High-Accuracy Theoretical Thermochemistry of Atmospherically

ARTICLE pubs.acs.org/JPCA

High-Accuracy Theoretical Thermochemistry of Atmospherically Important Sulfur-Containing Molecules Balazs Nagy,*,†,‡ Peter Szakacs,† Jozsef Csontos,† Zoltan Rolik,† Gyula Tasi,‡ and Mihaly Kallay† †

Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, Budapest P.O. Box 91, H-1521 Hungary ‡ Department of Applied and Environmental Chemistry, University of Szeged, Rerrich B. ter 1., H-6720, Szeged, Hungary

bS Supporting Information ABSTRACT: In this study, several sulfur-containing molecules with atmospherical importance were investigated by means of high-accuracy quantum chemical calculations including: HSO, HOS, HOSO2, HSNO, SH, CH2SO, CH2SH, S2COH, and SCSOH. After identifying the stable conformers of the molecules, a coupled-cluster-based composite model chemistry, which includes contributions up to quadruple excitations as well as corrections beyond the nonrelativistic and Born Oppenheimer approximations, was applied to calculate the ° ) and corresponding heat of formation (ΔfH0° and ΔfH298 ° ) values. In most of the cases, this study delivers more reliable estimates for the investigated thermodynamic entropy (S298 properties than those reported in previous investigations. Our data also suggest that the experimental heats of formation associated with the HSO molecule are very likely to belong to its structural isomer, HOS. It is also confirmed by the calculated thermodynamic properties including standard reaction entropies, enthalpies, and equilibrium constants that, in the reaction CS2 þ OH a CS2OH, the SCSOH structural isomer is produced. It is also noted that the currently accepted ΔfH0°(Sgas) = 274.73 ( 0.3 kJ/mol value is in need of revision, and based on a recent measurement, which is also confirmed by our computations, it is advised to update it to ΔfH0°(Sgas) = 277.25 ( 0.3 kJ/mol.

’ INTRODUCTION It is crucial to accurately determine the thermochemical properties of sulfur-laden molecules and radicals since they are involved in various important atmospheric processes such as the development of acid rain, or ozone depletion.1,2 Furthermore, sulfur-containing species are also featured in reactions that are linked to the so-called greenhouse effect.3,4 The HSO and HS radicals have an important part in ozone depletion. HS catalyzes the destruction of ozone molecules via the HS þ O3 f HSO þ O2 HSO þ O3 f HS þ 2O2 reaction cycle. The reaction of HSO and O3 can also yield HSO2 and O2 breaking the catalytic cycle.5 Nevertheless, several other reactions take place in the atmosphere in which HSO radicals can arise, such as HS þ NO2 f HSO þ NO5 or O(3P) þ H2S f HSO þ H.6,7 In the latter reaction, HOS or SO may also spring up.6 Furthermore, reacting with the O-atom, HSO may form SO, which can transform to SO3 and H2SO47 causing acid rain. The HOSO2 radical is a key intermediate of the SO2 catalytic oxidation process:8,9 OH þ SO2 þ M f HOSO2 þ M r 2011 American Chemical Society

ð1Þ

HOSO2 þ O2 f SO3 þ HO2

ð2Þ

SO3 þ H2 O þ M f H2 SO4 þ M

ð3Þ

In reaction 1, the notation M is introduced to indicate the socalled “third-body”, which absorbs the excess energy released in a kinetically third-order association process.10 The OH radical is regenerated from HO2 in a secondary process, HO2 þ NO f OH þ NO2. Due to the formation of H2SO4, this process also magnifies the chance of acid rain. In atmospherical circumstances, reaction 1 is slow, and therefore SO2 has relatively long lifetimes. However, reactions 2 and 3 are fast, hence HOSO2 and SO3 have short atmospheric lifetime.8 The most important reactions of the mercaptomethyl radical, CH2SH, are those with O2, NOx, and O3. According to the following reaction,11 CH2 SH þ O2 f CH2 S þ HO2

ð4Þ

HO2 is generated, which is among the most important intermediates in ozone chemistry. The reactions of CH2SH with NOx are important at elevated NOx concentrations, and the most favorable reactions proceed via addition to the carbon center; Received: April 12, 2011 Revised: May 24, 2011 Published: May 26, 2011 7823

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The Journal of Physical Chemistry A

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however, the abstraction is also possible yielding HNO and HONO, respectively.11 The parent molecule of sulfines, CH2SO, occurs in the atmosphere as an intermediate in the oxidation process of CH3S with O2.12 Its formation is also presumed13 in the reaction between CH3SO and O3 according to the equation CH3SO þ O3 f CH2SO þ OH þ O2. In the atmosphere, the CS2OH radical occurs as an intermediate during the oxidation of CS2 according to reactions 5 and 6 CS2 þ OH þ M a CS2 OH þ M

ð5Þ

CS2 OH þ O2 f products

ð6Þ

The main products of reaction 6 are most likely OCS, SH, SO2, and CO; however, the reaction is extremely complex and has more than 25 exothermic product channels.14,15 In reaction 5, the OH radical can attach to both the carbon and sulfur atoms of CS2. Consequently, two structural isomers of CS2OH can form, which are called the C-adduct, S2COH, and the S-adduct, SCSOH. Although the aforementioned species and reactions play a crucial role in atmospheric chemistry sometimes the accuracy of the thermodynamic properties detailed in well-known databases, such as the NIST-JANAF,16 JPL,17 and the Third Millenium Ideal Gas and Condensed Phase Thermochemical Database,18 is not satisfactory. Furthermore, discrepancy among the recommended values is also a common issue. Therefore, in this study we attempt to provide the most reliable estimates for the heat of formation and entropy values of HSO, HOS, HOSO2, HSNO, SH, CH2SO, CH2SH, S2COH, and SCSOH, as well as to resolve the existing discrepancies among the compilations. In order to reach these goals we apply highly accurate quantum chemical methods, which have been proved to be useful in similar scenarios.1929

