-O) 0.61 1 0.088 -0.014 -0.043 0.031 0.642 0.58 1 0.744 0.297 0.305 0.270 -0.023 0.007 -0.002 -0.018 F4,s(HON/ONO) 0.323 'The correlation contribution is a total contribution through the MP4 level. bReference 9. CScalefactors used are 0.731 3, 0.8758, 0.8653, 0.9033, 0.9079, and 0.8267 for N-0. 0-H, N=O, HON, OHO, and torsional force constants. dConstrained in the experimental least-squares refinement.
Ab Initio Study of Nitrous Acid
The Journal of Physical Chemistry, Vol. 95, No. 1, 1991 121
TABLE V: Vibrational Frequencies of cis-HONO and cis-DON0 (in cm-')
vi(0-H) v,(N=O) VAHON) v,(N-O/ONO) v,(ONO/N-O) Ud7)
" Reference 9.
unscaled freq
HONO scaled freq
exptl freq"
unscaled freq
DONO scaled freq
exptl freqb
3698.64 1746.23 1382.57 946.49 680.35 693.81
3461.35 1659.51 1293.29 850.32 615.49 63 1.96
3426.22 1640.52 b 851.93 609.0 639.80
2691 .I4 1732.78 1 132.83 914.55 621.54 545.88
2530.00 1648.46 1063.40 808.36 568.96 497.30
2530.W 1625.W b 813.49 601 .O 508.6
Not observed experimentally. Reference 3.
TABLE VI: Frequencies of trans-HONO and trans-DONO (in cm-')
ui(0-H) ~z(N-0) U,(HON) ~ qN( -O/ON 0) uS(ONO/N-O) Ud7) a
unscaled freq
HONO scaled freq
exptl freq
unscaled freq
DONO scaled freq
exptl freq
3844.16 1767.04 1350.52 895.92 664.04 602.07
3597.46 1678.57 1264.93 807.45 597.96 557.12
3590.71 1699.80 1263.18 790.12 595.62 543.88
2799.52 1757.20 1079.78 837.90 648.27 545.94
2619.89 1670.60 1013.39 746.56 588.99 420.84
2651 , I 3 1693.98 1012.68 723.27 590.20 416.50
Reference 9.
TABLE VII: Geometry and Energies of HONO at the Two-Pair GVB Level with Basis Set 6-311G** (Angles in de& Bond Distances in A, Energies in hartrees) torsion angle R(N-0) R(0-H) R(N=O) LHON LONO energy 0 1.391 0.950 1.169 106.35 1 12.60 -204.768 04 30 1.408 0.949 1.167 106.36 1 12.34 -204.764 65 60 1.444 0.947 1.164 105.45 1 1 1.46 -204.758 96 83.32 1.463 0.947 1.161 104.19 1 10.70 -204.757 20' 90 1.465 0.947 1.161 103.93 110.53 -204.757 34 I20 1.450 0.946 1.161 103.05 110.12 -204.761 05 150 1.424 0.945 1.162 103.38 110.03 -204.766 95 180 1.412 0.944 1.162 103.49 109.99 -204.769 82
~~
"The calculated barrier height (cf. ref 5) is 33 kJ/mol. TABLE VIII: Scaled" Force Constants for Nitrous Acid at Different Values of the Torsional Angle (Stretching Constants in aJ A-2, Bending Constants in aJ rad-2, Stretch-Bend Interaction Values in aJ A-' rad-')
torsional angle F(1 , I )(N--O) F(2.2) (0-H ) F(3,3)(N=0) F(4,4)(HON) F( 5.5 )(ON 0 ) F(6,6)(7) F(2,l) F(3,l) ~(4~1) F(5,l) F(6,l) F(3,2) F(4,2) F(5.2) F(6,2) F(4.3) F(5,3) F(6,3) F(5,4) F(6.4) F(6S)
0 (cis) 3.083 6.796 12.338 0.771 2.049 0. I59 0.109 1.315 0.280 0.405 0.001 0.037 -0.130 -0.10 0.672
-0. I75
30 2.856 6.813 12.277 0.735 1.988 0.063 0.057 1.33 1 0.295 0.392 -0.189 -0.006 0.016 -0.123 0.029 0.002 0.628 -0.002 -0.150 -0.01 8 0.023
60 2.416 6.969 12.241 0.652 1.868 -0.077 -0.005 1.349 0.293 0.359 -0.156 -0.022 0.01 1 -0.082 0.014 0.033 0.554 0.025 -0.087 0.014 0.054
90 2.199 6.996 12.317 0.609 1.813 -0.1 12 -0.01 7 1.359 0.268 0.370 0.016 -0.032 0.035 -0.026 0.009 0.068 0.522 0.052 0.023 0.03 1 0.054
120 2.356 7.045 12.420 0.648 1.855 -0.040 -0.020 1.389 0.273 0.441 0.148 -0.031 0.044 0.026 0.020 0.109 0.544 0.063 0.141 0.022 0.043
150 2.682 7.109 12.542 0.723 1.911 0.073 -0.029 1.421 0.297 0.516 0.136 -0.026 0.039 0.063 0.01 5 0.142 0.587 0.048 0.220 0.010 0.028
180 (trans) 2.841 7.126 12.600 0.760 1.928 0.127 -0.029 1.430 0.308 0.547 -0.026 0.036 0.079 0.154 0.608 0.247
"Scale factors are as follows: 0.8074, 0.7441, 0.8276, 0.7748, 0.7661, and 1.2784 for N-0 stretch, 0-H stretch, N=O stretch, HON bend, O N 0 bend, and the torsion force constants, respectively. for the N - 0 bond is only 0.73, showing that the description of this bond is still far from perfect, in agreement with the geometry results. Much of the error in the stretching force constants is due to errors in the (28) Pulay, P. In Applications of Molecular Electronic Structure Theory; Schaefer 111. H. F.. Ed.: Plenum: New York. 1977. D. 153. (29) Pulay, P.; Lee, J . G.; Boggs, J. E. J . Cbem. h y s . 1983, 79, 3382.
