Ab Initio Study of Pernitric Acid: Comparison with Experimental

Sep 26, 1996 - Vertical excitations are computed by CASPT2 for comparison with future high-resolution UV−visible spectra and match the low resolutio...
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J. Phys. Chem. 1996, 100, 15731-15734

15731

Ab Initio Study of Pernitric Acid: Comparison with Experimental Spectra Zhi Chen and Tracy P. Hamilton* Department of Chemistry, UniVersity of Alabama at Birmingham, Birmingham, Alabama 35294 ReceiVed: June 17, 1996X

A high-level ab initio theoretical study has been performed on the spectra and bond energies of pernitric acid, HO2NO2. Excellent agreement with experimental rotational constants, 15N NMR chemical shifts, HO2 + NO2 reaction enthalpy, and vibrational frequencies are obtained. Slight revisions of low-frequency normal modes have been made. Vertical excitations are computed by CASPT2 for comparison with future highresolution UV-visible spectra and match the low resolution UV-visible spectra of pernitric acid in solution. The optimized geometries reported are superior to previous microwave structures because assumptions of bond lengths and angles from the analogous nitric acid and hydrogen peroxide molecules introduce significant errors.

Introduction In recent years there has been considerable effort in the study of the preparation, decomposition photochemistry, and pulse radiolysis of pernitric acid (HO2NO2). Twenty years ago, Simonaitis and Heicken suggested that a complex of HO2 and NO2 could be important in atmospheric chemistry.1 The putative HO2NO2 complex could remove NO2 or produce other NOx species. The roles of nitrogen oxides in tropospheric air pollution and in the catalytic destruction of stratospheric ozone were known at that time.2,3 In 1977 Niki et al. reported gas-phase kinetics and Fourier transform infrared spectroscopy of pernitric acid. They verified its formation from HO2 and NO2 and concluded from the IR spectrum that HO2NO2 was a molecule, not simply a complex.4 Graham et al. studied the thermal decomposition of HO2NO2 and concluded that pernitric acid has a 12 s lifetime with respect to thermal decomposition at 1 atm of pressure and room temperature.5 HO2NO2 will have a much longer lifetime in the stratosphere, due to lower temperatures and pressure and due to the absence of wall effects (a major source of HO2NO2 loss in the kinetics experiments). Levine et al. suggested that the rate of pernitric acid formation in the troposphere will be similar to the rate of formation of peroxyacetyl nitrate, the well-known irritant in photochemical smog.6 They also conclude that HO2NO2 contributes to the oxidant character in those atmospheres. Hanst and Gay arrived at the same conclusion independently.7 Baldwin and Golden ran RRKM simulations of the reaction

HO2NO2 H HO2 + NO2

(1)

with N2 included as a third body, using the known frequencies for pernitric acid above 800 cm-1 and estimated frequencies for the remaining seven lower modes and all transition state modes.8 The activation energy they obtained was 23 kcal/mol, similar to the 26 kcal/mol activation barrier found for loss of NO2 from PAN.9,10 Suenram et al. used microwave spectroscopy to derive the lowest torsion frequency and some constrained structural parameters for HO2NO2.11 This enabled the clear identification of pernitric acid in the atmosphere.12 May and Peterson observed three more bands in the IR spectrum of HO2NO2, at 940, 722, and 919 cm-1, definitely assigning the mode at 940 cm-1 to the O-O stretch.13 Zhu et al. demonX

Abstract published in AdVance ACS Abstracts, September 15, 1996.

S0022-3654(96)01772-8 CCC: $12.00

strated that gas-phase HO2NO2 decomposes quickly into nitrous acid and nitric acid on surfaces.14 They ruled out the reaction