’ METHODS Several so-called model chemistries21,22,3054 have been developed during the last two decades to yield reliable thermochemical information; nevertheless, our approach is mostly inspired by the Weizmann-n (Wn)21,27,41,42 and HEAT family of protocols, 22,45,46 and it was successfully applied on species55,56 with importance in atmospheric chemistry. Although, the details of our protocol are given in ref 55, a brief description is in order here since the original approach was slightly modified at two points to address the problems associated with the presence of sulfur in the investigated species. The deficiencies due to the lack of tight d basis functions in the standard correlation consistent basis set families (cc-pVXZ,57,58 aug-cc-pVXZ59) are well-documented.6065 Therefore, where it was appropriate, cc-pVXZ and aug-cc-pVXZ were replaced, respectively, by cc-pV(X þ d)Z66 and aug-cc-pV(X þ d)Z.66 The other modification is based on the findings of Martin and associates,27 who, during an investigation on the convergence behavior of contributions beyond the coupled-cluster singles and doubles (CCSD) method, pointed out that a double-ζ basis set is not appropriate to capture the effects of quadruple excitations for second-row systems. Consequently, the CC singles, doubles, triples, and perturbative quadruples [CCSDT(Q)] calculations were performed with the ccpV(T þ d)Z basis set. To determine the conformers and the rotational barriers, a systematic search was performed around the torsional angles of the considered species using the CC singles, doubles, and perturbative triples CCSD(T) method with the cc-pVTZ basis set, i.e., the appropriate torsional angle was changed by 15°

increments, and the obtained conformations were partially optimized keeping the torsional angle fixed. After the conformational search, the obtained equilibrium structures were reoptimized at the CCSD(T)/cc-pVQZ level of theory. Then, the total energies of the molecules were calculated, assuming the additivity of the various contributions, according to the following scheme: E ¼ EHF þ ΔECCSDðTÞ þ ΔECCSDTðQ Þ þ ΔEcore þ ΔEZPE þ ΔEDBOC þ ΔEREL

ð7Þ

EHF is the basis set limit HartreeFock energy extrapolated from aug-cc-pV(X þ d)Z (X = T,Q,5) energies using the three-point extrapolation formula of Feller,67 E(X) = ECBS þ b 3 ecX. ΔECCSD(T) is the correlation energy calculated by the CCSD(T) method and extrapolated to the basis set limit using aug-cc-pV(X þ d)Z (X = Q,5) results and the two-point formula of Helgaker and associates,68 E(X) = ECBS þ B 3 X3. ΔECCSDT(Q) = ECCSDT(Q) ECCSD(T) is obtained with the cc-pV(T þ d)Z basis set, where EX refers to the correlation energy calculated with method X. ΔEcore, which is defined as the energy difference between the all electron and frozen-core approximation, is calculated with the CCSD(T) method extrapolating the ccpCVTZ and cc-pCVQZ basis set results by the above-mentioned formula of Helgaker and co-workers.68 The zero-point vibrational energy, ΔEZPE, is calculated relying on vibrational perturbation theory.69 Harmonic frequencies and anharmonicity corrections were determined at the CCSD(T)/cc-pVQZ and CCSD(T)/cc-pVTZ levels of theory, respectively. The diagonal BornOppenheimer correction70 (ΔEDBOC) is obtained at the CCSD/cc-pCVTZ level. The scalar relativistic contributions (ΔEREL) are evaluated by determining the expectation value of the mass-velocity and one- and two-electron Darwin operators at the CCSD(T)/cc-pCVTZ level. Furthermore, the energy lowering of the lowest spinorbit state with respect to the energy evaluated within a nonrelativistic approximation, was also considered. For C, S, and SH, respectively, 135 μEh, 892 μEh, and 859 μEh were calculated from the experimental finestructure splittings available in the NIST Atomic Spectra Database71 and in the NIST-JANAF tables.16 We also note here that due to the steep scaling of the CCSDT(Q) method with the number of virtual orbitals, for the S2COH, SCSOH, and HOSO2 molecules, a second-order Møller Plesset (MP2) frozen natural orbitals (FNO) technique7274 was utilized to estimate the CCSDT(Q) energy. In the framework of the MP2 FNO approximation, the natural virtual orbitals are constructed from the first order MP wave function, then the natural virtual orbitals with small populations are dropped; finally with the reduced basis set a pseudocanonical basis is constructed. In a recent paper, following Landau and associates,73 Rolik and Kallay74 have shown for a large set of molecules that it is practical to define a threshold, ε, for the retained natural orbitals as their cumulative occupation number normalized by the number of electrons. Therefore, CCSD(T), CC singles, doubles, and triples (CCSDT), and CCSDT(Q) energies, as well as ΔECCSDT(Q) contributions were calculated for the S2COH, SCSOH, and HOSO2 molecules with various ε values and the results with the largest ε were used to approximate the ΔECCSDT(Q) contributions. To measure the quality of the MP2 FNO approximation, the ΔECCSDT(Q) contributions were extrapolated to ε = 1, and the deviation from the extrapolated value was used as an estimate for the error. For S2COH ΔECCSDT(Q) is 5.184 mEh with ε = 0.995 and the linear extrapolation with ε = 0.9875, 0.99, and 0.995 gives 7824

dx.doi.org/10.1021/jp203406d |J. Phys. Chem. A 2011, 115, 7823–7833

The Journal of Physical Chemistry A 5.331 mEh. For SCSOH, ΔECCSDT(Q) is 4.208 mEh for ε = 0.975 and the linear extrapolation with ε = 0.925, 0.950, and 0.975 gives 4.522 mEh, while for the HOSO2 molecule ΔECCSDT(Q) is 2.731 mEh with ε = 0.975, and the result of the extrapolation with ε = 0.95 and 0.975 yields 2.246 mEh. The ΔECCSDT(Q) values used to calculate the heats of formation for S2COH, SCSOH, and HOSO2 are 5.184, 4.208, and 2.731 mEh with the estimated error of (0.147, ( 0.314, and (0.485 mEh, respectively. Consequently, the calculated error bars (see below) associated with the heat of formation of S2COH, SCSOH, and HOSO2 were increased by 0.4 kJ/mol, 0.8 kJ/mol, and 1.3 kJ/mol, respectively. In all calculations, the restricted (RHF) and unrestricted (UHF) HartreeFock orbitals were used for closed- and open-shell systems, respectively. The CCSDT(Q) calculations were carried out with the MRCC suite of quantum chemical programs76 interfaced to the CFOUR package,77 while all other calculations were performed with CFOUR. Standard molar enthalpies (H°) T at T = 0 and 298.15 K at a pressure of 1 bar as well as standard molar entropies (S°298) were computed via the standard formulas of statistical thermodynamics (STD) within the ideal gas approximation.78 For C, S, and SH, where the electronic ground state splits due to spinorbit interaction, the spinorbit states of the ground state were considered at the calculation of partition functions. For the rotational and vibrational degrees of freedom, the rigid rotorharmonic oscillator (RRHO) approximation was invoked. To correct the errors of the RRHO model for species with hindered rotations, a one-dimensional hindered rotor model7984 was used. The one-dimensional Schr€odinger equation,

p2 d2 ψ þ V ðθÞψ ¼ Eψ 2Ir dθ2

was solved using the Fourier grid Hamiltonian method of Marston and Balint-Kurti.85,86 Ir and V(θ) are the reduced moment of inertia and the potential obtained in the relaxed scan for the rotating top, respectively. To get an analytical form of the potential, V(θ) was expanded in a Fourier series, V ðθÞ ¼ c þ

