A computational study on the mechanism and kinetics of the reaction between CH₃CH₂S and OH

Abstract

The reaction mechanism of CH₃CH₂S with OH radicals is studied at the CBS-QB3 level of theory. Five substitution processes and eleven addition–elimination channels are identified for the title reaction. The calculated results indicate that addition–elimination channels CH₃CHS + H₂O, CH₂CH₂ + HSOH, CH₃CHSO + H₂ and CH₃CH₂SH + O are dominant. Other channels may be negligible due to the high barrier heights. Rate constants and branching ratios are estimated by means of the conventional transition state theory with zero curvature tunnelling over the temperature range of 200–3000 K. The calculation shows that the overall rate constant in the temperature of 200–3000 K is mainly dependent on the channels CH₃CHS + H₂O, CH₂CH₂ + HSOH and CH₃CH₂SH + O. The three-parameter expression for the total rate constant is fitted to be k_total = 7.42 × 10⁻²¹T^2.63 exp(−772.43/T) cm³ molecule⁻¹ s⁻¹ between 200–3000 K.

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1. Introduction

CH₃CH₂S, CH₃S, CH₂SH, CH₂S and HCS and other sulfur-containing small organic molecules released from fuel combustion and the oxidation of sulfur, have become one of the major pollution sources of the atmospheric environment.^1–3 These sulfur-containing compounds have been widely studied because of their negative effects on the Earth's environment.^4–8 CH₃CH₂S is a typical representative of sulfur-containing small organic molecules, which is the main product of laser photolysis of C₂H₅SSC₂H₅ or C₂H₅SH and also an important reaction intermediate.^9–11 Although this sulfur-contained small molecules shows a very low level in Earth's atmosphere, but it have a significant impact on climate change and acid rain formation. Therefore, the stability of this sulfur-contained small molecule, its reactivity with atmospheric free radicals and how to eliminate its effect on air pollution has attracted wide attention. OH are one of the most important atmospheric oxidant.^12,13 Outer shells of OH have unpaired electron, it always tends to get electronics, with high activity, and thus the role of atmospheric trace constituents from strong oxidants, for many important compounds, reaction with OH is their degradation rate-determining step.^14–16

The reaction of sulfur-contained small molecules with OH radical is one of the most important degradation processes in the atmosphere.^17–19 Zhang et al.²⁰ investigated the mechanism of the reaction of C₂H₅S with HO₂ at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-311G(2d,p) method. They obtained both hydrogen abstraction and addition–elimination reaction pathways on the singlet and triplet potential surfaces. Cao et al.²¹ theoretically investigated the reaction mechanism of CH₃SCH₂CH₃ with OH at the CCSD(T)/6-311++G(d,p)//MP2/6-31+G(2d,p). They measured The CVT/SCT rate constants of hydrogen abstraction channels over the temperature range of 200–900 K. However, the reaction of CH₃CH₂S with OH has not been reported so far to the best of our knowledge.

The objective of the present study on the reaction of C₂H₅S with OH is to exploit its possible reaction pathways, to shed light on the reaction mechanism, to provide new insight into the new sink of aliphatic thiols in the atmosphere, and fundamental foundations for preventing and eliminating air pollutions from aliphatic thiols. So in this paper, the reaction mechanism of CH₃CH₂S with OH radical is studied. Then based on the obtained mechanism information, the rate constants of the major channel are calculated.

2. Computational method

The quantum chemistry calculations reported in this work were carried out with Gaussian 09 ²² program packages. We used the B3LYP/CBSB7 and UB3LYP/CBSB7 ^23,24 method to optimize and characterize the closed-shell and open-shell stationary points respectively. At this level of theory, we also calculated the harmonic vibrational frequencies to verify the nature of the corresponding stationary points (minima or transition state), to provide the zero-point vibrational energy (ZPE) and to determine the thermodynamic contributions to the enthalpy and free energy. Moreover, to ensure that the transition states were connected to the desired reactants and products, we performed intrinsic reaction coordinate (IRC)^25–28 calculations. In order to obtain more accurate relative energies, based on the optimized geometries, we performed single-point CBS-QB3 ^29,30 and CCSD(T)/aug-cc-pVTZ³¹ for closed-shell and performed single-point UCBS-QB3 and UCCSD(T)/aug-cc-pVTZ calculations for open-shell stationary points. Finally, the kinetic properties of the system were calculated using conventional transition state theory (TST)^32–34 in the VKLab^35–37 program coupled with the steady state approximation.