HO2 + NO2 f HONO + O2

(2)

as a source of atmospheric nitrous acid. A reanalysis of the unimolecular decomposition of peroxynitrates by Zabel led to a slightly revised reaction enthalpy for reaction 1 of 21 kcal/mol.15 Zabel also states that there is no evidence for a barrier for the reverse reaction; therefore, the reaction enthalpy will be equal to the activation barrier for HO2NO2 decay into HO2 and NO2. Kenley et al. reported a synthesis of HO2NO2 without impurities or side products, reacting hydrogen peroxide with a nitronium ion source such as HNO3 or NO2BF4.16 This synthesis enabled them to also perform the first study of the decomposition of pernitric acid in aqueous solution, concluding that decay at pH 4.7 most likely happened via the dissociation of the pernitrate anion into nitrite and molecular oxygen. Lammel et al. also studied the decomposition of pernitric acid in aqueous solution, showing that the decay of HO2NO2 at low pH is much slower since the route involving pernitrate is unimportant.17 They also concluded that the pathway for pernitrate decay (nitrate + O atoms) suggested by Wagner et al. was incorrect.18 Løgager and Sehested performed pulse radiolysis experiments on HO2NO2 and its conjugate anion to arrive at a pKa of 5.85.19 This is outside the range 4.6-5.0 proposed by Lammel et al.,17 probably because they used a different mechanism in their kinetic model. Løgager and Sehested measured large rate constants for formation of HO2NO2 and O2NO2- from NO2 reacting with HO2 and O2-, respectively.19 They also argued that the decay of HO2NO2 into HO2 and NO2 is less important in aqueous solution than in the gas phase. Very recently Appelman and Gosztola prepared 1.5 M pernitric acid and were able to measure the 15N NMR chemical shifts, UV spectrum, and Raman spectrum of pernitric acid.20 They observed a monotonic increase in the absorbance from 290 to 230 nm, in contrast to the peak seen at 240 nm in earlier work.19 They pointed out that small errors in background subtraction can give spurious results. HO2NO2 has been detected in low-temperature matrix studies of nitric acid photochemistry in addition to many other interesting products.21 Theoretical work on the ground-state geometry and excitedstate spectrum of pernitric acid has been done by Saxon and © 1996 American Chemical Society

15732 J. Phys. Chem., Vol. 100, No. 39, 1996

Chen and Hamilton

TABLE 1: The Geometric Parameters for Pernitric Acid (Distances in Å, Angles in deg) HF/6-311++G**

B3LYP/6-311++G**

QCISD/6-31G**

MP2/6-311++G(2df,2pd)

expta

1.168 1.165 1.373 1.355 0.948 130.5 117.7 111.7 111.5 105.0 164.9 83.1

1.189 1.190 1.531 1.399 0.972 133.8 116.3 109.9 109.6 103.4 171.1 90.3

1.205 1.205 1.477 1.419 0.971 132.7 117.1 110.1 108.6 102.1 169.0 83.8

1.190 1.193 1.511 1.398 0.965 134.6 116.0 109.4 108.0 102.0 171.9 86.1

HNO3: 1.211 HNO3: 1.199 HNO3: 1.406 HO2: 1.335 HO2: 0.977 HNO3: 130.3 HNO3: 115.9 HNO3: 113.8

O2-N O3-N O4-N O-O H-O ∠O2NO3 ∠O2NO4 ∠O3NO4 ∠NO4O5 ∠OOH D(OONO3) D(HOON) a

synb

1.511

antib

1.515

102.9

101.2

72.8

106.2

HO2: 104.1

b

Reference 35. Reference 11.

Liu in 1985.22 Given the importance of pernitric acid in atmospheric chemistry, the difficulties in synthesizing pernitric acid, the difficulties of doing and assigning spectra, and the theoretical difficulties expected for a molecule with weak bonds and many lone pairs, we have revisited this problem at high levels of theory. Presented in this paper are theoretical calculations of the geometry, harmonic vibrational frequencies, vertical excitation energies, and 15N NMR chemical shifts for pernitric acid, along with N-O and O-O bond enthalpies.

Figure 1. Geometry and atom labeling of the pernitric acid molecule.

