J. Phys. Chem. 1988, 92, 641-644
64 1
HOSO, and HOSO, Radicals Studied by ab Initio Calculation and Matrix Isolation Technique Shigeru Nagase, Department of Chemistry, Faculty of Education, Yokohama National University, Yokohama 240, Japan
Satoshi Hashimoto, and Hajime Akimoto* Division of Atmospheric Environment, National Institute for Environmental Studies, P.O. Tsukuba-gakuen Ibaraki 305, Japan (Received: October 1 , 1986)
Sulfo (HOS02) and sulfodioxy (HOS04) radicals have been characterized by use of ab initio calculations at the HF/3-21G(*) level, and the results were compared with the infrared spectral data from low-temperature-matrixexperiments. The calculated vibrational frequencies and the isotope shift as well as a supplemental experimental result supported the assignment of the observed infrared absorption bands in the Ar matrix at 3539.9 (3528.6), 1309.2 (1308.7), 1097.3 (1096.0), and 759.5 (735.1) cm-' to the 0-H st, S(=O), asym st, S(=O), sym st, and S - O H st modes of the H'60S'602 (H1*OS'602)radical, respectively. The HOSO., radical was found to be located as a minimum on the potential surface, and the fully optimized geometry and vibrational frequencies were obtained, although the detection of the radical in the O2matrix was unsuccessful. Enthalpy changes for the reactions HOS02 + O 2 HOZ + SO3 (2) and HOSOZ+ O2 HOS04 (3) were calculated at the MP4(SDTQ)/6-3 lG**//3-21G(*) and MP3/6-3 lG**//3-21G(*) levels, respectively, and the results were discussed in comparison with the experimental evidence.
-
Introduction Sulfo (hydroxysulfonyl) radical (HOS02) is recognized' as an important intermediate in the atmospheric oxidation of SOz initiated by O H radicals OH SO2 (+M) -* HOS02 (+M) (1) The HOSOzradical thus formed is expected to react with oxygen in the atmosphere by either HOSOz + 0 2 HOz + SO3 (2) or HOS02 + O2 + M HOS04 + M (3) In their study of photooxidation of the C O / H O N O / N O / N02/S02mixture in air, Stockwell and Calvert2 have presented evidence that reaction 2 may be the dominant channel for the reaction of HOS02 radicals with oxygen. Further evidence supporting the predominance of reaction 2 has been reported in more recent direct kinetic studies.3-6 On the other hand, thermochemical estimates by Benson' put the enthalpy changes for reactions 2 and 3 to be 8 f 2 kcal mol-l endothermic and 16 kcal mol-l exothermic, respectively, thus favoring reaction 3 in contrast to the experimental evidence. Since reaction 2 followed by the reaction HOz + NO OH NO2 (4) constitutes chain-sustaining steps while reaction 3 does not, the experimental observations for the predominance of reaction 2 are of great importance in the atmospheric chemistry of both the troposphere' and stratosphere.* In spite of the atmospheric significance, spectroscopic properties of the sulfo and sulfodioxy (HOS04) radicals are scarcely known. In our attempt to characterize the intermediate radicals of the atmospheric oxidation of SO2,infrared spectroscopic detection in low-temperature matrices was initiated and the observation of
+
-+
-
+
+
( 1 ) Calvert, J. G.; Stockwell, W. R. SO2NO and NO, Oxidation Mechanism: Atmospheric Consideration; Butterworth: Boston, 1984: Chapter 1 and references cited therein. (2) Stockwell, W. R.; Calvert, J. G. Atmos. Environ. 1983, 17, 2231. (3) Margitan, J. J. J. Phys. Chem. 1984, 88, 3314. (4) Schmidt, V.;Zhu, G. Y.; Becker, K. H.; Fink, E. H. Eer. Bunsen-ges. Phys. Chem. 1985,89, 321. ( 5 ) Martin, D.; Jourdain, J. L.; Le Bras, G. J. Phys. Chem. 1986, 90,4143. ( 6 ) Gleason J. F.; Sinha, A.; Howard, C.J. J . Phys. Chem. 1987, 91, 719. (7) Benson, S. W. Chem. Rev. 1978, 78, 23. ( 8 ) Mckeen, S. A.; Liu, S. C.; Kiang, C. S. J . Geophys. Res. 1984, 89, 4873.
