J . Phys. Chem. 1993,97, 18-19
18
Theoretical Estimate of the Enthalpy of Formation of HSO and the HSO-SOH Isomerization Energy Sotiris S. Xantheas’ and Thom H. Dunning, Jr. Theory, Modeling and Simulation, Molecular Science Research Center, Pacific Northwest Laboratory,? Richland. Washington 99352 Received: October 2, 1992; In Final Form: November 16, 1992
The enthalpy of formation of HSO is estimated to be -5.4 f 1.3 kcal/mol through a series of multireference configuration interaction (MR-CI) calculations that systematically expand the orbital basis set. The estimated value of AHfo suggests that HSO may well be involved in a catalytic cycle that depletes ozone in the atmosphere. In contrast to all earlier theoretical studies, the computed energy difference between the HSO and SOH isomers is estimated to be 5.4 kcal/mol, with the HSO isomer being more stable.
The thermochemistry of HSO is of importance because this species is involved in the atmospheric oxidation of HS, one of the chemical processes that leads to acid rain.Il2 Experimental ~ t u d i e s have ~ - ~ shown that HSO can catalytically destroy ozone according to the scheme
HS + 0, -,HSO + 0, HSO
+ 0,
--.+ HS
20,
(1)
(2)
net: 20,-30, Unfortunately, the enthalpy of formation of HSO is not well established, so the thermodynamics of reaction 2 are uncertain. Assuming that the conclusions reached in ref 1 are correct, reaction 2 must beexothermic, a fact which constrains the heat of formation of HSO to be less than -2 kcal/mol. An upper limit for Nr0298(HSO) of 14.9 kcal/mol was provided5 by experimental studies of reaction 1. This value was subsequently reduced to 2.76and -1.4 f 1 .97kcallmol as a result of experimental studies of oxygen atom addition to H2S. Previous ab initio calculations estimated8 a value of -0.4 f 3.0 kcal/mol. In light of this uncertainty, a consensus value of -1 kcal/mol was adopted4 in kinetic studies of the reaction of HSO with NO2 and 03.The standard enthalpies of formation (at 0 K) of O3and HS are9 34.7 f 0.4 and 32.6f 1.2kcal/mol, respectively. In order for reaction 2 to be exothermic, the enthalpy of formation of HSO must be less than -2.1 f 1.6 kcal/mol. Another problem of interest is the energy difference between HSO and its SOH isomer. All theoretical studiess~lO~ll to date predict SOH to be more stable than HSO by 3-10 kcal/mol. In contrast, only HSO has been o b ~ e r v e dexperimentally. ~~~~~ However, in the theoretical studies, the difference between the two isomers was found to decrease both upon enlargement of the basis set and upon useof a more accurate level of theory. A more thorough theoretical study is clearly warranted. We have computed the enthalpy of formation of HSO and the HSO-SOH energy difference using the MR-CI method and the recently developed correlation-consistent polarized valence basis sets.I4 The MR-CI method, based on a complete active space self-consistent-field (CASSCF) wave function, has been shown to yield results comparable to that obtained from full CI calculations for diatomic and triatomic molecules.’5 The internally contracted method of Werner and Knowles16 was used to +
Pacific Northwest Laboratory is operated by Battelle Memorial Institute
for the US.Department of Energy under Contract No. DE-AC06-76RLO 1830.
efficiently and effectively handle the large CI expansions considered here (up to 165 million configuration state functions). The correlation consistent basis sets provide a systematic way of expanding the orbital basis set. Benchmark calculations on the first- and second-row diatomic molecules17indicate that the larger correlation consistent basis sets provide results near the “complete” basis set limit and that the “complete” basis set limit can be obtained by extrapolating the results obtained with these basis sets. All calculations were performed using the G A M E W Eand MOLPR0I6 suites of programs. Given the standard enthalpies of formation (at 0 K) of H and SO (51.6 and 1.2f 0.3kcal/m01,~respectively), the enthalpy of formation of HSO can be computed from the H S O bond energy and the vibrational frequencies of HSO. For reference, the results of CASSCF+ 1+2 calculations with the cc-pVQZ basis set for SO, HSO,and SOH are reported in Table I (with the measured values in parentheses). As can be seen, the calculated equilibrium bond length and vibrational frequency for SO, with errors of 0.01 A and 16 cm-I, are in good agreement with the available experimental data. The calculated D o ( H S 0 ) is 56.2kcal/mol. Calculations with the cc-pVTZ and cc-pV5Z basis sets at the CASSCF+1+2 level yield DO = 55.1 and 56.9 kcal/mol, respectively. Extrapolating the calculated values of the H S O dissociation energy, we predict Do(HS0) = 57.0 f 0.3kcal/mol (see Figure 1). The binding energies computed with the CASSCF+1+2 method, even in the complete basis set limit, will still be in error. To obtain an estimate of the error in the H S O bond energy, we can compare with corresponding calculations on the H S molecule. For HS, CASSCF+1+2 calculation^^^ predict DO= 82.3kcal/ mol (extrapolated to the “complete” basis set limit); the experimentally measured value is 83.5 f 0.7 kcal/mol.20 Assuming that the error in H-SO is at least as much as that in HS,we estimate D,(H-SO)