Results and Discussion Methodology The Gaussian 94 program was used in optimization of molecular structures and harmonic vibrational frequency calculations.23 All stationary points were characterized by vibrational frequency computations. The levels of theory employed were Hartree-Fock (HF), the Becke3-Lee-Yang-Parr (B3LYP) density functional,24,25 second-order Møller-Plessett perturbation (MP2) theory, and quadratic configuration interaction theory with single and double substitution (QCISD) with the 6-31G** basis set, HF, B3LYP, and MP2 with the 6-311++G** basis, and MP2 with a 6-311++G(2df,2pd) basis set. Bond energies were computed using the complete basis set extrapolation method known as CBS-q26 in addition to some of the methods given above. The ACES II program27 was used to compute the 15N NMR chemical shieldings at the HF28 and MP229 levels of theory for nitric and pernitric acid. The chemical shift of pernitric acid was computed by subtracting the theoretical chemical shielding for nitric acid from the computed shielding for pernitric acid. The chemical shifts were computed at geometries optimized at many levels of theory. The MOLCAS-3 computer code30 was used to compute vertical excitation energies from computing the complete active space self-consistent field (CASSCF) energies for the first five electronic states at the B3LYP/6-31G** optimized ground-state geometry. The basis set used in the CAS was a 4s3p1d atomic natural orbital (ANO) basis from a 14s9p4d3f primitive set for N and O and a 3s1p ANO basis from a 8s4p3d primitive set.31 The active space consisted of 10 electrons in 10 orbitals, chosen from Hartree-Fock orbitals since the lowest lying electronic states arise from excitation from the highest occupied molecular orbitals (MOs) to the lowest unoccupied MOs. To eliminate convergence difficulties from root flipping, state averaging with equal contributions from the five electronic states was specified for the orbital optimization procedure. The CASSCF energy was corrected using secondorder perturbation theory (CASPT2 theory)32 to account for dynamic electron correlation. Normal mode assignments were made by animation of the modes and by the potential energy distribution in terms of internal coordinates.33

Structures. The ground state of pernitric acid is the C1 structure shown in Figure 1. The molecule is nearly planar except for the hydrogen which is nearly orthogonal to the plane. The two planar forms having cis and trans arrangements of HOON are transition states for the rotation of the O-H bond, with rotation barriers that are typical of single bonds. The Cs cis geometry is 1.5, 1.2, and 2.7 kcal/mol above the C1 minimum at the HF/6-31G**, B3LYP/6-31G**, and MP2/6-31G** levels of theory, respectively. The Cs trans geometry is 3.1, 4.0, and 3.7 kcal/mol above the C1 minimum at the HF/6-31G**, B3LYP/6-31G**, and MP2/6-31G** levels of theory, respectively. Zero-point vibrational energy is incorporated into the relative energies. The cis arrangement is slightly favored due to intramolecular hydrogen bonding. This is in excellent agreement with the results obtained by Saxon and Liu (their relative energies do not have zero-point energy included).22 The rest of the paper will deal with the C1 structure at higher levels of theory, as it is clearly the only minimum energy conformer. Table 1 lists the bond lengths, bond angles, and dihedral angles of HO2NO2 at various levels of theory, along with some experimental values for HNO3,35 H2O2,35 and pernitric acid. Note that the experimental pernitric acid values were obtained by using assumed distances and angles (from HNO3 and H2O2) for the parameters not listed in the HO2NO2 column. The assumed O-O bond length from hydrogen peroxide is apparently too short, and the assumed O3NO4 bond angle from nitric acid is 4° too large. Suenram et al.11 correctly chose the bond length that is most different from nitric acid or hydrogen peroxide; the N-O4 distance is 0.1 Å longer in pernitric acid than in nitric acid. This is also the distance that is not predicted well at lower levels of theory. HF theory predicts it to be very short, and MP2 with a small basis greatly overestimates the bond distance.22 The HF, B3LYP, and MP2 optimized structures with the 6-31G** basis are given in supporting information. The C1 minimum is intermediate between the syn and anticlinal structures proposed from the microwave experiment. The most direct comparison that can be made is between the experimental rotational constants (A ) 11 994, B ) 4665, C ) 3397 MHz)11 and the computed ones. For example, the B3LYP/

Ab Initio Study of Pernitric Acid

J. Phys. Chem., Vol. 100, No. 39, 1996 15733

TABLE 2: Harmonic Vibrational Frequencies (in cm-1) for Pernitric Acid HF/6-311++G** 1 2 3 4 5 6 7 8 9 10 11 12 a

140 321 438 658 828 901 1046 1235 1558 1617 1923 4087

O-NO2 tors. HOON tors. NOO bend NO2 rock NO2 scissor umbrella N-O4 str. OO str. sym. NO2 str. OOH bend. asym. NO2 str. OH str.