0022-3654/88/2092-0641$01.50/0
-
the HOS02 radical in the argon matrix has been reported prev i o ~ s l y . ~Except for our infrared observation, ESR detectionlo in an aqueous solution is so far the only ditect spectroscopic observation of the radical. No gas-phase detection of HOS02 has been reported to the knowledge of the authors except for the mass spectral observation6 converting to SO). As for the HOS04 radical, no experimental data is available in either gas or condensed phases. In order to get better insight into these radicals and to obtain support for the identification of the previously reported r a d i ~ a lab , ~ initio calculations of the molecular geometries and vibrational fundamental frequencies for the ground states of the HOS02and HOS04radicals have been carried out at the 3-21G(*) level, as well as additional experiments of infrared spectroscopy for the H , 0 H / S 0 2 / A r , 0 2 matrices at 11 K. The energetics of reactions 2 and 3 will also be discussed on the basis of the ab initio calculations at the MP4(SDTQ)/6-31G** level at the HF/32 1G(*) optimized geometries and compared with the experimental evidence and thermochemical estimate. The optimized geometry and some electronic properties of HOS02 have so far been reported by Boyed et al." using the smaller STO-3G(*) basis set.
Experimental Section The details of the experimental setup have been described previo~sly.~ The photolysis of H202in Ar or Oz (1/100-1/250) at 185 nm by a Hg resonance lamp or that of H 2 0 in Ar (1/250) at 147 nm by a Xe resonance lamp was utilized as an O H radical source. After mixing with SO2 in Ar or O2 (1/250), the reaction mixture was deposited on the cold CsI surface at 11 K. In order to sort out the absorption bands due to the O H radical reaction from those due to the H atom reaction, a matrix isolation experiment coupled with a discharge flow reactor was also carried out. In this experiment, a microwave discharge lamp for photolysis was substituted by a discharge flow tube with a sampling pinhole of ca. 0.3 mm in diameter. A mixture of H2/Ar (1/100) was discharged though a microwave cavity, and a S 0 2 / A r (1 /250) mixture was added downstream. A part of the reaction mixture was collected on the CsI cold surface through the pinhole. Typical total pressure of the discharge region was 0.2 Torr, and the flow rate was ca. 6 mmol h-'. (9) Hashimoto, S.; Inoue, G.; Akimoto, H. Chem. Phys. Letr. 1984, 107, 198.
(10) Flockhart, B. D.; Ivin, K. J.; Pink, R. C.; Sharma, B. D. J. Chem. SOC.,Chem. Commun. 1971, 339.
(1 1) Boyed, R. J.; Gupta, A,; Langler, R. F.; Lownie, S. P.; Pinock, J. A. Can. J . Chem. 1980, 58, 331.
0 1988 American Chemical Society
642
The Journal of Physical Chemistry, Vol. 92, No. 3, 1988
TABLE I: Observed and Calculated Fundamental Frequencies of H160S160,and H'80S160,
HI60SO2, vibratl mode
HISOSO,
A SO, sym st
I60
I80 A S-OH st
160
'80
A
wavenumber, cm-I calcd exptl 3818 3805 13 1319 1318 1 1125 1122 3 921.9 889.3 32.6
3539.9 3528.6 11.3 1309.2 1308.7 0.5 1097.3 1096.0 1.3 759.5 735.1 22.4
Nagase et al. TABLE II: Calculated Vibrational Frequencies of Isotopically Labeled HOSOz Radicals
vibratl freq, cm-l ratio calcd/exptl 1.078 1.078
vibratl mode H-0 st SO2 asym st H-0-S in-plane bend SO2 sym st
1.007 1.007
S-OH st SO3 def
1.025 1.024
SO3 def H-0-S out-of-planebend
so2SClSS
H160S1602 H1'0SL602H 1 8 0 S 1 8 0 2 3818 1319 1181 1125 922 544 49 1 437 252