6

∑ fai cosðiθÞ þ bi sinðiθÞg i¼1

Furthermore, Ir was calculated using the frequency scheme as described in refs 87 and 88, and its dependence on θ was neglected. The partition function for the hindered rotor, which was obtained by direct eigenvalue summation, was used to correct the ZPE, entropy, and thermal correction values. Heat of formation values were derived from the calculated enthalpies taking the elemental reaction approach.22,55,56 For instance, the heat of formation of CH2SO was calculated according to the following equations: 1 C þ S þ H2 þ O2 ¼ CH2 SO 2 Δf HTo ðCH2 SOÞ ¼ HTo ðCH2 SOÞ HTo ðCgas Þ HTo ðSgas Þ 1 HTo ðH2 Þ HTo ðO2 Þ þ Δf HTo ðCgas Þ þ Δf HTo ðSgas Þ 2

The reference state of the elements were defined as it is standard in thermochemistry, except for sulfur and carbon where the gaseous atoms were used as references. ΔfH0°(Sgas), 277.25 ( 0.3 kJ/mol, was calculated using the dissociation energy of S2,

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D0 = 35636.9 ( 2.5 cm1, as recently measured by Frederix and associates;89 ΔfH0°(Sgas) = ΔfH0°(Sgas,NIST) 0.5 3 ΔD0, where ΔfH0°(Sgas,NIST), 274.73 ( 0.25 kJ/mol, is the currently accepted value for the heat of formation of gaseous sulfur at 0 K,16 and ΔD0, 420.5 cm1, is the difference between the dissociation energy measured by Ricks and Barrow,90 (35216.4 ( 2.5 cm1) and that obtained by Frederix and co-workers89 (35636.9 ( 2.5 cm1). Our calculations, 35602.5 ( 250.8 cm1 (see below), and those of Feller and associates,43 35585.7 ( 104.9 cm1, strongly support the value reported in ref 89 in contrast to that of ref 90. The excellent results obtained in our benchmark calculations with ΔfH°(S 0 gas) = 277.25 ( 0.3 kJ/mol, detailed below, also indicate that the currently accepted value for ΔfH0°(Sgas), 274.73 ( 0.25 kJ/mol, ° (Sgas) = 279.50 ( 0.3 kJ/mol was is in need of revision. ΔfH298 calculated using the temperature correction available in ref 16. For ΔfH°(C 0 gas), the ab initio value of ref 24, 711.65 ( 0.32 kJ/mol, was adopted. To calculate the heat of formation at 298.15 K, the thermal ° ΔfH0°, were obtained from the NIST-JANAF corrections, ΔfH298 tables, resulting in ΔfH°298(Cgas) = 717.13 ( 0.32 kJ/mol. To obtain reliable error estimates on the calculated properties, the errors introduced by the various approximations were also investigated thoroughly in ref 55. Based on a comparison to accurate data, a size and composition-dependent error estimate were introduced; i.e., to determine the 95% confidence limit of the calculated heats of formation for a given species, 0.4 and 1.5 kJ/mol were taken as uncertainty for every first-row and chlorine atom, respectively. The validity of this approach was also proven in refs 56 and 29. To further check the above error estimates and whether the 1.5 kJ/mol uncertainty can be extended to other second-row atoms, especially for sulfur, reliable experimental heat of formation and entropy values were collected. Unfortunately, the available accurate experimental information is very scarce, and only four molecules, H2S, S2, SO, and SO2, were found with small, well-defined error bars. The recommended values listed in the NIST-JANAF database16 for ΔfH°0 of H2S, S2, SO, and SO2 are, respectively, 17.6 ( 0.8 kJ/mol, 128.3 ( 0.3 kJ/mol, 5.0 ( 1.3 kJ/mol, and 294.3 ( 0.2 kJ/mol. The corresponding values yielded by our protocol with the error bars calculated as defined above are 17.5 ( 2.3 kJ/mol, 127.4 ( 3.0 kJ/mol, 5.6 ( 1.9 kJ/mol, and 296.1 ( 2.3 kJ/mol. The error bar associated with our entropy data is based on a statistical analysis of a benchmark data set of 15 molecules and radicals, and in ref 55, a root-mean-square deviation of 0.6 J K1 mol1 was obtained against accurate entropy values. Thus, our conservative estimate for the 95% confidence limit associated with our entropy calculations was (1.5 J K1 mol1. This limit was also successfully tested in refs 56 and 29. The recommended values ° of H2S, S2, extracted from the NIST-JANAF16 compendium for S298 SO, and SO2 are, respectively, 205.8 ( 0.0 J K1 mol1, 228.2 ( 0.1 J K1 mol1, 221.9 ( 0.0 J K1 mol1, and 248.2 ( 0.1 J K1 mol1. The corresponding values yielded by our protocol are 205.6 ( 1.5 J K1 mol1, 228.1 ( 1.5 J K1 mol1, 222.0 ( 1.5 J K1 mol1, and 248.3 ( 1.5 J K1 mol1. It can be observed that both our heat of formation and entropy values agree well with those obtained in accurate experiments supporting our error estimates associated with our protocol introduced in ref 55.