B3LYP/6-311++G**

MP2/6-311++G(2df,2pd)

139 302 363 450 651 736 813 989 1355 1419 1804 3710

152 320 378 457 669 753 795 994 1326 1445 1942 3804

QCISD/6-31G** 134 298 377 514 682 748 836 988 1381 1452 1800 3797

expt

O-NO2 tors. asym. NOO, O4NO3 bend HOON tors. N-O4 str. sym. NOO, O4NO3 bend umbrella NO2 scissor OO str. sym. NO2 str. OOH bend asym. NO2 str. OH str.

145a 340b 483b 654b 722b 803c 945b 1304c 1397c 1728c 3540c

Reference 11. b Reference 20. c Reference 4.

6-311++G** geometry gives A ) 11 971, B ) 4568, C ) 3346 MHz, and the MP2/6-311++G(2df,2pd) structure has predicted rotational constants of A ) 11 958, B ) 4707, C ) 3418 MHz. The HF/6-311++G** rotational constants are more in error, at A ) 13 006, B ) 5054, C ) 3695 MHz. Vibrational Frequencies. Most of the vibrational frequencies that were unobserved when Saxon and Liu22 performed their theoretical study have now been observed. Appelman and Gosztola20 give a series of assignments for the known spectrum, which has only one missing low-frequency vibration. Table 2 contains the vibrational frequencies and mode assignments from our calculations. The computed HF stretching frequencies are larger than the correlated ones, as expected. The major difference between the HF frequencies and the frequencies computed at the correlated levels is in the N-O4 stretch, which drops precipitously from 1046 cm-1 in HF theory to correlated values that range from 450 to 514 cm-1. This trend is in concordance with the trend in the theoretical N-O4 bond distances; that is, the N-O4 distance is longer in the correlated geometries. Other qualitative differences between HF and correlated frequencies result from mixing of the NOO bend, O4NO3 bend, and NOOH torsion. The mode assignments of Appelman and Gostzola are identical to ours for the higher frequencies down to 722 cm-1, which can also be referred to as a NO2 wag. The lowest band at 145 cm-1 is clearly the O-NO2 torsion. The band at 654 cm-1 is best described as a symmetric combination of NOO and O4NO3 bending motions, and 483 cm-1 is probably the N-O4 stretch. This is the reverse of their assignment. The frequency at 340 cm-1 is probably the NOOH torsion instead of an NOO bend, although this mode was visually similar to the one expected to be seen slightly below 300 cm-1. This vibration strongly couples the NOO and O4NO3 internal coordinates asymmetrically. The frequencies used in Baldwin and Golden’s RRKM simulations were quite reasonable, and their estimate of 71.6 eu for the entropy at room temperature8 is in excellent agreement with ab initio values, e.g. 71.1 eu at the B3LYP/6-311++G** level of theory. Baldwin and Golden did not have access to any theoretical methods to compute the entropy or unobserved vibrational frequencies. NMR Spectrum. The computed 15N NMR shieldings and chemical shifts are given in Table 3. The gauge-invariant atomic orbital34 methods were chosen. The differences in shielding between pernitric acid and nitric acid were used to determine the chemical shifts. It is clear that the geometry used affected the shifts very little even though shieldings were quite sensitive to geometry and level of theory. The chemical shifts for HF/ 6-31G**, B3LYP/6-31G**, and MP2/6-31G** geometries are not listed in Table 3, but are very similar also. At the HF level

TABLE 3: (in ppm)

15N

SCF NMR Chemical Shieldings and Shifts geometryb

wave functiona SCF

HOONO2 HONO2 shift HOONO2 HONO2 shift

MP2

HF

B3LYP

MP2

QCISD

-91.0 -88.9 -2.1 5.5 15.9 -10.4

-128.8 -130.3 1.5 -2.2 14.3 -16.5

-136.0 -139.2 3.2 -2.8 14.5 -17.3

-145.5 -146.6 1.1 1.9 14.3 -12.4

expt

-28.3 -28.3

a

Gauge-invariant atomic orbital method and 6-31G** basis set were used. b The geometry was optimized at the level of theory indicated using 6-311++G** basis, except for the QCISD geometry, which was optimized with the 6-31G** basis set.

