J. Phys. Chem. 1988, 92, 5352-5357
5352
TABLE XI: Calculated RHF/6-31G** Isotopic Frequency Shifts (cm-I) for the (Cbloroformvlheroxv Radical syn-2A” a’ CO str 0’0“ str CO‘ str CCI str
ocof/cofo”, s
a“
antb2A“ a‘
a”
syn-lA’
a‘
a” antb2A’ a’
a”
ClCO bend OCO’/CO’O”, a wag torsion CO str 0’0”str CO‘ str CCI str oco”co’o’’, s ClCO bend OCO’/CO’O”, a wag. torsion CO str 0‘0‘’str CO’ str CCI str oco”co’o’’, s ClCO bend OCO’/CO’O’’, a wag, torsion CO str 0‘0’’ str CO’ str CCI str oco”co’o’’, s ClCO bend OCO’/CO’O”, a wag torsion
-1 -66 -24 -8 -14
-4 -10 -2 -5
-5 1 -1 -33 -7 -3 -1 -1 -24 -600
-8 0
-44 -43 -15 -22 -3
-10 -2 -7 -1
-48 -34 -5 -9 -13
-28 -4 -10
-17 -1 -5 -1
-54
0
-46 -37 -5 -8 -14 -30 -2
-46 -1 -1 -14 -3
-8 -27 -1
0
-2 -8
-2 -23
-4 -10 -14 -5
0
0
-50 -18 -16 -7 -3 -1 -1 -240
-44 -2
-50 -13 -23 -1 -2 -1 -9 -24 -1
-44
0 -7
-1
-14 -4 -16 -1 -5 -1 0
-2 -9 -5 -7 -1 5 -5 0
fluorideI9 (1930 cm-I) and may be attributed to fluorine hyperconjugation leading to higher carbonyl bond orders in the fluorinated molecules.20 Unscaled isotopic shifts calculated for FC(O)IsOz, Fi3C(0)02, (18) Pinchas, S.; Laulicht, I. Infrared Spectra of Labelled Compounds; Academic: New York, 1971. (19) Mallinson, P. D.; McKean, D. C.; Holloway, J. H.; Oxton, I. A. Spectrochim. Acta A 1915, 31, 143. (20) Francisco, J. S.; Williams, I. H. Chem. Phys. 1985, 95, 71.
and FC(I80)Ozare given in Table IX. The lsOz shift predicted for the C F stretching mode is rather large for the syn conformer (-17 cm-I) compared to that for the anti conformer (-6 cm-I) of the ground state. Apart from this possibility, there does not appear to be any feature that would allow the two conformers to be distinguished. Table X contains the unscaled RHF/6-3 l G * frequencies and infra_redintensitjes calculated for the syn and anti conformers of the X2A” and A2A’ states of CIC(0)Oz. Again, the strongest absorptions are predicted for the CO, O’O”, and CO’ stretching modes, whose frequencies reflect the corresponding bond-length differences between the ground and excited states in the manner described above. The 0’0”and CO’ modes are somewhat mixed in nature. The carbonyl stretching frequency (scaled by 0.86) for the lowest energy antL2Affradical is 1814 cm-I, closer to that for H C ( 0 ) 0 2 than for FC(0)02. The CCl stretching mode is predicted to have very similar frequencies in the ground and excited states but is very considerably higher in the syn conformers (678 cm-l scaled by 0.89 for sym2A”) than in the anti conformers (501 cm-’ scaled by 0.89 for antb2Aff). Since the corresponding change in the CC1 stretching force constant is small and in the opposite direction, this effect must have a purely mechanical origin. Dempster2I has similarly argued that the observed variation in CC1 stretching frequencies for different conformers of primary chloroalkanes may be adequately explained in terms of Wilson G matrix effects only. Unscaled isotopic frequency shifts for the (chloroformy1)peroxy radicals are given in Table XI as a possible aid to the assignment of experimental spectra.