’ RESULTS Conformational Analysis. Figure 1 shows the potential energy curves for the CH2SO, HSNO, HOSO2, CH2SH, S2COH, and SCSOH molecules; the equilibrium structures of CH2SO, cis-, and 7825



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Figure 1. Potential energy curves calculated at the CCSD(T)/cc-pVTZ level of theory; every molecular coordinate was fully relaxed except the scanned torsional angle. (a) CH2SO; (b) HSNO; (c) HOSO2; (d) CH2SH; (e) S2COH; (f) SCSOH.

trans-HSNO, CH2SH, S2COH, and SCSOH can be seen in Figure 2. In the case of CH2SO only one distinguishable minimum exists and the rotation around the CS bond is strictly forbidden at room temperature by a 21800 cm1 high barrier (see Table 1). The trans conformer of HSNO was found to be more stable than the cis isomer by 3.3 kJ/mol. The separating torsional barrier is about 3000 cm1, and the vibrational frequency, which

can be assigned to the torsional motion, is about 400 cm1. Since the potential wells around both minima can be well described by a simple square function, and the 7th excited vibrational state is not accessible at 298 K, the harmonic oscillator treatment of the corresponding conformers is appropriate. For HOSO2, two distinguishable conformers (nonsuperimposable mirror images) can be obtained around the SO bond. Depending on the direction 7826



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Table 2. Heats of Formation (in kJ/mol) as Well as Entropies (in J K1 mol1) for the Species Studied in This Work species HSO

ΔfH0°

ΔfH298 °

19.6 ( 2.3

22.6 ( 2.3

21.8 ( 4.2

24.7 ( 4.2

S298 ° 241.4 ( 1.5

ref 93, MRCI 25.5 ( 5.4

ref 94, CASSCF

5.9

ref 136, CCSDT

19.9

ref 92, G2

2.4 ( 2.3

5.3 ( 2.3

3.8 ( 2.9

6.1 ( 2.9

240.0 ( 1.5

refs 6 and 17b

2.9 ( 5.4

ref 94, CASSCF

5.6 ( 7.9

ref 91b

375.7 ( 4.4

366.6 ( 2.5

374.1 ( 3.0

ref 9, CC

373.0 ( 6.0

ref 95

385.4 360.8

294.1 ( 1.5

368.8 g395.4

trans-

112.4 ( 2.7

107.3 ( 2.7

ref 96, G2 280.8

refs 8 and 98

266.4 ( 1.5

this work

HSNO 95.2 ( 5.0 cis-HSNO 115.8 ( 2.7

Table 1. The Treatment of Low-Frequency Motionsa molecules treatment

ν~

barrier(s) ΔZPE Δ(H298 ° H0°) Δ d

e

e

refs 17 and 99

vib

390.0

21782

HSNO

vib

319.8

3001

HOSO2

hind

301.0 1267, 1423 0.3

0.2

6.7

0.2

0.1

2.4

CH2SH

hind

93.6

2140

S2COH

vib

567.4

3253

SCSOH

hind

216.5 346, 976

0.1

0.2

110.7 ( 2.7

ref 100 266.1 ( 1.5

112.0 ( 8.0

S°298e

CH2SO

refs 18 and 137 ref 97, G3X

94.0 ( 20.0

c

this work

ref 100 294.1

364.8

b

this work

HOSO2 367.5 ( 4.4

385.0 ( 10.0

Figure 2. Graphical representation of the equilibrium structures determined at the CCSD(T)/cc-pVQZ level of theory. (a) CH2SO; (b) cisHSNO; (c) trans-HSNO; (d) CH2SH; (e) S2COH; (f) SCSOH.

this work ref 7, CCSD(T)

22.6 ( 5.4

HOS

sourcea

SH

ref 101, CCSD(T)

138.6 ( 0.4 141.2 ( 0.5

ref 105 141.9 ( 0.5

ref 102, CC

141.0 ( 0.8

ref 43, CC

142.6 ( 0.8

143.1 ( 0.8

142.8 ( 1.9

143.4 ( 1.9

142.5 ( 3.0

ref 113, CC 195.4 ( 1.5

143.0 ( 2.8

The wavenumbers (ν~) and barrier heights are given in cm1; The ZPE and thermal correction (H298 ° H0°) values are given in kJ/mol, while the entropy data (S298 ° ) is in J K1 mol1. b The notation “vib” or “hind” indicates whether the given motion was treated as a harmonic-oscillator or hindered-rotor. c The wavenumber associated with the low-frequency motion. d The height of the barrier along the low-frequency motion. e The difference between the results of the harmonic-oscillator and hindered-rotor treatment for the given quantity. a

136.5 ( 5.0

139.3 ( 5.0

141.8 ( 6.3

142.4 ( 6.3

137.5

137.6

ref 107 195.6 ( 0.0

28.3 ( 3.1

ref 16 ref 108

197.9

ref 111, G3MP2B3

141.0

ref 32, G3

138.0

ref110, G3(MP2)

140.6 CH2SO

this work ref 109

143.0 ( 3.0

7.6

this work

35.1 ( 3.1

ref 112, W2 261.4 ( 1.5

this work

30.0 ( 6.0

refs 17 and 120

52.0 ( 10.0

ref 123, CCSD(T)

38.0 ( 10.0

ref 125, DFT

CBS-QB3

of the rotation, the rotational barrier heights are 1267 cm1 and 1423 cm1. Since the frequency, 301 cm1, which can be associated with the torsional motion, is comparable to the barriers, this motion was treated within the framework of the one-dimensional hindered rotor model; consequently, the ZPE, thermal correction to the enthalpy, and the entropy values were corrected by 0.3 kJ/mol, 0.2 kJ/mol, and 6.7 J K1 mol1, respectively, for HOSO2. In the case of CH2SH, a 2140 cm1 rotational barrier exists between the two nondistinguishable planar minima, and a 94 cm1 low frequency vibration belongs to the torsional motion. Although the barrier is high enough to restrict the rotation, the shape of the potential curve can not be described accurately within the harmonic approximation (see the Supporting Information for the anharmonicity constants). Therefore, the one-dimensional

8.0 ( 10.0

ref 117

33.1 ( 10.3 3.0 ( 14.0

ref 126, cc-CA

9.0 ( 14.0

ref 119, CAS-SDCI

50.2 ( 20.9

ref118, NF ref121, W10

26.9 CH2SH

165.3 ( 3.1

160.2 ( 3.1

157.7 ( 8.4

this work ref 128

e164.4 ( 0.8

ref 128 145.7 ( 9.2

7827

270.0 ( 1.5

ref 17

169.9

ref129, G2

170.7

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Table 2. Continued species

ΔfH°0

ΔfH°298 110.5 ( 4.6

SCSOH 111.4 ( 5.0

108.9 ( 5.0 112.0 ( 5.0

S°298

321.0 ( 20.0 refs 17 and 133c 321.8 ( 1.5 g318.8

114.6 ( 5.9 S2COH

65.4 ( 4.6

60.3 ( 4.6

sourcea

this work ref 134c ref 132d

296.9 ( 1.5

this work

a

Unless otherwise noted, the data are obtained from experiment. If a composite scheme is used in a theoretical study, only the highest-level method is indicated. For further details on the experimental setup or on the theoretical methods please refer to the appropriate literature. NF empirical result, no direct experimental findings. CC - coupled-cluster based model chemistry. b It was assumed in the original report that HSO was observed in the experiment. c It was speculated that the SCSOH isomer formed. d No attempt was made to determine the structure of the formed isomer.