These calculations made use of the energies obtained at the CBS-QB3 level of theory and the partition functions computed at the B3LYP/CBSB7 level of theory. The tunnelling correction to the rate constants was computed using the zero-order approximation of a vibrationally adiabatic potential energy surface (PES) with zero curvature. In this case, the unsymmetrical Eckart potential energy barrier was used to approximate the potential energy curve.

3. Results and discussion

The values 〈S²〉 of all the species involving the C₂H₅S + OH reaction were shown in Table S1.† As illustrated in Table S1,† after spin annihilation for the singlet, doublet and triplet species, the values of 〈S²〉 were respectively nearly 0.0000, 0.7500, and 2.0000 at the B3LYP/CBSB7 level of theory, so the spin contamination is not severe. All optimized geometries of the reactants, complexes, transition states, and products involving the nucleophilic substitution reaction and addition–elimination channels at the B3LYP/CBSB7 level of theory along with the available experimental^38–42 values were displayed in Fig. 1, 3 and 5. For the species (OH, ¹CH₃CHS, H₂O, ¹CH₂CH₂S, ¹CH₂S, CH₃, CH₃OH, CH₄, CH₂CH₂ and H₂), the mean absolute deviations of bond lengths and bond angles between the calculated values at the B3LYP/CBSB7 level of theory and the corresponding experiment ones are 0.006 Å and 0.06°, respectively. So the calculated bond lengths and angles at the B3LYP/CBSB7 level of theory are acceptable. Besides, experimental data is not available with which to judge the accuracy of our results, therefore Table S2† lists the relative energies (ΔE), enthalpies (ΔH(298)), and free energies (ΔG(298)) to the reactants (C₂H₅S + OH) at the CBS-QB3 level as well as the heats of formation for every channel evaluated by CCSD(T)/aug-cc-pVTZ//B3LYP/CBSB7 calculations. By comparing the reaction enthalpy results obtained with CCSD(T)/aug-cc-pVTZ//B3LYP/CBSB7 and CBS-QB3, energetic results agree to 1–2 kcal mol⁻¹. Therefore, the CBS-QB3 level of theory was able to describe the title reaction reliably. So potential energy profile of nucleophilic substitution reaction and addition–elimination channels for the reaction of CH₃CH₂S with OH at the CBS-QB3 level of theory were presented in Fig. 2, 4 and 6.

Fig. 1 The geometrical structures of the optimized reactants, transition states, products and imaginary frequencies (ν, cm⁻¹) of transition states involving the singlet and triplet nucleophilic substitution reaction of C₂H₅S + OH at the CBS-QB3 level of theory.

Fig. 2 Schematic energy diagram for the singlet and triplet nucleophilic substitution reaction of C₂H₅S + OH at the CBS-QB3 level of theory.

3.1. Reaction mechanism

Five substitution processes (R1–R5) and eleven addition–elimination channels (R6–R16) were modeled for the title reaction, which were listed in Scheme S1–S3,† as well as Fig. 2, 4 and 6, where “IM” and “IMF” denote post-reactant complex and pre-product complex of the corresponding reaction pathway, respectively. For simplicity, the singlet and triplet species are signed 1 and 3 as superscription.

3.1.1 Nucleophilic substitution mechanism. For the nucleophilic substitution reaction of C₂H₅S + OH, two singlet channels (Channels R1 and R2) and three triplet channels (Channels R3, R4 and R5) were modeled as depicted in Scheme S1† and Fig. 2.

Singlet channels of Channel R1 and R2 proceeded by the oxygen atom of OH radical respectively attacking to the carbon atom of α-CH₂ and β-CH₃, simultaneously C(1)–C(2) bond breaking. The corresponding transition state was TS1 and TS2, respectively. In TS1, the breaking C(1)–C(2) bond shown in Fig. 1 was elongated by 0.686 Å compared with that in CH₃CH₂S, while the forming O–C(2) bond was 0.630 Å longer than that in SCH₂OH. In TS2, the breaking C(1)–C(2) bond is elongated by 0.359 Å compared with that in CH₃CH₂S, while the forming O–C(2) bond is 0.495 Å longer than that in CH₃OH. The barrier height of Channel R1 and R2 was 24.78 and 18.23 kcal mol⁻¹, respectively.