Acknowledgment. The award of a NATO travel grant is gratefully acknowledged. We are grateful to Wayne State University Computer Center and Chemistry Department for ample provision of Computing resources and to W.S.U. for a Research Award (J.S.F.). Registry No. H02, 3170-83-0; HC(0)02, 56240-83-6; FC(0)02, 115408-73-6; Cl(O)O2, 115408-74-7; 12C180,,115408-75-8; I3CI6O3, 115408-76-9; 180=i2Ci602,115408-77-0; 160,i2C1802,115408-78-1; DC(0)02, 92285-17-1; DC(0)1802, 92285-18-2; FC(0)I802, 11540879-2; FI3C(O)O2,115408-80-5; FC(I80)O2, 1 1 5408-8 1-6; C1C(0)1802, 115408-82-7; C113C(0)02,115408-83-8; C1C(i80)02,115408-84-9.
(21) Dempster, A. B. J . Mol. Spectrosc. 1970, 35, 18.
Isomers of Nitric Acid and Chlorine Nitratet M. P. McCrath, M. M. Francl,’ F. S. Rowland, and W. J. Hehre* Department of Chemistry, University of California, Irvine, California 9271 7 (Received: April 11, 1988) Ab initio molecular orbital calculations at the HF/6-31G* and MP2/6-31G* levels have been performed on nitric acid and chlorine nitrate. Equilibrium geometries and electric dipole moments obtained from the MP2/6-3 l G * calculations are in good agreement with the respective experimental values; normal-mode (harmonic) vibrational frequencies and frequency shifts due to isotopic substitution calculated at this level support the most recent gas-phase infrared assignments for chlorine nitrate but suggest a reversal in the assignment of v5 and v6 for nitric acid. Calculations at the same levels of theory were also performed on peroxynitrous acid (HOONO) and chlorine peroxynitrite (ClOONO). The former is found to be 35 kcal/mol less stable than nitric acid at the MP2/6-31G* level; chlorine peroxynitrite is 30 kcal/mol higher in energy than chlorine nitrate. The possible role of these high-energy isomers in atmospheric processes is discussed. Introduction Nitric acid and chlorine nitrate are involved in many of the approximately 100 chemical reactions believed to influence the ‘Dedicated to the memory of Ed Lee, our friend and colleague. (1) Present address: Department of Chemistry, Bryn Mawr College, Bryn Mawr. PA.
0022-3654/88/2092-5352$01.50/0
balance of ozone in the stratosphere.2 Both molecules are produced in radical combination reactions involving NOz’
HO’
+ N02’ + M
C10’
+ NOz’ + M
-+
+
0 1988 American Chemical Society
HON02
+M
(1)
ClONOz
+M
(2)
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988 5353
Isomers of Nitric Acid and Chlorine Nitrate The effectiveness of reactions 1 and 2 in removing NO2*and HO' or C10' from free radical chains that destroy ozone catalytically depends both upon their rates and on the rates of photodissociation reactions 3 and 4. HON02
2HO' + NO2'
(3)
C10N02
2 C1' + ON02'
(4)
While nitric acid can also be removed by reaction with HO radicals, the primary stratospheric removal process for chlorine nitrate is photolysis by (4) and by a minor pathway forming 0
atom^.^.^
The kinetics of nitric acid and chlorine nitrate formation may not be as simple as implied by the simple elementary processes 1 and 2. Of particular concern is the possibility that the species may be formed indirectly via intermediate isomers and that these isomers have available reaction channels other than those leading directly to nitric acid and chlorine nitrate, respectively. In parlinkage in the molecule ticular, isomers with the peroxide (*) might be expected to photolyze far more rapidly in the 290400-nm range and therefore never reach the more stable chemical isomer in the atmosphere. The possibility of isomers has been raised in kinetic investigations of (1)5 and (2): There is evidence in solution-phase studies for initial formation of peroxynitrous acid, HOONO, upon reaction of HO' and NO2*,' although efforts to detect this species in the gas phase have thus far proven unsuccessful.* Recent experimental studies of chlorine nitrate formation from C10' and N02*99'0provide no support for the intermediacy of high-energy isomers, Le., ClOONO, in conflict with recent calculations of Bhatia and Hall." The calculations presented here seek to shed light on the participation of high-energy isomers in nitric acid and chlorine nitrate formation.