Schr€odinger equation was solved for this normal mode and this resulted in 0.2 kJ/mol, 0.1 kJ/mol, and 2.4 J K1 mol1 corrections for the ZPE, the thermal correction to the enthalpy, and the entropy values, respectively. Similarly to the case of CH2SH, two nondistinguishable planar minima exist for S2COH around the CO bond, and the rotational barrier, 3250 cm1, is high enough to restrict the rotation at room temperature. However, in contrast to CH2SH, the harmonic oscillator approximation holds well (see the Supporting Information for the anharmonicity constants). For SCSOH, similarly to HOSO2, two distinguishable minima (nonsuperimposable mirror images) can be found around the CSOH dihedral angle, and depending on the direction of the rotation, the rotational barriers are 346 cm1 and 976 cm1 high between them. Since the frequency of the torsional motion is 216 cm1, this motion was treated as a hindered rotation; consequently, the ZPE, thermal correction to the enthalpy, and the entropy values were corrected by 0.1 kJ/mol, 0.2 kJ/mol, and 7.6 J K1 mol1, respectively, for SCSOH. In the following, the relevant heats of formation and entropy data of the investigated species is discussed briefly. Our results as well as previous experimental and computational findings are summarized in Table 2. HSO and HOS. After analyzing their cross molecular beam experiment Davidson and co-workers obtained 5.6 ( 7.9 kJ/mol for the heat of formation of HSO at 298 K.91 Investigating the O(3P) þ H2S f HSO þ H reaction in a similar way, Balucani and associates determined ΔfH0°(HSO) = 3.8 ( 2.9 kJ/mol.6 The JPL database17 refers to the study of Davidson and his coworkers,91 as well as that of Balucani and associates,6 and sug° (HSO) = 6.1 ( 2.9 kJ/mol. Nevertheless, there is a gests ΔfH298 large gap between the values of experimentally and theoretically determined heats of formation. Goumri and co-workers = 19.9 kJ/mol using the Gaussian-2 reported ΔfH°(HSO) 0 (G2) approach.92 Xantheas and Dunning determined the heat of formation at 0 K, 22.6 ( 5.4 kJ/mol, using multireference configuration interaction calculations.93 Later, based on a complete active space self-consistent field (CAS-SCF) study,94 they reported ° (HSO) and 25.5 ( 5.4 kJ/mol and 2.9 ( 5.4 kJ/mol for ΔfH298 ° (HOS), respectively. Grant and associates carried out ΔfH298 = 21.8 ( CCSD(T) calculations which yielded ΔfH°(HSO) 0 4.2 kJ/mol and ΔfH°298(HSO) = 24.7 ( 4.2 kJ/mol.7 In an attempt to reconcile the experimental and theoretical data the structural isomer of HSO, HOS was also investigated in this study. It turned out that the computed values,

= 2.5 ( 2.3 kJ/mol and ΔfH°298(HOS) = ΔfH°(HOS) 0 5.3 ( 2.3 kJ/mol, agree well with those obtained from experi° (HSO). On the basis of these ments for ΔfH0°(HSO) and ΔfH298 agreements it is very likely that in the experiments, instead of the assumed HSO, HOS was observed. ° (HSO), ΔfH0°(HOS), and ΔfH298 ° For ΔfH0°(HSO), ΔfH298 (HOS) our study provides the most reliable estimates 19.6 ( 2.3 kJ/mol, 22.6 ( 2.3 kJ/mol, 2.4 ( 2.3 kJ/mol, and 5.3 ( 2.3 kJ/mol, respectively. This study also presents the first ° data for both HSO and HOS, 241.4 ( 1.5 J K1 mol1 S298 and 240.0 ( 1.5 J K1 mol1, respectively. HOSO2. Gleason and Howard investigated the reaction HOSO2 þ O2 f HO2 þ SO3 in a low-pressure discharge flow reactor to study the temperature dependence of the rate coefficient,8 and a lower limit was established for the heat of formation of HOSO2, ΔfH°298(HOSO2) g 395.4 kJ/mol. In order to measure the reaction enthalpy of the reaction OH þ SO2 H HOSO2, Blitz and associates used flash photolysis/laser induced fluorescence system, and suggested ΔfH°298(HOSO2) = 373.0 ( 6.0 kJ/mol.95 Li and McKee studied the same reaction as Gleason and Howard; however, with the theoretical G2 ° (HOSO2).96 method and reported 364.8 kJ/mol for ΔfH298 Somnitz carried out G3X calculations and, based on a B3LYP/ aug-cc-pV(Tþd)Z optimized geometry, ΔfH°(HOSO 0 2) = ° (HOSO2) = 368.8 kJ/mol were 360.8 kJ/mol and ΔfH298 suggested.97 In a CC-based composite study Klopper and his coworkers determined the heat of formation of HOSO2 at both 0 K, 366.6 ( 2.5 kJ/mol, and 298 K, 374.1 ( 3.0 kJ/mol.9 Our best estimates for the enthalpy values, 367.5 ( 4.4 and 375.7 ( 4.4 kJ/mol at 0 and 298.15 K, respectively, are in line with the accurate computational results of ref 9 and the experimental data of ref 95. Since the most accurate heats of formation data come from theoretical studies, this work and that of Klopper and associates, a short comparison of the approaches is in order here. Klopper and his colleagues did not investigated the effects of electron correlation beyond the CCSD(T) term; however, the core-correlation was not separated from the valencevalence correlation in their study. The separated treatment of the coreand valence-region in our correlation calculations can introduce an error of about (0.5 kJ/mol46,55 in the heat of formation values, while the ΔECCSDT(Q) term, according to our calculations, contributes 2.3 ( 1.3 kJ/mol to ΔfHT°(HOSO2). It is also a significant difference that in ref 9 the CCSD(T)-term was calculated using double- and triple-ζ basis sets, while here quadruple- and quintuple-ζ basis sets were used to estimate the CCSD(T) contribution. As it was verified in several studies, the use of double- and triple-ζ quality basis sets for the calculation of the CCSD(T) contribution can result in errors of several kJ/mol. Therefore, the error bar given in ref 9 for the ΔfHT°(HOSO2) data might be a bit optimistic, and we think that our results are more accurate. ° our protocol yields 294.1 ( 1.5 J K1 mol1, the same For S298 value listed in ref 18 but considerably different from that of Patrick and Golden.98 The source and the accuracy of the frequencies and the geometry used to calculate the value of 280.8 J K1 mol1 in ref 98 is unknown. It is reported without an error bar, and the lowfrequency motion was treated as a harmonic oscillator. The frequencies and the geometry used to calculate the entropy data of 294.1 J K1 mol1 in ref 18 are based on BAC-MP4 results, and the lowest vibration was treated as a hindered rotational motion. Our computations are more accurate than those used to calculate the entropy listed in Burcat’s database, and our entropy data, 7828