Similar with singlet Channel R1, the triplet oxygen-to-(α)carbon nucleophilic substitution channel (R3) is also located to produce SCH₂OH + CH₃. The barrier height of Channel R3 is 31.95 kcal mol⁻¹, which is higher by 7.17 kcal mol⁻¹ than that of the singlet channel R1, showing that the formation of SCH₂OH + CH₃ mainly take from Channel R1. The triplet oxygen-to-(β) carbon nucleophilic substitution channel (R4) is located to produce CH₃OH + ³CH₂S with the energy barrier of 33.34 kcal mol⁻¹. Compared with the barrier of singlet oxygen-to-(β) carbon nucleophilic substitution channel (R2), the barrier height of Channel R4 is higher by 15.11 kcal mol⁻¹, indicating that oxygen-to-(β) carbon nucleophilic substitution reaction mainly occurs on the singlet potential energy surface.

Differently from singlet nucleophilic substitution reaction that oxygen-to-sulfur nucleophilic substitution could not taken place due to the stability of ¹CH₃CH₂SOH, the triplet oxygen-to-sulfur nucleophilic substitution channel (R5) is located to produce CH₃ + CH₂SOH. The barrier height of Channel R5 was 30.02 kcal mol⁻¹. This was lower by 1.93–3.32 kcal mol⁻¹ than that of triplet Channels R3 and R4, but it was higher by 5.24–11.29 kcal mol⁻¹ than that of singlet Channels R1 and R2. From above mechanism elucidation, it can be concluded that triplet nucleophilic substitution mechanisms are more unfeasible than the singlet because of the higher barrier heights. The nucleophilic substitution reaction of C₂H₅S + OH should mainly occur on the singlet PES. Moreover, singlet oxygen-to-(β) carbon nucleophilic substitution channel (R2) is most favorable nucleophilic substitution channel.

3.1.2 Addition–elimination mechanism. For the addition–elimination reaction of C₂H₅S + OH, four channels (Channels R6–R9) of H₂O formation were modeled as depicted in Scheme S2† and Fig. 4, meanwhile seven channels (Channels R10–R16) of CH₄, C₂H₄, H₂, CH₃CH₂SH and CH₃OH formations were modeled as depicted in Scheme S3† and Fig. 6.
3.1.2.1 The channel of H₂O formation. Five hydrogen atoms of the CH₃CH₂S are distributed into the two groups, which are, H atom in α-CH₂ (α-position carbon atom adjacent to the sulfur atom) and β-CH₃ (carbon atom stands away from the sulfur atom). Thus, two possible reaction of hydrogen abstraction from CH₃CH₂S by OH radical are investigated on both singlet and triplet potential energy surface (singlet channels (R6 and R7) and triplet channels (R8 and R9)). Moreover, similar with the reaction between CH₃SCH₂CH₃ and OH,⁴³ each reaction can occur in more than one pathway due to the effect of sulfur atom of CH₃CH₂S.

Before the transition state and the products, singlet channels R6 and R7 (shown in Fig. 4) begin with the ¹CH₃CH₂SOH intermediate, whose structure is loose with the O atom of OH and the S atom of CH₃CH₂S separation of 1.699 Å. The relative energy of ¹CH₃CH₂SOH to the reactants (CH₃CH₂S + OH) is −69.82 kcal mol⁻¹ at the CBS-QB3 level of theory. For channel R6, starting from ¹CH₃CH₂SOH, products (CH₃CHS + H₂O) were obtained via transition state TS6a, TS6b, which were labeled as Path R6a and R6b, respectively. Transition state TS6a, and TS6b differentiated mainly from each other in the relative orientation of the hydrogen atoms of OH radical. Such geometrical discrepancy may leads that TS6b was only lower by 0.12 kcal mol⁻¹ than that of TS6a.

For channel R7, beginning with ¹CH₃CH₂SOH, products (CH₂CH₂S + H₂O) can be obtained via TS7a and TS7b, respectively. The difference between TS7a and TS7b mainly lies in dihedral angle ∠HO(4)H(7)C(2) (in Fig. 3). Hydrogen atom of the OH radical is directed toward the sulfur atom in TS7a (∠HO(4)H(7)C(2) = 109.8°), while it is stays away from the sulfur atom in TS7b (∠HO(4)H(7)C(2) = −92.6°). The imaginary frequencies of TS7a and TS7b are 1602i cm⁻¹ and 1490i cm⁻¹, respectively. The relative energy of TS7a and TS7b to the reactants (CH₃CH₂S + OH) is respectively −2.04 and −2.40 kcal mol⁻¹, which is higher by 15.60–15.84 kcal mol⁻¹ than that of TS6a (−17.88 kcal mol⁻¹) and TS6b (−18.00 kcal mol⁻¹), indicating that, for singlet H-abstraction channels, Channel R6 is easily to occur for the lower barrier heights compared to channel R7.