Quantum Mechanical Methods To obtain information on the relative thermodynamic stabilities, equilibrium structures, and infrared vibrational spectra of peroxynitrous acid, as well as on possible isomers of chlorine nitrate, we employed the analytical gradient method.12 Analytical first derivatives of molecular energies with respect to internal nuclear coordinates were used as input to the Schlegel algorithm" for finding stationary point geometries on molecular energy hypersurfaces. Gradients in symmetry coordinates were used as input to the method formulated by Hout et al.14 for calculating quadratic force constants numerically by differentiating the gradients. These data, together with specified nuclear masses (of any isotopic combination), yielded harmonic normal mode freq~encies,'~ leading to characterization of the stationary-point geometries as minima, saddle points, etc. Electric dipole moment vectors, as~
TABLE I: Equilibrium Structures and Dipole Moments for Nitric Acid, HO'NOf geom RHF/ RHF/ RMP2/ Darameter 4-31Gb 6-31G*c 6-31G*d exutle r(N0') r (Nocis) r (HN..) 0 , A r(o' L(O'NOcis) L(O'NOtranS) L(H0'N)
I4
1.373 1.219 1.194 0.961 116.2 114.9 107.7 3.03
1.334 1.188 1.172 0.955 116.1 114.8 105.3 2.86
1.411 1.225 1.215 0.983 115.8 113.6 102.2 2.30
1.406 1.211 1.199 0.964 115.9 113.8 102.2 2.17
'Bond lengths in angstroms, bond angles in degrees, dipole moments in debyes. *From ref 24. cFrom ref 25. dThis work. CFromref 23. TABLE II: Equilibrium Structures and Dipole Moments for Chlorine Nitrate. CIO'NO,' RMP2/ RHF/ RHF/ exptlc 6-31G* 4-31Gb 6-31G*b 1.416 1.372 1.547 1.46 1.199 1.172 1.202 1.215 1.197 1.172 1.206 1.215 1.768 1.666 1.701 1.70 118.5 118.6 117.3 117 111.3 110.7 107.6 110 115.8 115.7 111.1 111 2.59 2.15 0.77
'Bond lengths in angstroms, bond angles in degrees, dipole moments in debyes. bThis work; see ref 28. CFromref 26. sociated with each of (at most) 3N - 6 ( N atoms) gradients calculated to construct a force constant matrix, were used to build an analogous matrix of numerical first derivatives of Cartesian dipole moment components with respect to symmetry nuclear coordinates. Such a matrix, supplemented with three additional dipole moment derivatives (with respect to orientational coordinates), contains sufficient information to yield infrared intensities.16 The major computations in this study were done with the GAUSSIAN 82 system of programs.'' The polarized split valence 6-31G*I8 basis set was used throughout. Restricted Hartree-Fock (RHF) level comp~tations'~ were run on a VAXstation II/GPX machine at U.C. Irvine. The computations taking into account the effect of electron correlation employed restricted second-order Maller-Plesset perturbation theory (RMP2);20these were run on the CRAY XMP at the San Diego Supercomputer Center. The frozen-core approximation2' was not used. Structures were fully optimized within the constraints of their molecular point groups. Less intensive computations involving generating (creating distorted structures, reading in their gradients and dipoles, calculating normal coordinates, etc.) and analyzing harmonic vibrational spectra were performed by using a modified version of the GAUSSIAN 85 program system.22
~~
(2) Anderson, J. G. Annu. Rev. Phys. Chem. 1987, 38, 489. (3) Smith, W. S.; Chou, C. C.; Rowland, F. S. Geophys. Res. Left. 1977, 4, 517. (4) Margitan, J. J. J. Phys. Chem. 1983, 87, 674. (5) Robertshaw, J. S.; Smith, I. W. M. J. Phys. Chem. 1982, 86, 785. (6) Molina, M. J.; Molina, L. T.; Ishiwata, T. J . Phys. Chem. 1980, 84, 3100. (7) (a) Halfpenny, E.; Robinson, P. L. J . Chem. SOC.1952, 928. (b) Mahoney, L. R. J. Am. Chem. SOC.1970, 92, 5262. (8) Burkholder, J. B.; Hammer, P.D.; Howard, C. J. J . Phys. Chem. 1987, 91, 2136. (9) Wallington, T. J.; Cox, R. A. J . Chem. SOC.,Faraday Trans. 2 1986, 82, 275. (10) Griffith, D. W. T.; Tyndall, G. S.; Burrows, J. P.; Moortgat, G. K. Chem. Phys. Lett. 1984, 107, 341. (11) Bhatia, S. C.; Hall, J. H., Jr. J. Chem. Phys. 1985, 82, 1991. (12) Pulay, P. In Modern Theoretical Chemistry; Schaefer, H. F., 111, Ed.; Plenum: New York, 1977; Vol. 4, p 153. (13) Schlegel, H. B. J . Cornput. Chem. 1982, 3, 214. (14) Hout, R. F. Jr.; Levi, B. A.; Hehre, W. J. J . Compuf.Chem. 1983, 4, 499. (15) Wilson, E. B., Jr.; Decius, J. C.; Cross, P.C. Molecular Vibrations; McGraw-Hill: New York. 1955.