58.2 f 1.0 kcal/mol
The above DOleads to an enthalpy of formation N f ” ( 0 K) of HSO of -5.4 1.3 kcal/mol. This suggests that reaction 2 is indeed exothermic. The fact that the error in the H S O bond energy is probably larger than the error in the H-S bond energy will tend to increase Do(H-SO), making reaction 2 more exothermic. The estimated value of -5.4 kcallmol should then be considered as a upper limit for the enthalpy of formation of HSO. Our estimates for the energy difference between HSO and SOH, A&, which includes zero-point energy corrections (in kcal/ mol) are illustrated in Figure 2 for the various levels of theory and basis sets. In this figure we have also plotted our results at
*
0022-3654158 12097-001 8$04.00/0 0 1993 American Chemical Society
Letters
The Journal of Physical Chemistry, Vol. 97, No. 1, 1993
TABLE I: Computed Energies, Structures, and Harmonic Vibrational Frequencies for SO, HSO, and SOH (from CASSCF+1+2 Calculations with a cc-pVQZ Basis Set)
calculations show a smooth convergence, predicting HSO to be more stable than SOH by 5.4 kcal/mol at the "complete" basis set limit. This result is expected to contribute to a better understanding of recent scattering data2I on the O(3P,'D) H2S system that were analyzed using the previous theoretical estimate, which predicted SOH to be 10 kcal/mol more stable than HSO. In conclusion, we estimate the enthalpy of formation of HSO to be -5.4 f 1.3 kcal/mol. Thus, reaction 2 is exothermic, and the cycle described by reactions 1 and 2 may well be involved in the catalytic destruction of ozone. In contrast to all previous theoretical studies,8*10J1 we predict HSO to be more stable than SOH by approximately 5.4 kcal/mol. A full report involving the characterization of all critical points (minima and transition states) on both the 2A" ground and 2A' first excited states as well as the dissociation pathways to H(2S) + SO(jZ-) is in preparation.
H+SO DO(kcal/mol)
RXH(A)
Rso (A)
1.491 (1.481)
h s o (deg) W I (cm-I) w2 (cm-I) w3 (cm-I)
1135 (1 151)
' References 5 and
HSO
SOH
56.2 1.361 1.506 105.0 2620 (2271,2570)' 1078 (1063,1164)" 966 (1013,1026)'
53.1 0.963 1.645 106.4 3729 1202 821
19.
52
.
Y
n) . 48
-
+ mZ'exp(-m3'X)
ml
VaIu.
ml
57 025
+
Acknowledgment. We thank Dr. A. R. Ravishankara of the National Oceanic and Atmospheric Administration for bringing the significance of this system to our attention. This work was performed at Pacific Northwest Laboratory under the auspices of the Division of Chemical Sciences, Office of Basic Energy Sciences, U.S.Department of Energy, under Contract DE-AC0676RLO 1830. Computer resources were provided by the Division of Chemical Sciences and by the Scientific Computing Staff, Office of Energy Research, at the National Energy Research Supercomputer Center (Livermore, CA) and Florida State University (Tallahassee, FL).
Sh ' 54 '
19
Err01 0 270
.
References and Notes Figure 1. Calculated CASSCF+l+2 binding energies (DO) for H-SO.
r
1
j
a
(1) Wang, N. S.;Howard, C. J. J. Phys. Chem. 1990, 94,8787. (2) Friedl, R. R.;Brune, W. H.; Anderson, J. G. J . Phys. Chem. 1985, 89, 5505. (3) Black, G.J. J. Chem. Phys. 1984,80, 1103. (4) Wang, N. S.; Lovejoy, E. R.; Howard, C. J. J . Phys. Chem. 1987, 91,5743.Lovejoy, E. R.;Wang, N. S.; Howard, C. J. J. Phys. Chem. 1987, 91,5749. ( 5 ) Shurath, U.; Weber, M.; Becker, K. H. J. Chem. Phys. 1977,67,1IO. (6) Slagle, I. R.;Baiocchi, F.; Gutman, D. J . Phys. Chem. 1978,82, 1333.
~
e
I
w Basis set Figure 2. Energy separation (with respect to HSO) between the two isomers in kcal/mol a t various levels of theory with respect to the quality of the basis set. Estimated values include zero-point energy corrections ( S O ) .
the MP2 level of theory for the sake of comparison with previous studies. At the MP2 level with the smaller sets, SOH is seen to be more stable than HSO,although, in agreement with previous studies, the absolute value of the energy separation decreases with increasing basis set size. The U o ' s from theCASSCF+1+2
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