The Journal of Physical Chemistry A 294.1 ( 1.5 J K1 mol1, has a well-defined uncertainty. There° (HOSO2). fore it is preferred for S298 HSNO. The available data on the thermochemical properties of HSNO is rather scarce. Based on the laser induced fluorescence investigation99 of the reaction HS þ NO þ M f HSNO þ M ° (transthe JPL database17 suggests 95.2 ( 5.0 kJ/mol for ΔfH298 HSNO). An earlier compilation of Heynes and Wine100 lists 94.0 ( 20.0 kJ/mol for ΔfH°298(trans-HSNO). In order to determinate the proton affinity of cis-HSNO, Nguyen and associates determined its heat of formation at 298 K using CCSD(T) calculation with the 6-311þþG(3df,2p) basis set, and obtained 112.0 ( 8.0 kJ/mol.101 It can be observed that this study provides the most reliable ° (trans-HSNO), and estimates for ΔfH0°(trans-HSNO), ΔfH298 S°298(trans-HSNO), 112.4 ( 2.7 kJ/mol, 107.3 ( 2.7 kJ/mol, and 266.4 ( 1.5 J K1 mol1, respectively. Our 298 K heat of formation value is in reasonable agreement with the previous computational result101 and is within the error bar of the experimental result of Heynes and Wine,100 while significantly differs from the value recommended by the JPL database.17 Although the authors of ref 99 noted that based on the comparison of bond-strengths in CH3SH and H2S as well as in the corresponding oxygenated analogs, CH3OH and H2O, the bond-strength of HS-NO [DH°298(HS-NO)] should lie between ° (HS-NO) = 139.0 kJ/ 99.8 and 137.5 kJ/mol, they used DH298 mol to better match the experimental temperature dependence of k0 for the HS þ NO þ He f HSNO þ He reaction. Nevertheless, the authors concluded that “measuring association kinetics does not provide a very sensitive means to deriving thermodynamic parameters”. If one uses, instead of 139.0 kJ/mol, the midpoint of the range from 99.8 to 137.5 kJ/mol for DH°298(HS-NO), 118.7 ( ° (trans-HSNO) = 114.4 ( 19.5 kJ/mol 18.9 kJ/mol then ΔfH298 ° (trans-HSNO) = can be obtained via the equation ΔfH298 ° (HS) þ ΔfH298 ° (NO) DH298 ° (HS-NO) with the ΔfH298 auxiliary data of ΔfH°298(HS) = 141.9 ( 0.5 kJ/mol102 and ° (NO) = 91.1 ( 0.1 kJ/mol. This result for ΔfH298 ° ΔfH298 (trans-HSNO) is also in line with our 107.3 ( 2.7 kJ/mol data. The only available heat of formation data for the cis isomer of HSNO has been published by Nguyen and colleagues101 at 298 K. Since the method used here is more accurate than that of ref = 115.8 ( 2.7 kJ/mol, ΔfH°298(cis101 our ΔfH°(cis-HSNO) 0 HSNO) = 110.7 ( 2.7 kJ/mol, and S°298(cis-HSNO) = 266.1 ( 1.5 J K1 mol1 values are preferred. ° (trans-HSNO) and S298 ° (cis-HSNO) values published The S298 here are the first available entropy data for these molecules in the literature. SH. Among the investigated species in this work the SH radical has attracted the most attention so far. Although accurate and consistent calculations have been reported in the literature there exists some discrepancy between these results and that obtained from an accurate experiment. Therefore, SH is also investigated in this study. The NIST-JANAF database16 lists 136.5 ( 5.0 and and ΔfH°298(SH), respectively. 139.3 ( 5.0 kJ/mol for ΔfH°(SH) 0 These values come from the photoionization study of Dibeler and Liston103 and the SH ionization energy measurements of Morrow.104 The photoionization mass spectrometric study of Traeger105 resulted in ΔfH°298(SH) = 138.6 ( 0.4 kJ/mol, however, it was also pointed out that the use of a more reliable estimate for the SHþ appearance energy106 would change the NIST-JANAF data ° (SH) = 139.3 ( 5.0 kJ/mol to ΔfH298 ° (SH) = 142.0 ( from ΔfH298 3.0 kJ/mol. Berkowitz and co-workers107 evaluated the performance