(16) Fogarasi, G.; Pulay, P. In Vibrational Spectra and Strucfure;Durig, J. P., Ed.; Elsevier: Amsterdam, 1985; Vol. 14, p 125. (!7).Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H.B.; Fluder, E. M.; Pople, J. A. GAUSSIAN 82; Carnegie-Mellon University: Pittsburgh, 1983. (18) (a) Hehre, W. J.; Ditchfield, R. D.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257. (b) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J. Pople, J. A. Ibid. 1982, 77, 3654. (c) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. (19) Roothaan, C. C. J. Rev. Mod. Phys. 1951, 23, 69. (20) (a) Mlzrller, C.; Plesset, M. S . Phys. Rev. 1934, 46, 618. (b) Pople, J. A,; Krishnan, R.; Schlegel, H. B.; Binkley, J. S . Inf.J . Quantum Chem., Quantum Chem. Symp. 1979, No. 13, 225. (c) Pople, J. A. In Geometrical Derivatives of Energy Surfaces and Molecular Properties; Jorgensen, P., Simons, J., Eds.; Reidel: Dordrecht, 1985; NATO AS1 Ser. C, Vol. 166, p 109. (21) For discussion, see: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986; p 36. (22) Hout, R. F.; Francl, M. M.; Kahn, S. D.; Dobbs, K. D.; Blurock, E. S.; Pietro, W. J.; McGrath, M. P.; Steckler, R.; Hehre, W. J., University of California, Irvine.
5354
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988
McGrath et al.
TABLE III: Normal-Mode Vibrational Frequencies (cm-I) for HO’NO,“ theor freq (abs i d ) descr of mode HO’ str NO2 a str HO’N bend NO2 s str NO2 scissors O‘N str O’N02 in-plane bend O’N02 out-of-plane bend H0’-N torsion
RHF/6-3 1G 4028 (3.9) 1981 (15) 1505 (4.2) 1607 (8.5) 783 (0.19) 1140 (2.7) 685 (0.30) 909 (0.88) 538 (3.9)
RMP216-3 1G* 3659 (2.2) [996, 0, 9961 1904 (4.6) [13, 43, 561 1373 (2.6) [315, 0, 3151 1352 (5.1) [0, 19, 191 661 (0.088) [5, 0, 51 911 (4.5) [ l , 11, 121 581 (0.26) [36, 2, 381 759 (0.21) [ l , 20, 201 506 (3.5) [132, 0, 1321
“Numbers in brackets are 1H-2H, I4N-l5N, and ‘HI4N-’HI5N isotopic frequency shifts. *Units are D2 Figure 1 of ref 32.