TABLE 4: Vertical Excitation Energies (in eV) HOONO2 statea

∆E CASPT2

∆E CAS

character

2 3 4 5

4.903 5.171 5.853 7.009

5.041 5.433 6.468 7.535

NO2 n f π* NO2 n f π* HO2 n f pσ* NO2 n⊥ f π*

a

Energies computed at the B3LYP/6-31G** geometry.

of theory, the chemical shielding at N is nearly identical for HNO3 and HO2NO2. When electron correlation is incorporated via MP2 theory, the chemical shifts computed are -10 to -17 ppm, which are closer to the experimental shift at -28.5 ppm.20 Electronic Spectrum. Table 4 presents the vertical excitation energies computed at the B3LYP/6-31G** geometry. CASPT2 predicts two states near 5 eV, (approximately 250 nm). This is the region where the first electronic excitation is observed.19,20 The CAS and CASPT2 vertical excitation energies are lower than previous CI results because in the CI study the orbitals used were optimized for the ground state, lowering its energy relative to the rest of the states.22 All states are well described by one-electron excitations, the descriptions of which are given by Saxon and Liu and in Table 4.22 Bond Energies. The bond energies of the N-O4 and O-O bonds are computed to predict the stability of gas-phase HO2NO2. Straightforward computation of bond energies is inaccurate, given the difference in the number of electron pairs, and hence electron correlation, unless accurate energies are used. The CBS-q method attempts to estimate the complete basis set limit for HF and some of the correlation energy.25 The CBS-q enthalpy for reaction 1 is 22 kcal/mol, compared to the 21-23 kcal/mol from various kinetic models. The O-O bond strength is 32 kcal/mol, indicating that unimolecular decay of pernitric acid in the gas phase will occur by scission of the N-O4 bond. HF/6-311++G** actually predicts a negative enthalpy of -12 kcal/mol for reaction 1, whereas B3LYP/6-311++G** gives

15734 J. Phys. Chem., Vol. 100, No. 39, 1996 16 kcal/mol and MP2/6-311++G** predicts 26 kcal/mol for the 0 K enthalpy of reaction 1. Conclusions There is a single C1 symmetry energy minimum conformer of pernitric acid at all levels of theory, which is consistent with the previous results of Saxon et al.22 The agreement between structures optimized at correlated levels of theory and experimental rotational constants is impressive. For HO2NO2 the B3LYP method predicts known vibrational bands better than MP2, even with a large basis set, and is equal in quality to QCISD/6-31G**. Minor reassignments of low-frequency modes are suggested, and the unobserved frequency should be ∼280 cm-1. The 15N NMR chemical shifts computed at the MP2/6-31G** level are -10.4, -16.5, and -17.3 (average -14.5) ppm, using the HF/6-311++G**, B3LYP/6-311++G**, and MP2/6311++G** geometries, respectively. Agreement with the experimental chemical shift of -28.5 ppm may result from improving the basis or electron correlation method employed. The CBS-q enthalpy of 22 kcal/mol for the reaction HO2NO2 H HO2 + NO2 is in excellent agreement with the 21-23 kcal/ mol values from various kinetic models. The CASSCF and CASPT2 vertical excitation energies are included for comparison with future experimental studies of excited states. Acknowledgment. We would like to thank Dr. Nathan Harris for helpful comments on the manuscript. Supporting Information Available: Table of pernitric acid optimized geometries (1 page). Ordering information is given on any current masthead page. References and Notes (1) Simonaitis, R.; Heicklen, J. Phys. Chem. 1976, 80, 1. (2) Leighton, P. A. Photochemistry of Air Pollution; Academic Press: New York, 1961. (3) Crutzen, P. J. J. Geophys. Res. 1971, 76, 7311. (4) Niki, H.; Maker, P. D.; Savage, C. M.; Breitenbach, L. P. Chem. Phys. Lett. 1977, 45, 564. (5) Graham, R. A.; Winer, A. M.; Pitts, J. N., Jr. Chem. Phys. Lett. 1977, 51, 215. (6) Levine, S. Z.; Uselman, W. M.; Chan, W. H.; Calvert, J. G.; Shaw, J. H. Chem. Phys. Lett. 1977, 48, 528. (7) Hanst, P. L.; Gay, B. W. EnViron. Sci. Technol. 1977, 11, 1105. (8) Baldwin, A. C.; Golden, D. M. J. Phys. Chem. 1978, 82, 644. (9) Kenley, R. A.; Hendry, D. G. J. Am. Chem. Soc. 1977, 99, 3198.