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of three experimental techniques (radical kinetics, gas-phase acidity cycles, and photoionization mass spectrometry) used to measure bond energies, and 143.3 ( 3.0 kJ/mol was recommended for ΔfH°298(SH). Nourbakhsh et al.108 measured the time-of-flight spectra of the CH3 and SH fragments during the photodissociation ° (SH) = 142.4 ( 6.3 kJ/mol. In a of CH3SH and obtained ΔfH298 kinetic equilibrium study,109 on the reaction Br þ H2S f SH þ HBr, 142.5 ( 3.0 kJ/mol and 143.0 ( 2.8 kJ/mol were obtained, and ΔfH°298(SH). respectively, for ΔfH°(SH) 0 The G3, G3(MP2), and G3MP2B3 model chemistries provided 141.0 kJ/mol,32 138.0 kJ/mol,110 and 137.6 kJ/mol111 for ΔfH°298(SH), respectively, while the W2 model chemistry41 of Martin and associates41 yielded 140.6 kJ/mol for ΔfH°298(SH).112 Peebles and Marshall113 also used a composite approach; the FC CCSD(T)/CBS limit was estimated from aug-cc-pV(Q,5,6)Z basis set results using the three-point extrapolation formula of Martin and Lee,114,115 then additional corrections considering the corevalence correlation, the anharmonicity, and the relativisitic effects were taken into account. 142.6 ( 0.8 and 143.1 ( and ΔfH°298(SH), 0.8 kJ/mol were obtained for ΔfH°(SH) 0 respectively. Csaszar and associates102 also studied the thermochemistry of the SH radical by means of the focal-point analysis. The HF/CBS energy and the FC CCSD(T)/CBS correlation energy were determined from (Q,5,6) and (5,6) extrapolations, respectively, using the aug-cc-pV(Xþd)Z basis sets. CCSDT and FCI calculations were also performed to assess the electron correlation beyond the CCSD(T) method, and the deficiencies of the BornOppenheimer and nonrelativistic approximations were also taken into account. ΔfH0°(SH) = 141.2 ( 0.5 kJ/mol, as ° (SH) = 141.9 ( 0.5 kJ/mol were reported. well as ΔfH298 Recently, Feller, Peterson, and Dixon43 surveyed several factors needed to predict atomization energies accurately, and heat of formation values for several radicals and molecules were calculated as well. They applied a similar approach to that used by Csaszar and associates,102 and for the SH radical ΔfH°298 = 141.0 ( 0.8 kJ/mol was obtained. ° (SH) = Our results, ΔfH0°(SH) = 142.8 ( 1.9 kJ/mol and ΔfH298 143.4 ( 1.9 kJ/mol, agree well (within the given error estimates) with previous accurate theoretical43,102,113 and experimental109 values. However, the above values are inconsistent with the result reported by Traeger105 in a photoionization mass spectrometry study, which indicates that the error bar, ( 0.4 kJ/mol, calculated in ref 105 is somewhat optimistic. ° (SH), the authors of the NIST-JANAF tables16 recFor S298 ommend 195.6 ( 0.0 J K1 mol1 calculated from the rotational and vibrational constants of Rosen,116 while the G3MP2B3 calculations of Janoschek and Rossi111 yielded 197.9 J K1 mol1. ° (SH) = 195.4 ( 1.5 J K1 mol1, confirms the Our result, S298 experimental value. CH2SO. For the sulfine heat of formation only a single experimental result, ΔfH°298(CH2SO) = 8.0 ( 10.0 kJ/mol, has been published by Bouchoux and Salpin117 since the molecule was generated in 1976. However, this value is not a direct experimental result either; it was derived from the measured gas-phase basicity and proton affinity of CH2SO. As it can be seen in Table 2, this experimental data is significantly higher than Benson’s previously estimated value of 50.2 ( 20.9 kJ/mol;118 however, it is in line with Ruttink’s CAS-SDCI/CASSCF/DZ(2df,2d,p)þf(S) result, 9.0 ( 14.0 kJ/mol.119 A few years later, Ruttink and associates120 revisited their previous calculations with the aid of the CBS-QB3 model chemistry. By averaging the results for 10 reactions, they obtained ΔfH°298(CH2SO) = 30.0 ( 6.0 kJ/mol. 7829



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Table 3. Calculated Standard Reaction Enthalpies (ΔrH° [kJ/mol]), Standard Reaction Entropies (ΔrS° [J K1 mol1]), Standard Gibbs Energies of Reaction (ΔrG° [kJ/mol]), Equilibrium Constants K [cm3/molecule], and Uncertainty Factors (f ) at 298 K reactiona

ΔrH°

ΔrS°

ΔrG°

K

fb

CS2 þ OH a S2COH

93.2 ( 5.9

124.4 ( 1.6

56.1 ( 6.4

2.73 1010

2.6

CS2 þ OH a SCSOH

45.1 ( 6.3

99.8 ( 1.6

15.3 ( 6.8

1.96 1017

2.7

experimental findings

45.6 ( 4.2

100.4 ( 18.4

15.7 ( 9.7

1.40 1017

1.4c

a

Heat of formation data for CS2 and OH were taken from ref 17; the entropy data for CS2 and OH are from ref 17; the experimental reaction enthalpy and entropy were taken from ref 133; the experimental equilibrium constant is from the JPL database.17 b An upper or lower bond of the equilibrium constant K can be obtained by multiplying or dividing the value of K by the uncertainty factor f. According to the laws of error propagation f was calculated using the formula of δ(ΔrG°)/(RT), where δ(ΔrG°), R, and T are the uncertainty in the standard Gibbs energy of reaction, the ideal gas constant, and the temperature in Kelvin, respectively. c It is obtained from ref 17.

The JPL database17 adopted this value as well. Heydorn et al.121 obtained ΔfH0°(CH2SO) = 26.9 kJ/mol using the W10 122 model chemistry, a modified W141 protocol for molecules containing second-row atoms. Ventura and associates also studied the heat of formation of sulfine in three subsequent papers. In the first paper,123 ΔfH°298(CH2SO) was calculated to be 52.0 ( 10.0 kJ/mol using the isodesmic reaction CH2SO þ SO a CH2S þ SO2. For geometry optimizations and single-point calculations the B3LYP and B3PW91 density functionals were used with various Pople’s basis sets up to 6-311þþG(3df,2pd). The DFT results were also confirmed with calculations carried out with the CCSD(T) method, and finally, the values obtained at the B3PW91/ 6-311þþG(3df,2pd) and FC-CCSD(T)/6-311þþG(2df,2pd) levels of theory were averaged and accepted as ΔfH°298(CH2SO). In their second paper,124 the previously calculated value of 52.0 ( 10.0 kJ/mol was confirmed on the basis of DFT, MP2, and CCSD(T) calculations with Dunning’s correlation-consistent basis sets. In order to solve the discrepancy between Ruttink and associates’ CBS-QB3120 and their previous results,123,124 Ventura and co-workers125 performed DFT calculations on three additional reaction schemes not considered earlier. They concluded that the discrepancy is connected to the presence of the triplet SO in the isodesmic reaction (see above) used to calculate the heat of formation of sulfine. On the basis of a true isodesmic reaction CH2SO þ SO2 a CH2S þ SO3, ΔfH°298(CH2SO) = 38.0 ( 10.0 kJ/mol was obtained125 at the B3LYP/6311þþG(3df,2pd) level of theory. Applying the correlation consistent composite approach (ccCA) Williams and Wilson126 obtained 33.1 ( 10.3 kJ/mol for ΔfH°298(CH2SO) using a Schwartz-type127 inverse quartic extrapolation formula. ° (CH2SO) Our best estimates for ΔfH0°(CH2SO) and ΔfH298 are 28.3 ( 3.1 and 35.1 ( 3.1 kJ/mol, respectively. Our 0 K heat of formation value agrees with that obtained in a W10 study, and it also has a well-defined error bar. Our results obtained for ΔfH298 ° (CH2SO) is in accordance with the computational results of refs 126 and 120; however, our associated confidence interval is considerably tighter. Consequently, our results provide the most accurate estimates for the heats of formation of CH2SO. For ° (CH2SO), this study delivers the first data, 261.4 ( 1.5 J K1 S298 mol1. It is also noted that due to the huge rotational barriers no internal rotation is allowed around the torsional angle. CH2SH. Three independent investigations, an experimental and two theoretical studies, were published in 1992 in connection with the thermochemical properties of the CH2SH radical. Ruscic and Berkowitz,128 studied the photoionization mass spectra of CH2SH and CH3S, and ΔfH°(CH 0 2SH) = 157.7 ( 8.4 kJ/mol