Results and Discussion Evaluation of Theoretical Models. Careful consideration was given to choosing a level of theory sufficient to obtain useful results, but not computationally excessive. Experimental equilibrium structures and infrared spectra for nitric acid and chlorine nitrate were used to test theoretical models for this study. Equilibrium Structures and Electric Dipole Moments. Cox and R i ~ e r o sdetermined ~~ the structure of nitric acid, labelled HO’N02, from the microwave spectra of five isotopomers, and deduced both the magnitude and direction of the electric dipole moment vector from Stark-effect measurements. The experimental data are compared to results obtained from two Hartree-Fock level geometry optimizations, one with the split valence 4-31G basis set,24 the other with the more flexible polarized 6-31G* basis set,25 in Table I. With one exception, the Hartree-Fock level bond lengths are too short; without exception the bond angles are too large. The 6-3 lG* bond angles are slightly c l w r to experimental values than the 4-31G angles, but the reverse is true for bond lengths. Disconcertingly, the O’N bond length error increases from -0.033 8, at RHF/4-31G to -0.072 8, at RHF/6-3 1G*. This suggests that limiting Hartree-Fock theory cannot adequately describe the electronic structure of nitric acid. In support of this contention is the fact that while the R H F dipole moment vectors are directed well (pa/pb) = 2.36 with 4-31G, 2.55 with 6-31G*, 2.25 experimentally, they are roughly 1 D too large in magnitude. An experimental structure for chlorine nitrate, labeled C10”02, has been suggested by Chance and Traub26on the basis of the microwave spectrum of the molecule earlier observed by Suenram and co-~orkers.~’This structure appears along with calculated RHF/4-31G28 and RHF/6-31G* (this work) equilibrium geometries in Table 11. Again with one exception, calculated bond lengths are too short, and, without exception, bond angles are too large. The errors are even larger than those for nitric acid. The O’N bond length error again increases with basis set flexibility, from -0.04 8, at RHF/4-31G to -0.09 k, at RHF/6-3 1G*. While the larger errors (relative to nitric acid) are likely due in part to uncertainties in the experimental structure, it must be. admitted that the electronic structure of chlorine nitrate is unacceptably described with single-determinant wave functions. The second-order Mdler-Plesset treatment of electron correlation, using the 6-31G* basis set, is well documented to reproduce experimental structural parameters of many small molecules better than the underlying Hartree-Fock treatment, especially for molecules with bonds involving oxygen.29 Calculated RMP2/ (23) Cox, A. P.; Riveros, J. M. J . Chem. Phys. 1965, 42, 3106. (24) Nguyen, M.; Hegarty, A. F.; J. Chem. Soc., Perkin Trans, 2 1984,
obsd freq (re1 int)c 3550 (0.1) [929, 0, 9281 1709 (1) [22, 37, 531 1331 (0.8) [317, 4, 3191 1325 (1) [17, 4, 341 647 (0.05) [6, 0, 61 879 (0.7) [-9, 8, 21 579 (0.04) [38, 1, 381 762 (0.08) [-1, 19, 191 456 (0.06) [114, 01 amu-l. ‘Obtained graphically from
6-31G* structures for nitric acid and chlorine nitrate, provided in Tables I and 11, are in much closer agreement with the microwave structures than the corresponding R H F geometries. Reversing the R H F trend, the RMPZ bond lengths are too long (with one exception), and the bond angles are uniformly too small, although errors for most parameters are near the experimental uncertainty ranges. The one RMPZ parameter that is markedly different from the experimental value is the O’N bond length in chlorine nitrate. The theoretical error seemingly goes from -0.09 k, at R H F to +0.09 A at RMP2. While the RMP2 O’N bond length might be expected to be somewhat too long, an error of the magnitude noted seems out of line, especially considering the close agreement between theory and experiment for the analogous O’N bond length in nitric acid. The discrepancy likely reflects the large uncertainty in the experimental structure for chlorine nitrate. The magnitudes of the RMP2 dipole moments are much less than the corresponding R H F magnitudes. For nitric acid, IpMP21 is only 0.1 D larger than the experimental value, although its direction is skewed by about 10’ (pa/pb = 1.47) from experiment. The direction of the RMPZ dipole moment in chlorine nitrate is significantly perturbed as compared to RHF, reflecting the large changes in geometrical and electronic structure due to electron correlation. Vibrational Spectra. A theoretical studyN of 36 small molecules at the R H F and RMPZ levels (6-31G* basis set) reported harmonic vibrational frequencies respectively 13% and 7% higher (on average) than the observed frequencies. The harmonic approximation was found to account for nearly half the average RMP2 error. Another theoretical study3’ involving 13 small molecules at R H F and RMP2 levels found qualitative agreement between theoretical and experimental relative infrared intensities, provided that split valence polarized or larger basis sets were employed. While it was found that Hartree-Fock absolute intensities were sometimes improved with electron correlation, the authors of the study stressed the importance of the harmonic approximation in limiting the accuracy of theoretical infrared intensities. The present spectra for nitric acid and chlorine nitrate from RMP2/6-3 lG* level calculations are consistent with these earlier studies. On the other hand, spectra obtained by using the corresponding Hartree-Fock model are not as good as might have been expected, perhaps a reflection of the inability of the theory to properly reproduce the experimental equilibrium geometries. The theoretical and observed infrared frequencies of nitric acid are collected in Table 111. The experimental frequency assignments listed for normal modes v5 (NO2scissoring) and v6 (O’N stretching) have been switched from the assignments proposed by McGraw et al.32 Our results support the assignments made