The most significant deviation between our results and those of Deeley and Millsg is the value of the N-O/N=O coupling constant, which is significantly higher in the empirical force field. Considering the difficulties theorv has with the N - 0 sinele bond. but also t h i problems of the experimental determinatioiof force it is not which is more accurate' Note that Deeley and Millsg were forced to use constraints in their force field determination. The effect of this is relatively mild in the
122
The Journal of Physical Chemistry, Vol. 95, No. I, 1991
TABLE I X Vibrational Frequencies of cis-HONO and &-DONO at Two-Pair GVB Level of Theorv" (in . cm-') fundamental HONO DON0 number scaled frea exatl freab scaled frea exotl freab VI
"2
u3 "4 05
"6
3485.2 1647.5 1315.7 831.1 621.1 648. I
3426.22 1640.52 a
85 I .93 609.0 639.80
2537.3 1643.5 1053.8 807.7 574.0 509.0
2530:Oc 1625.OC a
813.49 601 .O 508.6
DNotobserved experimentally. bobserved by Deelye and Mills, ref
Coffin and Pulay TABLE X Scaled Vibrationnl Frequencies of trans-HONO and trans-WNO at Two-Pair CVB Level (in cm-') trans-DONO fundamental trans-HoNo number scaled freq exptl freq' scaled freq exptl freq" VI
y2
u3 84
us u6
3571.3 1678.1 1277.4 786.7 612.4 542.3
3590.71 1699.80 1263.18 790.12 595.62 543.88
2601.9 1671.3 998.9 750.9 597.9 409.1
2651.13 1693.98 1012.68 723.27 590.20 416.50
"Observed by Deeley and Mills, ref 9.
9. 'Observed by McGraw, Bernitt, Hisatsune, ref I .
trans isomer: only four coupling constants have been constrained, and their values are small in the ab initio force field. We conclude that the force field of trans nitrous acid is fairly well determined, and it is probably between the scaled ab initio and the experimental force field. These two agree very well, except for the N - O / N = O coupling mentioned. The situation is different for the cis species. In this case, there were fewer experimental observables available, and Deeley and Mills were forced to constrain eight force constants. Some of the constrained values, taken from the trans isomer, deviate strongly from our ab initio values, and we believe that the cis force field of Deeley and Mills9 is only qualitatively correct. As a guide for the introducing constraints, Deeley and Mills have used the force field of Finnigan et aL4 Unfortunately, the latter belongs to the qualitatively wrong assignment for the trans isomer, as shown by its very low N - 0 stretching constant and its high value for the 0-N=O diagonal bending constant. The possibility of a qualitative misassignment arises here because the uncoupled N - O vibrations are unusually close. The two observed and 0-N=O bands, in the 700-800-cm-' and in the 600-cm-' regions are essentially in-phase and out-of-phase combinations of the N - 0 and 0-N=O vibrations. It is interesting that the early ab initio calculation of Skaarup and Boggs" was already sufficient to detect the misassignment in the force field of ref 4. A redetermination of the force field of cis-nitrous acid, using the scaled ab initio values as a guide for constraints, would most probably yield a significantly improved empirical force field for this molecule. The fundamental vibrational frequencies of cis- and transnitrous acid and cis- and trans-nitrous acid-d, obtained from the MP4(SDQ) calculations, both before and after the SQMZ5scaling, are given in Tables V and VI. The agreement, particularly for u4 in trans-HNO, and D N 0 2 , and u5 in cis-HN02 and D N 0 2 , is less good than usual, due to the difficulty of reproducing the relative N - 0 bond length and the N - 0 force constant in the two isomers.
The torsional surface of H O N O is another interesting feature of this molecule that has been extensively s t ~ d i e d . l ~ * ~Our ~,l~-~~ purpose is to generate the relevant part of the potential surface for molecular dynamics studies of the isomerization process. In the reaction path Hamiltonian method of Miller et al.,30 the quadratic potential function is needed along the reaction path. The latter was calculated as described in the Calculations section, at the two-pair GVB26 level of theory using 6-31 1G** basis set of Pople et al.20 The GVB calculations are much less expensive than MP4(SDQ) ones, and the scaled force field obtained by this method gives approximately the same fundamental frequencies [compare Tables V and VI to IX and XI. We generated a series of quadratic force fields along the torsional coordinate. The relaxed geometries and energies at 30-deg intervals along the H U N 4 torsional coordinate are shown in Table VII. The quadratic force constants along the reaction coordinate were scaledZ5by the scale factors shown at the bottom of Table VIII. The latter were determined from a simultaneous best fit to the frequencies of cis- and trans-HONO and -DON0.25 The scaled force fields are reported in Table VIII, and the agreement between these and those of Deeley and Millsg is good for the cis and trans cases, except as noted before in the discussion of the MP4 force constants (from Table IV). The calculated vibrational fundamental frequencies are shown in Tables IX and X, along with experimental values for c o m p a r i ~ o n . ~The scaled theoretical frequencies for the cis and trans species are quite good. The good reproduction of the frequencies and force constants for the cis and trans isomers indicates that the surface is adequately reproduced at intermediate torsional angles. Acknowledgment. This research has been supported by the National Science Foundation under grant No. CHE-88 14143. Registry No. HONO, 7782-77-6. (30) Miller, W.H.; Handy, N. C.; Adams, J. E. J . Chem. Phys. 1980, 72, 99.