3805 1318 1175 1122 889 542 485 430 250
1.214 1.210
3805 1280 1162 1084 883 528 468 419 250
h
Isotope shift (cm-I)
Computational Details Geometries were fully optimized at the spin-unrestricted Hartree-Fock (HF) level with the split-valence 3-21G(*) (polarization functions only on sulfur) basis set.I2 The computed expectation values of the spin-squared operator ( S 2 )from the unrestricted H F wave functions were 0.76 and 0.79 for the HOS02 and HOSO, radicals, respectively, and were close to the correct value of 0.75 for a pure doublet. Harmonic vibrational frequencies were calculated by using the HF/3-2 1G(*) analytical energy derivatives. Force constant matrix and normal coordinates (not presented here) are available upon request. In order to obtain more reliable energies, single-point calculations were carried out at the HF/3-21G(*) optimized geometries; with the large 6-31G** (polarization functions on all atoms) basis set,I3 the effect of electron correlation was incorporated by means of Mdler-Plesset (MP) perturbation theory up to fourth order (MP4SDTQ).I4 In these calculations, all single (S), double (D), triplet (T), and quadruple ( Q )excitations were included, with the constraint that corelike orbitals were doubly occupied. This will be denoted by MP4SDTQ/6-31**//3-21G(*), the // symbol meaning "at the geometry of". Zero-point correction was made with harmonic vibrational frequencies at the HF/3-21G(*) level. The thermochemical quantities such as enthalpies (H), entropies (S), and Gibbs free energies (G) were evaluated within the framework of the ideal gas, rigid rotor, and harmonic oscillator approximations on the basis of the statistical treatment.15 For this purpose, the MP/6-31G**//3-21G(*) energies and the HF/3-21G(*) geometries and frequencies were employed. Results and Discussion HOS02 Radical. Photolysis of H 2 0 / A r at 147 nm during deposition produced matrix isolated OH radicals as confirmed by the absorption bands at 3452.2 and 3428.2 cm-l agreeing well with the data of Acquista et a1.16 The origin of the two bands has not been clarified but might be due to the species at different matrix sites. Photolysis of H202/Arat 185 nm also produced the bands at nearly the same wavenumber (3452 and 3427 cm-I) with a slightly broader bandwidth than those obtained in the photolysis of H 2 0 . When H,O/Ar or H 2 0 2 / A r was photolyzed during codeposition with S 0 2 / A r mixture, the O H bands disappeared and new bands appeared at 3539.9, 1309.2, 1286.8, 1285.4, 1097.3, (12) Pietro, W. J.; Francl, M. M.; Hehre, W. J.; Defrees, D. J.; Pople, J. A,; Binkley, J. S . J . Am. Chem. SOC.1982, 104, 5039.
(13) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.;Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. (14) MP2: Binkley, J. S . ; Pople, J. A. Int. J. Quantum Chem., Symp. 1975, 9, 229. MP3: Pople, J. A,; Binkley, J. S.;Seeger, R. Int. J . Quantum Chem., Symp. 1976, 10, 1. MP4: Krishnan, R.; Frisch, M. J.; Pople, J. A. J . Chem. Phys. 1980, 72, 4244. (1 5 ) Herzberg, G. Molecular Spectra and Molecular Structure. II. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand: New York, 1945; pp 501-530. (16) Acquista, N.; Schoen, L. J.; Lide, Jr., D. R. J . Chem. Phys. 1968, 48, 1537.
IO 7.7-
',,.,:I.,,
..
'\ ',. ( ,
1.44 I
. I
, ',
,, ..
@ Figure 1. Optimized geometry of the HOS02 radical at the HF/3-21G(*) level. Distances are in angstroms and angles are in degrees. LHOISO, = 1.3.