2043. Note: Figure 1 is mislabeled.
(25) Included in: Whiteside. R. A,: Frisch. M. J.: Poole. J. A. Eds. Curnegie-Mellon Quantum Chemistry Archive: 3rd ed.;‘ CamegiGMellon: Pittsburah. PA. 1983. (26) ehance, K. V.; Traub, W. A. J . Mol. Spectrosc. 1982, 95, 306. (27) (a) Suenrarn, R. D.; Johnson, D. R.; Glasgow, L. C.; Meakin, P. Z . Geophys. Res. Lett. 1976,3,611. (b) Seunram, R. D.; Johnson, D. R. J. Mol. Spectrosc. 1977, 65, 239. (28) All ClN03 RHF/4-3 1G structures given in this work were calculated from the geometrical parameters reported in ref 11 as starting values.
(29) (a) DeFrees, D. J.; Levi, B. A.; Pollack, S. K.; Hehre, W. J.; Binkley, J. S.; Pople, J. A. J. Am. Chem. SOC.1979, 101, 4085. (b) Reference 21, Chapter 6. (30) Hout, R. F., Jr.; Levi, B. A.; Hehre, W. J. J . Comput. Chem. 1982, 3, 234. (31) Yamaguchi, Y.; Frisch, M.; Gaw, J.; Schaefer, H. F., 111; Binkley, J. S. J. Chem. Phys. 1986, 84, 2262. (32) McGraw, G. E.; Bernitt, D. L.; Hisatsune, I. C. J. Chem. Phys. 1965, 42, 237.
Isomers of Nitric Acid and Chlorine Nitrate
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988 5355
TABLE I V Normal-Mode Vibrational Frequencies (cm-’) for C10’N02’
theor freq (abs i d )
SYm
of mode (A’) y2 (A’) u3 (A‘) v4 (A‘) y5 (A’) y b (A’) y7 (A’) ya (A’‘) vq (A’‘) VI
descr of mode NO2 a str NO2 s str C10’ str NOz scissors O’N str O’NOZin-plane bend ClO’N bend O’NOz out-of-plane bend torsion
RHF/6-31G* 1953 (15) 1558 (8.9) 962 (1.3) 1060 (5.7) 549 (0.056) 790 (0.078) 315 (0.018) 887 (0.80) 110 (0.0033)
obsd freq (re1 int)c
RMP2/6-31G 1970 (3.7) [45] 1323 (5.2) [ l l ] 800 (0.51) [ l ] 763 (4.0) [lo] 397 (2.1) [2] 531 (2.0) [2] 252 (0.0095) [ l ] 697 (0.24) [ 181 130 (0.015) [O]
1735 (1) [41] 1292 (0.9) [I21 809 (0.5) [SI 780 (0.5) [7] 434 (0.2) [2] 560 (0.3) [3] 270 (0.01) 711 (0.1) [17] 120d
‘Numbers in brackets are I4N-l5N isotopic frequency shifts. bunitsare DzA-2 amu-’. cObtained graphically from Figure 3 of ref 39. dFrom ref 26.