Chen and Hamilton (10) Cox, R. A.; Roffey, M. J. EnViron. Sci. Technol. 1977, 11, 900. (11) Suenram, R. D.; Lovas, F. J.; Pickett, H. M. J. Mol. Spectrosc. 1986, 116, 406. (12) Rinsland, C. P.; Zander, R.; Farmer, C. B.; Norton, R. H.; Brown, L. R.; Russell, J. M., III; Park, J. H. Geophys. Res. Lett. 1986, 13, 761. (13) May, R. D.; Peterson, D. B. J. Mol. Spectrosc. 1991, 150, 647. (14) Zhu, T.; Yarwood, G.; Niki, H. EnViron. Sci. Technol. 1993, 27, 982. (15) Zabel, F. Z. Phys. Chem. 1995, 188, 119. (16) Kenley, R. A.; Trevor, P. L.; Lan, B. Y. J. Am. Chem. Soc. 1981, 103, 2203. (17) Lammel, G.; Perner, D.; Warneck, P. J. Phys. Chem. 1990, 94, 6141. (18) Wagner, F.; Strehlow, H.; Busse, G. Z. Phys. Chem. 1980, 123, 1. (19) Løgager, T.; Sehested, K. J. Phys. Chem. 1993, 97, 10047. (20) Appelman, E. H.; Gosztola, D. J. Inorg. Chem. 1995, 34, 787. (21) Koch, T. G.; Sodeau, J. R. J. Phys. Chem. 1995, 99, 10824. (22) Saxon, R. P.; Liu, B. J. Phys. Chem. 1985, 89, 1227. (23) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; HeadGordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, ReVision A.1; Gaussian, Inc.: Pittsburgh, PA, 1995. (24) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (25) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1993, 98, 5648. (26) Petersson, G. A.; Tensfeldt, T. G.; Montgomery, J. A., Jr. J. Chem. Phys. 1991, 94, 6091. (27) ACES II, an ab initio program system authored by J. F. Stanton, J. Gauss, J. D. Watts, W. J. Lauderdale, and R. J. Bartlett. The package also contains modified versions of the MOLECULE Gaussian integral program of J. Almlo¨f and P. R. Taylor, the ABACUS integrals derivative program of T. U. Helgaker, H. J. A. Jensen, P. Jørgensen, and P. R. Taylor, and the PROPS property integral package of P. R. Taylor. (28) Wolinski, K.; Hinton, J. F.; Pulay, P. J. Am. Chem. Soc. 1990, 112, 8251. (29) Gauss, J. Chem. Phys. Lett. 1992, 191, 614. (30) Andersson, K.; Blomberg, M. R. A.; Fu¨lscher, M. P.; Kello¨, V.; Lindh, R.; Malmqvist, P.-A° .; Noga, J.; Olsen, J.; Roos, B. O.; Sadlej, A. J.; Siegbahn, P. E. M.; Urban, M.; Widmark, P.-O. MOLCAS, Version 3; University of Lund: Sweden, 1994. (31) Widmark, P.-O.; Malmqvist, P.-A° .; Roos, B. O. Theor. Chim. Acta 1990, 77, 291. (32) Andersson, K.; Malmqvist, P.-A° .; Roos, B. O. J. Chem. Phys. 1992, 96, 1218. (33) Zerbi, G. In Vibrational Intensities in Infrared and Raman Spectroscopy; Person, W. B., Zerbi, G., Eds.; Elsevier: Amsterdam, 1982; p 23. (34) Ditchfield, R. Mol. Phys. 1974, 27, 789. (35) Harmony, M. D.; Laurie, V. W.; Kuczkowski, R. L.; Schwendeman, R. H.; Ramsay, D. A.; Lovas, F. J.; Lafferty, W. J.; Maki, A. G. J. Phys. Chem. Ref. Data 1979, 8, 619.

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