Fig. 3 The geometrical structures of the optimized transition states, intermediates, products and imaginary frequencies (ν, cm⁻¹) of transition states involving the singlet and triplet channels of H₂O formation in the addition–elimination reaction of C₂H₅S + OH at the CBS-QB3 level of theory.

Similar to the singlet H-abstraction processes (Channels R6 and R7), the corresponding triplet α-CH₂ site and β-CH₃ site H-abstraction reaction were found beginning with the formation of intermediate ³CH₃CH₂SOH before the transition state and the products. From the geometrical point of view as depicted in Fig. 3, the bond distance between the O atom of OH and the S atom of CH₃CH₂S in ³CH₃CH₂SOH complex is stretched by 0.419 Å compared with the corresponding bond distance in ¹CH₃CH₂SOH. Such discrepancy may lead that the relative energy of ³CH₃CH₂SOH to the reactants (CH₃CH₂S + OH) is higher by 59.5 kcal mol⁻¹ than that of ¹CH₃CH₂SOH to the reactants (CH₃CH₂S + OH). Starting from ³CH₃CH₂SOH complex, triplet α-CH₂ site and β-CH₃ site H-abstraction reaction occurs via Channel R8 (TS8a, TS8b) and Channel R9 (TS9a, TS9b and TS9c), respectively. Compared with the corresponding transition states in singlet H-abstraction processes (Channels R6 and R7), triplet transition states shown in Fig. 3 were different in two respects. First, there is not the formation of S–O bond in triplet transition states. Second, the C–H–O bond angle in triplet transition state is less bent (e.g., ∠O(4)H(5)C(1) 134.7° in TS6a vs. 160.3° in TS8a; ∠O(4)H(7)C(2) 154.4° in TS7a vs. 173.4° in TS9a). It is shown in Fig. 4 that the relative energy of TS8a and TS8b in Channel R8 is lower by 1.23–5.91 kcal mol⁻¹ than that of the TS9a, TS9b and TS9c in Channel R9. This indicates that triplet α-CH₂ H-abstraction reaction (Channel R8) is easily to take place than triplet β-CH₃ site H-abstraction reaction (Channel R9). However, compared with singlet α-CH₂ H-abstraction reaction (Channel R6), the relative energy of TS8a and TS8b in Channel R8 is higher by 16.70–17.34 kcal mol⁻¹ than that of the TS6a, and TS6b in Channel R1.

Fig. 4 Schematic energy diagram for the singlet (a) and triplet (b) channels of H₂O formation in the addition–elimination reaction of C₂H₅S + OH at the CBS-QB3 level of theory.

Fig. 5 The geometrical structures of the optimized transition states, intermediates, products and imaginary frequencies (ν, cm⁻¹) of transition states involving the singlet addition–elimination reaction of C₂H₅S + OH at the CBS-QB3 level of theory.

According to the discussed above, for the activity of hydrogen abstraction, the singlet channels are stronger than triplet channel, and for the activity of hydrogen abstraction of the singlet channel, the α-carbon atom is stronger than β-carbon atom (the order is: α-CH₂ (R6) > β-CH₃ (R7) > α-CH₃ (R8) > β-CH₃ (R9)). Atomic Mulliken charge of α-carbon atom (α-CH₃, 0.0464e) is more electropositive than that of β-CH₃ (0.1231e), which leads to the C–H bond of α-position weaker than that of β-position. On the other hand, the stability orders of the product radicals, ¹CH₃CHS > ¹CH₂CH₂S > ³CH₃CHS > ³CH₂CH₂S, produced by R6, R7, R8 and R9, respectively, is in consistent with the activity order of hydrogen abstraction. This is possibly because the substituent at the unpaired electron position influences on the stability of the above-mentioned radicals.