by earlier investigator^^^ of 879 cm-I for the O’N stretch, with the scissor mode appearing around 600 cm-I (647 cm-I). McGraw et al. assigned 879 cm-I to v5, because they expected a 10-15-cm-’ I5N isotopic shift for this mode and because the choice led to lower frequency errors in their normal-coordinate analysis calculations. The isotopic shifts (see Table 111) for the RMP2/6-31G* scissoring mode at 661 cm-I are essentially identical with the shifts for the 647-cm-I experimental band, showing no I5N shift but small deuterium shifts. In addition, the RMP2/6-31G* O’N stretch (91 1 cm-’)/N02 scissors (661 cm-I) intensity ratio of about 50 supports the fact that the experimental 879-cm-I band is much more intense than the 647-cm-I band. Therefore, we have interchanged the experimental frequencies assigned to v5 and v6 by McGraw et al. With the above switch, the RMP2/6-31G* nitric acid spectrum reproduces the order of the experimental frequencies. The average absolute percentage deviation from experiment of the RMP2/63 1G* frequencies is 4.1%, with all frequencies too large, except v8, which is 3 cm-I too small. The RHF/6-31G* calculations do not properly order the relatively close v2 and v3 modes ( A ~ 2 3 ” p ‘ ~ = 6 cm-l). The average deviation (18.9% all frequencies too large) is outside the often-quoted 10-15% error range. Two RMP2/ 6-31G* modes stand out with significantly larger errors: the NO2 asymmetric stretching mode, v2, and the O’N bond torsion mode, vg, both with frequencies 11% higher than experiment. The intensity of the torsional mode is also poorly described by the theory, predicted to be much too strong. Neither R H F or RMPZ models orders the intensities correctly, but both levels separate the stronger modes vl, v2, v3, v4, and v6 from the much less intense v5, v7, and vg modes, vg excepted. Calculated and experimental chlorine nitrate spectra are given in Table IV. The RMP2/6-31G* assignments agree with the most recent experimental tabulation34 in that the ordering of the two assigned sets of frequencies is the same. As with nitric acid, the R H F calculations do not correctly order two relatively close modes, v3 and v4 (Av34cxPt1= 29 cm-I). The theoretical 6-31G* frequencies deviate on average 22.9% and 5.5% from experiment ( R H F and RMP2, respectively). Except for vg, all of the R H F frequencies are too large; the RMP2 frequencies, excepting the two highest ( v l and v2) and lowest (vg), are too small. If experimental harmonic frequencies were available, the RMPZ frequencies would seem even more red shifted. This means that the RMP2/6-31G* model provides a description of the bonding in chlorine nitrate that underestimates the strength of the C10’ and O’N bonds (vl and v2 are NO2 stretching modes). The calculated intensities are not ordered correctly at the R H F or RMPZ levels, but the RMPZ calculations separate the more intense modes, v1-v6, from the much weaker v7-v9 modes. The very weak R H F intensities of v5 and v6 are in poor agreement with experiment. Combining the RHF dipole moments from the RMP2 calculations with the RMP2 force constants leads to significantly improved “RHF” intensities for these two modes, showing that the poor (RHF) intensities are mainly due to the poor R H F force constants. ~~~
~~~
~~
(33) Cohn, H.; Ingold, C. K.; Pwle, H. G. J . Chem. SOC.1952, 4272. (34) Wilson, W. W.; Christe, K. 0. Inorg. Chem. 1987, 26, 1573.
TABLE V: Equilibrium Structures, Dipole Moments, and Relative Energies for Conformers of Peroxynitrous Acid‘,* trans- ciscistransparameter cis-perp perp cis trans trans 1.149 (1.182) 1.150 1.161 1.150 1.151 1.355 (1.490) 1.364 1.322 1.342 1.353 1.377 (1.440) 1.377 1.386 1.395 1.393 0.953 (0.980) 0.951 0.957 0.952 0.951 115.6 (113.9) 109.7 115.5 115.9 109.9 113.7 (109.7) 107.1 115.8 111.9 105.4 104.0 (101.0) 103.0 104.5 99.2 100.1 -7.3 (-5.0) 176.8 103.2 85.8 (91.9) 18:]c 2.36 2.32 1.87 (1.88) 1.13 2.34 1.1 1.7 2.7 0.9 0
:Ic
E]‘
transcis 1.151 1.345 1.388 0.955 111.3 108.7 104.5 l8:Ic 2.14
5.3
Bond lengths in angstroms, bond angles in degrees, energies in kcal/mol. *RHF/6-31G* except for cis-perp conformer, where RMP2/6-31G1 values are given in parentheses. CConstrained. E
TABLE VI: Normal-Mode Vibrational Frequencies (cm-’) for HOO’N=O
theor freq (abs int) descr of mode H O str N=O str HOO’ bend
00’ str O’N=O bend
O‘N str a a HO-0’ torsion
RHF/6-31G*
RMP2/6-31GS
4048 (1.8) 2022 (5.0) 1588 (1.3) 1196 (0.86) 960 (1.5) 925 (4.1) 404 (0.23) 438 (0.36) 213 (2.7)
3677 (0.95) 1692 (3.7) 1398 (1.4) 946 (0.060) 814 (0.92) 439 (6.2) 384 (0.063) 337 (0.12) 211 (1.5)
“The 0’-N=O torsion and OO’N bend modes are coupled and cannot be exclusively assigned.