was recommended. Combining the result of an earlier measurement for the appearance potential of CH2SHþ with their ionization potential of CH2SH, Ruscic and Berkowitz128 deduced an upper limit to the CH bond strength in CH3SH. On the basis of the bond dissociation reaction H CH2SH f H þ CH2SH, an upper limit to ΔfH0°(CH2SH), 164.4 ( 0.8 kJ/mol, was also calculated. The recommended data, ΔfH°298(CH2SH) = 145.7 ( 9.2 kJ/mol, of the authors of the JPL database17 is based on the measurements of Ruscic and Berkowitz.128 Curtiss and associates129 and Chiu and co-workers130 carried out G2 calculations independently on several CSHn radicals and ions. They obtained 169.9 and 170.7 kJ/mol for ΔfH0°(CH2SH), respectively. Nevertheless, both results fail to satisfy the ΔfH0°(CH2SH) e 164.4 ( 0.8 kJ/mol limit (see above). Our protocol yields ΔfH°(CH 0 2SH) = 165.3 ( 3.1 kJ/mol and ° (CH2SH) = 160.2 ( 3.1 kJ/mol. Our 0 K heat of ΔfH298 formation value is consistent with previous calculations, as well as with the upper limit reported by Ruscic and Berkowitz.128 Considering the latter as well as our results ΔfH°(CH 0 2SH) is probably located in the 162.2 to 165.2 kJ/mol interval. Our ° (CH2SH) = 270.0 ( 1.5 J K1 mol1, is the entropy data, S298 first available entropy value for this compound. S2COH and SCSOH. As mentioned earlier, two structural isomers exist for CS2OH, the C-adduct S2COH and the S-adduct SCSOH, and it was a key question to atmospheric chemists whether it was the former or the latter that was observed in reaction 5 (see ref 131 and references therein). The first direct experimental observation of both adducts, with a lifetime greater than 0.9 μs at 298 K, has been reported recently by Petris and associates.15 Hynes et al.132 investigated the kinetics of reaction 5 via pulsed laser photolysis and obtained ΔfH°298(CS2OH) = 114.6 ( 5.9 kJ/mol. Murrells and co-workers133 and Diau and Lee134 also studied the kinetics of the reaction between OH and CS2 by laser-induced fluorescence techniques, and determined ΔfH°298(CS2OH) = 110.5 ( 4.6 kJ/mol and ΔfH°298(CS2OH) = 112.0 ( 5.0 kJ/mol, respectively. It was also speculated in ref 134 that probably the S-adduct springs up in the reaction. The results obtained in refs 133 and 134 agree reasonably, nevertheless, the associated uncertainty is less in the former study, and its data is recommended in the JPL database.17 Using a modified G1 protocol, G10 (ref 135), McKee135 calculated both adducts to be more stable relative to OH þ CS2. For the formation of the S-isomer, the G10 method of McKee135 yielded a 36.8 kJ/mol smaller energy barrier than that for the formation of the C-isomer. The existence of this smaller energy barrier for the thermodinamically disfavored isomer led the author of ref 135 to conclude that the S-isomer was the adduct 7830


The Journal of Physical Chemistry A observed experimentally. McKee and Wine131 used a procedure similar to the G2(MP2,SVP) method to study the atmospheric oxidation of CS2. Eventually, QCISD(T)/6-311þG(3df,2p) relative energies were approximated by combining QCISD(T)/6-31G(d) and MP2/6-311þG(3df,2p) results using B3LYP/6-31G(d) geometries and zero-point energies. Their results confirmed McKee’s previous findings,135 i.e., both adducts were found to be more stable relative to OH þ CS2 system. A reaction coordinate calculation was also carried out for the addition of OH to the sulfur atom of CS2 in order to investigate the activation barrier to this process. At the B3LYP/6-31þG(d) level no such barrier could be located, while the approximate QCISD(T)/6-311þG(3df,2p) calculations resulted in an energy barrier of 3.7 kJ/mol.131 Our results for the C- and S-adducts of CS2OH are ΔfH0°° (S2COH) = 60.3 ( 4.6 kJ/ (S2COH) = 65.4 ( 4.6 kJ/mol, ΔfH298 = 111.4 ( 5.0 kJ/mol, and ΔfH°298(SCSOH) = mol, ΔfH°(SCSOH) 0 108.9 ( 5.0 kJ/mol. These values suggest that it is very likely that the S-adduct was observed in previous experimental studies. Furthermore, the comparison of our reaction heats, reaction entropies, Gibbs energies of reaction, and equilibrium constants data with those obtained in experiments for the CS2 þ OH reaction (see Table 3) also confirms the formation of SCSOH in the experiments. For S°298 Murrells and co-workers obtained 321.0 ( 20.0 J K1 mol1,133 while Diau and Lee established a lower limit of S°298 g ° = 296.9 ( 1.5 J 318.8 J K1 mol1.134 Our entropy values are S298 ° = 321.8 ( 1.5 J K1 mol1 K1 mol1 for the C-adduct and S298 for the S-adduct. It is worth noting that this study is the first one which reports data on the heats of formation and entropy of the S2COH isomer.

’ CONCLUDING REMARKS This study confirms the significance of theoretical studies in thermochemistry, and presents several heat of formation and entropy values for sulfur containing molecules with atmospheric relevance. The presented values are the most reliable estimates for most of the considered molecules. On the basis of our calculations, the currently accepted heats of formation of HSO, HOS, cis- and trans-HSNO, CH2SO, and CH2SH may need to be revised. This study also reports the first estimates with welldefined error bars for the heats of formation of S2COH, and for the entropies of HSO, HOS, HOSO2, cis- and trans-HSNO, CH2SO, CH2SH, SCSOH, and S2COH. ’ ASSOCIATED CONTENT

bS

Supporting Information. Total energies, equilibrium geometries, rotational constants, harmonic frequencies, and anharmonic corrections. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT Financial support has been provided by the European Research Council (ERC) under the European Community’s Seventh Framework Programme (FP7/2007-2013), ERC Grant Agreement No. 200639, and by the Hungarian Scientific Research Fund (OTKA), Grant No. NF72194. G.T. thanks the

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MOP project (4.2.1./B-09/1/KONV-2010-0005) for finanTA cial support.

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