and 759.5 cm-' as reported previ~usly.~ Experiments using the H2160-H2'80 ( l : l ) / A r and S 0 2 / A r mixture gave the isotopeshifted bands at 3528.6, 1308.7, 1096.0, and 735.1 cm-' corresponding to four of the above six bands, but no isotope shift was observed for the bands at 1286.8 and 1285.4 cm-'. Thus, in our previous note: the bands at 3539.9 (3528.6), 1309.2 (1308.7), 1097.3 (1096.0), and 759.5 (735.1) cm-' were assigned to the HI60SO2(H180S02)radicals, and the bands at 1286.8 and 1285.4 cm-] were thought to be attributed to some other species that does not contain an O H group. In the present study, an experiment was carried out to obtain a spectrum when discharged H2/Ar was mixed with S02/Ar. The observed spectrum does show two peaks at 1287.5 and 1285.5 cm-' which agree well with the unidentified peaks noted above, thus confirming that these two peaks are not due to the reaction of O H radical but the reaction of H atom with SO2. All the bands which were assigned to the HOS02 radical did not appear in the reaction of H SO2. Table I compares the observed vibrational frequencies of the HI60Sl6O2and H'80S1602radicals with the calculated values obtained at the HF/3-21G(*) level. As shown in Table I, the calculated vibrational frequencies were 7.8, 0.7, 2.5, and 21.4% higher than the observed ones for the H-0 stretching, S(=O), asymmetric stretching, S(==O), symmetric stretching, and S - O H stretching modes, respectively. An uneven ratio of the calculated to observed frequencies of different vibrational modes has been noted12 in the compounds containing hypervalent sulfur atoms. An important point to be noted in Table I is that the values and the trend of the 160-180 isotope shift are reproduced satisfactorily for all the observed vibrational modes. Table I1 cites the vibrational fundamentals calculated for three isotopic species of H'60S'602, H180S1602, and H'80S1802.The H-0-S bending mode as calculated at 118 1 and 1175 cm-] for H160S'602and H'80S'602, respectively, would be overlapped by the strong absorption of SO, centered at ca. 1150 cm-'. All other low-frequency modes should appear out of observation range. Thus, the identification of the infrared bands of the HOSO, radical has been strongly supported by the additional experimental evidence and the theoretical prediction. Figure 1 presents the HF/3-21G(*) optimized geometry of the HOSO, radical. As shown in Figure 1, the structure of HOSOl is nonplanar, as found by Boyed et al." with the smaller STO3G(*) basis set. The S=O bond length of 1.441 8, in HOSO,
+
(17) Deleted in proof.
H O S 0 2 and HOSO, Radicals
The Journal of Physical Chemistry, Vol. 92, No. 3, 1988 643
TABLE III: Calculated Electronic Properties of HOSO,
atomic spin densities
net atomic charges
atom
STO-3G(*)
3-21G(*)
6-31G**
STO-3G(')
3-21G(*)
6-31G**
H
-0.01 0.12 0.18 0.38 0.33
0.01 0.08 0.34 0.24 0.34
0.00
0.23 -0.24 0.42 -0.21 -0.20
0.45 -0.7 1 1.33 -0.57 -0.50
0.41 -0.65 1.39 -0.61 -0.54
01
S 0 2
0 3
0.07 0.42 0.22 0.29
is appreciably longer than the calculated (1.419 A)17and experimental (1.43 1 A)'* values in SOz. This should explain the lowered experimental frequencies of the S(=O), asymmetric and symmetric stretching modes, 1309 and 1097 cm-I, respectively, as compared to those for SO2, 1356 and 1153 cm-' in the Ar matrix.*O The calculated HO-S bond length of 1.587 8, is close to the observed value of 1.574 AI9 for HISO,, which would represent a typical single bond. The nature of the radical is better understood from the atomic spin densities and net atomic charges shown in Table 111. The spin densities are delocalized on all three atoms of the -SO2 group. It should also be noted that the S, H, 01,02,and O3atoms are highly charged, implying a substantial polarization in all the associated bonds. This gives a large dipole moment of 2.88 (321G(*)) and 2.91 D (6-31G**//3-21G(*)) to the radical. The characteristics of the electronic structure of HOSOz may be represented by resonance structures
1.458
(3 Figure 2. Optimized geometry of the H O S 0 4 radical at the HF/3-21G(*) level. Distances are in angstroms and angles are in degrees. LHO,SO, = 0.5; L0504SOI = 179.1; L04SOI02 = 89 4 TABLE IV: Calculated Electronic Properties of HOS04
atomic spin densities atom H
I
I1
0 1
I11