Relative Stabilities of Isomers of Nitric Acid and Chlorine Nitrate. While it is apparent that Hartree-Fock theory is not appropriate for fully characterizing the structures and normalmode frequencies and intensities of peroxynitrous acid and for possible isomers of chlorine nitrate, RMP2/6-3 1G* calculations on nitric acid and chlorine nitrate show that a reasonable (if not useful) level of accuracy can be obtained even a t this relatively simple level of correlated theory. R H F calculations are, however, not without utility, and have been employed here to investigate the relative stabilities of structural isomers of chlorine nitrate, so as to furnish a rough guide for identifying structures that merit further study. In addition, the conformational preference of peroxynitrous acid can be reliably determined at the R H F level. For example:g RHF/6-31G* calculations for HOOH and FOOF yield dihedral angles of 115’ and 84O, respectively, compared to experimental values of 120’ and 87.5’. Isomers of Nitric Acid. Calculated equilibrium geometries corresponding to six different arrangements of peroxynitrous acid, including four planar conformers (C, symmetry) and two conformers of CIsymmetry are provided in Table V. For all three pairs of conformers differing in rotation about the HO0’-NO bond, a cis arrangement is preferred. To verify this preference,
5356 The Journal of Physical Chemistry, Vol. 92, No. 19, 1988 TABLE VII: Energies and Enthalpies" (kcal/mol) for the Reactions XO NO2
+
XO
X=H AH(0 K)
A&C
I
RMP2/6-31G*
-53.1
exptlb I1
RMP2/6-31G*
"AH(0 K) = AE,,, 1376-1 378.
+
+ NO2
-17.8
K). AH(298 K) = A&,
-47.0 -47.8 -14.3
+ AEib(298
we performed single-point higher-level RMP2/6-31 l++G** calculations on the two best conformers of peroxynitrous acid given in Table V. Previous work by Turner3' demonstrated that this level of theory correctly favors the trans conformer of nitrous acid relative to the cis. Here, the 6-31 l++G** calculations show a difference of 1.3 kcal/mol between cis-perp and trans-perp conformers, the former being the preferred. The fact that the two most stable conformers for peroxynitrous acid exhibit nearly perpendicular arrangements about the 00 single bond is expected in light of previously available structural information for peroxides. The RMP2/6-31G* geometry for the best (cis-perp) conformer also exhibits nearly perpendicular HOO' and O'NO planes and is also included in Table V. As expected, all bond lengths are larger and all bond angles smaller than their respective R H F values. The R H F and RMP2 structures of peroxynitrous acid were both characterized as potential energy minima; their calculated infrared spectra are provided in Table VI. Peroxynitrous acid is known as a transient molecule in solution. In addition, its UV spectrum has been recorded,35 and its 00' bond energy estimated as -20 kcal/mo1.8,35 When produced by reaction of H O and NO2 radicals, peroxynitrous acid dissociates (pK, = 5.3), leaving the stable OONO anion; the undissociated acid isomerizes spontaneously, forming nitric acid.36 Burkholder et a1.* have attempted to form peroxynitrous acid by the reaction analogous to (1) in the gas phase and record its infrared spectrum in the 1850-3850-cm-' region, which includes among the fundamentals only the HO stretching mode. Peroxynitrous acid was not observed, because either the only product of reaction was nitric acid, or the yield was