where the counterpart of the equivalent structures for I and I1 are omitted. It would be interesting here to compare the results to those reported by Boyed et al." with the STO-3G(*)basis. It can be seen that the greatest spin density resides on the S atom and the extent of the charge polarization is more pronounced at the 63 1G** and 3-21G(*) levels than at the STO-3G(*)level, suggesting more significant contribution of resonance structures I1 and I11 S a z , S a 3 ,and H-0' at the higher calculation levels. The bond lengths by the STO-3G(*)basis set are 1.629, 1.474, 1.465 and 0.994 A, respectively, and are all longer by 3-4% than those given in Figure 1. HOSO,Radical. Under the optimized conditions for observing HOS02 by codepositing S02/Ar and H202/Ar under irradiation, a fraction of Ar in the SOz mixture was replaced by 02.The HOSOz band intensity decreased drastically when only 4% of Ar was substituted by O2 (SO2/O2/Ar = 1/10/250). All the absorption bands of HOSOz disappeared for the codeposition of SOZ/O2and H2O2/OZduring irradiation, but no new band was recognized except for the weak diffuse bands of unidentified products in the range of 1300-1280 cm-' and the bands of O3at 2108, 1034, and 702 cm-I. Bands ascribed to SO3 (1385.8 cm-' in O2 matrix)z0 and HOz (1391.6 cm-1)20,z1were not observed either. The HF/3-21G* optimized geometry of the HOSO, radical is shown in Figure 2. As depicted in Figure 2, the S-0 bond configuration around the S atom is similar to that of H2S04. The S=O bond distances (1.414 and 1.406 A) are appreciably shorter than those in the H O S 0 2 discussed before and are close to the calculated value for SOz (1.419 A) and also to the experimental value19 in H2S04 (1.422 A). The calculated HO-S and S-00 bond distances (1.549 and 1.620 A, respectively) are slightly shorter and appreciably longer than the observed HO-S bond lengthI9 in HzSO4 (1S74 A), respectively, suggesting a lower bond energy for S-00 than for HO-S. Calculated electronic properties ~~~
~
(18) Morino, Y.; Kihchi, Y.; Saito, S.; Hirota, E. J. Mol. Spectrosc. 1964, 13, 95. (19) Kuczkowski, R. L.; Suenram, R. D.; Lovas, F. J. J . Am. Chem. SOC.
1981, 103, 2561.
(20) Tso, T.-L.; Lee, E. K. C. J . Phys. Chem. 1984, 88, 2776.
1.406
109y
S 0 2
0 3 0 4
05
3-21G("[/ 3-21G' )
net atomic charges
6-31G**// 3-21G(*)
3-21G(')// 3-21G(')
6-31G**// 3-21G(')
0.00 0.00 0.00 0.00 0.00 -0.18
0.47 -0.69 1.65 -0.56 -0.52 -0.42 0.08
0.42 -0.63 1.73 -0.61 -0.57 -0.39 0.06
0.00 -0.01 0.00
0.00 0.00 -0.20 1.21
1.18
of the HOSO, radical are given in Table IV. The spin density is almost localized on the terminal oxygen atom, giving the features of a more common peroxy radical to the H O S 0 4 radical. The S atom is highly, positively charged, and the four surrounding 0 atoms are all negatively charged. Thus, the bonds in the H O S 0 4 radical are highly polarized as in the case of HOSOZ, giving an even larger dipole moment of 3.16 (3-21G(*))and 3.22 D (6-31G**//3-21G(*)). The calculated vibrational frequencies are 3835, 1588, 1349, 1184, 1025,929,680,626,564,552,449,416,312,233,and 107 cm-'. Apparently, the first five frequencies correspond mainly to the H-0 stretching, S(=O), asymmetric and symmetric stretching, H-0-S in-plane bending, and S-OH stretching modes, respectively. . J 1 the lower frequency modes reflect mixed motion of molecules and the exact assignment is not possible without potential energy analysis, which was not made in this study. The predicted frequencies of the S(=O), asymmetric and symmetric stretching modes are very close to those for SO2 (1573 and 1341 cm-', respectively) calculated with the same basis set,12 reflecting the close S=O bond distances as noted above. Thermochemistry. The energy changes ( A E ) calculated at several levels of theory for the reactions HOS02 O2 H 0 2 + SO3 (2)
+
-
and
HOS02 + O2
M
HOS04
(3) are summarized in Table V. The calculated enthalpy (AH'), entropy (ASo),and free energy (AGO) changes at 298.15 K are given in Table VI. The calculated entropies of H 0 2 , SO3, and O2at the MP4(SDTQ)/6-3lG**//3-21G(*) level are 53.7, 58.7, and 46.9 gibbs mol-' which agree well with the empirical valuesz2 H. J . Phys. Chem. 1985.89, 845. (22) Benson, S.W. Thermochemical Kinetics, 2nd ed.;Wiley: New York, 1916; pp 292-293. (21) Bandow, H.; Akimoto,
644
The Journal of Physical Chemistry, Vol. 92, No. 3, 1988
-
-
TABLE V: Calculated Energy Changes ( A E ) for the Reactions HOS02 + O2 HOz + SO3 (2) and HOSOz + O2 HOSOl (3) AE, kcal/mol reaction reaction calculation 2 3 HF/6-31G**//3-21G(*) 16.3 1 .o MP2/6-3 1G**//3-2 lG(*) 16.1 8.4 MP3/6-31G**//3-21G(*) 12.8 1.2 MP4(SDTQ)/6-3lG**//3-2lG(*)11.9 corrected for zero-point energy 12.4" 4.3b Based on the MP4(SDTQ)/6-31G**//3-31G(*) calculation. Based on the MP3/6-31G**//3-21G(*) calculation.
TABLE VI: Calculated Thermochemical Properties for the Reactions HOSOl + O2 -.H02 + SO3 (2) and HOS02 + O2 -.HOS04 (3)
ab initio calcn"
H02 +
AH,,,, kcal/ mol 12.3
HOSOi
3.2
reaction (2) HOS02
so3
(3) HOSO2
+ 02
+0 2
-*
4
AS298,
AG298r thermochem est' AH,,,, mol kcal/mol 12.8 8 f 2
gibbs/ kcal/ mol -1.7 -37.3
14.4
-16 f 5
MP4(SDTQ)/6-3lG**//3-21G(*) for reaction 2 and MP3/631G**//3-21G(*) for reaction 3.
of 54.4, 61.3, and 49.0 gibbs mol-', respectively. Table VI also cites the thermochemical estimates of AH' by B e n ~ o n .The ~ thermochemical values for HOS02 radical are based on the enthalpy change (125 f 2 kcal mol-I) between HOS020H and 2 0 H + S 0 2 and the assumption that the bond energy difference between DHl0(HOSO2-OH) and DH2'(HO-S0,) to be 50 f 2 kcal mol-'. The value of DHl' - DH2' was considered to be a reorganization energy of the SO2group and taken to be the same as those for the symmetrical alkyl sulfones. This treatment7 gives DH2'(HO-S02) = 37 f 2 kcal mol-', AHfo(HOS02)= -98 f 2 kcal mol-', and thus the endothermicity of 8 f 2 kcal mol-' for reaction 2. The thermochemical estimate for H O S 0 4 radical is based on the estimated heat of formation of HOS0200H (-153 f 2 kcal mol-I) by group additivity and the assumption that the 0-H bonds dissociation energy, DH' (HOS0,OO-H) is equal to that in H202(90 f 1 kcal mol-'). This treatment' leads to a value of AHf0(HOSO200) = -114 f 4 kcal mol-' and the exothermicity of 16 f 5 kcal mol-' for reaction 3 using the Hr (HOS02) value estimated above. As seen in Table VI, the enthalpy change (AH298) for reaction 2 is 12.3 kcal mol-' endothermic at the MP4(SDTQ) level, while it is 8 f 2 kcal mol-' endothermic according to the thermochemical estimate by Benson.' In an attempt to go beyond the MP4(SDTQ) level, correlation energy contributions (E(");n > 4) due to orders of perturbation higher than 4 were estimated by means of an extrapolation procedure proposed by Pople et al.23 The extrapolation formula used for the total correlation energy (E(corr)) is p o " ) = ( ~ ( 2 )+ ~ ' 3 ) ) / ( 1 - ~ ( 4 ) / ~ ( 2 ) ) This formula is related to a series of extrapolation procedures put forward by Bartlett and S h a ~ i t t . Total ~ ~ energies obtained by use of the extrapolation formula yields an estimate 10.6 kcal mol-' for the AH298value. This value is closer to Benson's estimated value of 8 f 2 kcal/mol-'. However, neither of these values can be reconciled with the recent experimental results for the kinetics of the reaction of HOSO, and 0,.Margitan,3 Martin et al.,5 and Gleason et a1.6 are in agreement on a rate constant of -4 x cm3 molecule-'
Nagase et al. s-I for reaction 2, which suggests that the barrier height for the reaction should be less than -2 kcal mol-'. The agreement between the rate constants obtained at 4 Torr by Gleason et aL6 and at 200 Torr by Margitan3 suggests that the termolecular channel, reaction 3, is quite slow. The possibility that vibrationally excited H O S 0 2 formed by reaction 1 might be responsible for reaction 2 is unlikely, since the experiment by Schmidt et al., revealed that more than 90% of the OH is regenerated in reactions 1-4 at 760 Torr of synthetic air. This result also gives an upper cm3 molecule-' s-l at the atmospheric limit for k3 of 5 4 X pressure. Further, detection of SO3 as a reaction product by Gleason et aL6 strongly supports that reaction 2 is the dominant channel. All this evidence implies that the predicted value of AH for reaction 2 by the present ab initio calculation is higher than the true value by more than 10 kcal mol-'. A source,of error in the theoretical calculations may be based on the choice of equilibrium geometry. The MP4(SDTQ)/631G** calculations were carried out at the HF/3-21G(*) optimized geometries. At this point, it is instructive to note, for example, that the SO bond length and the OS0 bond angle of SO2change only by 0.005 %, from 1.419 to 1.414 %,and only by 0.1' from 118.7' to 118.8', respectively, when the basis set is improved from HF/3-21G(*) to HF/6-31G**.I2 The corresponding change in the SO bond length of SO3is also small and only 0.006 %, from 1.411 to 1.405 These suggest that the effect of oxygen d orbitals (not included in the 3-21G(*) basis set) is rather small in geometry optimization. In addition, the calculated geometries of SO2 and SO3agree well with the experiment.I2 As is assessed from these examples of sulfur-containing species, it is expected that the geometry of H O S 0 2 is well approximated at the H F / 3-21G(*) level. Reaction 2 involves a significant change in hybridization and bonding characteristics. The discrepany between theory and experiment may be ascribable to the fact that the 6-31G** basis set is not sufficiently flexible for the adequate incorporation and well-balanced treatment of electron correlation in reactants and products. In addition, a more sophisticated theoretical method would be necessary to remove the discrepancy. On the other hand, the thermochemical estimate by Benson may be subject to the assumption that the reorganization energy of the SO2group in H O S 0 2 0 H is equivalent to that in CH3S02CH3. The HOSO, radical is located as a minimum on the potential energy surface. As Table VI shows, the formation of the radical from HOS02 and O2(reaction 3) is calculated to be 3.2 kcal mol-I endothermic at the MP3/6-3 1G** level, while it is thermochemically estimated to be 16 f 5 kcal mol-' exothermic. Because of the size of the HOSO, radical, we were unable to perform the MP4/6-3 1G** calculations. This prevents us from extrapolating the Merller-Plesset series to infinite order. In conclusion, the ab initio calculation for the HOS02 radical gave a substantial support for the assignment of the observed infrared spectrum. The geometries and electronic properties of the HOS02 and HOS04 radicals were well characterized in the present study, although further improvements are required for the theoretical prediction of reliable enthalpy changes for the reactions involving these radicals.
Acknowledgment. All calculations were carried out at the Computer Center of the Institute for Molecular Science, by using the GAUSSIAN 8025 and GAUSSIAN 8226 programs in the center library program package. Registry No. 7440-37-1.
HOS02, 104267-22-3; HOS04, 11 1997-44-5; Ar, ~~~~~
~~~
(25) Binkley, J. S.; Whiteside, R. A.; Drishnan, R.; Seeger, R.; DeFrees, D. J.; Schlegel, H. B.; Topiol, S.; Kahn, L. R.; Pople, J. A. Program No. 406, Quantum Chemistry Program Exchange, Indiana University, Bloomington, IN.
(23) Pople, J. A.; Frisch, M. J.; Luke, B. T.; Binkley, J. S. Inf. J . Quantum Chem., Symp. 1983, 17, 307. (24) Bartlett, R. J.; Shavitt, I. Chem. Phys. Lett. 1977, 50, 190.
(26),Binkley, J. S . ; Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. Department of Chemistry, Carnegie-Mellon University, Pittsburgh, PA.