3.1.2.2 The channels of CH₄ formation. As described above that ¹CH₃CH₂SOH was much more stable than ³CH₃CH₂SOH, all the addition–elimination channels R10–R16 were taken into account beginning with pre-reactant complex ¹CH₃CH₂SOH. Similar with the reaction between CH₃ and C₂H₅OH,⁴⁴ Channels R10 and R11 in Fig. 6 have been considered that the C atom of CH₃ respectively abstracts the hydrogen atom from C(1) and O(4) sites in ¹CH₃CH₂SOH with the H₃C⋯H–X bond (where X denotes HCSOH and CH₂SO) in their transition states. For Channel R10, as shown in Fig. 5, one of the two H atoms of the CH₂ group in ¹CH₃CH₂SOH can migrate toward the C atom in the CH₃ group to produce CH₄ + HCSOH via TS10. The breaking C(1)–C(2) bond was elongated from 1.523 Å in ¹CH₃CH₂SOH to 2.198 Å in TS10. The barrier height of R10 was 79.09 kcal mol⁻¹. Channel R11 leads to the formation of CH₄ + CH₂SO via TS11. The product CH₂SO can be further formed to cyclic geometry (c-CH₂SO) via transition state TS11-1 with the barrier height of 52.11 kcal mol⁻¹. The breaking O–H bond in TS11 was 1.216 Å much longer than the corresponding value in ¹CH₃CH₂SOH. The forward potential barrier of Channel R11 at the CBS-QB3 level was 74.52 kcal mol⁻¹, which was lower by 4.57 kcal mol⁻¹ than that of Channel R10. The higher C–H dissociation energy (C–H, 473.0 kJ mol⁻¹; O–H, 436.0 kJ mol⁻¹) of CH₂SOH moiety may be responsible for the higher barrier of Channel 10.

Fig. 6 Schematic energy diagram for the singlet addition–elimination reaction of C₂H₅S + OH at the CBS-QB3 level of theory.

3.1.2.3 The channels of C₂H₄ formation. For Channel R12, our result presented in Fig. 5 shows that HOSH elimination from ¹CH₃CH₂SOH occurs via a four-centered (H(9)–S(3)–C(2)–C(1)) transition state TS12 with C₁ symmetry. The dihedral angle of the H atom in the four centered-ring H(9)-S(3)-C(2)-C(1) is −0.5°. The breaking C–H and C–S bonds in TS12 are 0.333 and 0.552 Å longer than those in ¹CH₃CH₂SOH. TS12 lies below the reactants C₂H₅S + OH by 13.28 kcal mol⁻¹ at the CBS-QB3 level, which is respectively lower by 22.55 kcal mol⁻¹ and 17.98 kcal mol⁻¹ than the corresponding values of TS10 and TS11. This indicates that HOSH elimination (Channel R12) is much favorable than the C atom of CH₃ respectively abstracts the hydrogen atom from C(1) and O(4) sites in ¹CH₃CH₂SOH (Channels R10 and R11) kinetically.
3.1.2.4 The channels of H₂ formation. As shown in Fig. 5, Channels R13 and R14 are the C–H cleavage and the H₂-elimination reactions. Differently from Channel R13 that the H atom of the OH group and one of the two H atoms from the CH₂ group in ¹CH₃CH₂SOH form H₂ via HHO(4)S(3)C(1) five-member-ring transition state TS13, in Channel R14, two H atoms each from the CH₃ and OH groups in ¹CH₃CH₂SOH, form a HHO(4)S(3)C(1)C(2) six-member-ring transition state TS14, resulting in H₂ elimination to produce H₂, CH₂=CH₂ and SO. Comparing the two H₂-elimination processes in Channels R13 and R14, we see that TS14 is about 11.58 kcal mol⁻¹ higher than TS13. The difference may be ascribed to the fact that a strong stereo repulsion force from the CH₃ group exists and additional C(1)–S(3) bond breaking in TS14.
3.1.2.5 The channels of CH₃CH₂SH and CH₃OH formation. As shown in Fig. 5, we also calculated other reaction channels consisting CH₃CH₂SH + O (Channel R15) and CH₃OH + CH₂S (Channel R16) channels. Channel R16 may be negligible for the high relative energy (9.45–34.13 kcal mol⁻¹) of TS16 to the transition states TS10–TS15. Such energy discrepancy is possibly due to the two bonds (S(3)–O(4) and C(1)–C(2)) cleavage, which makes the Channel R16 much harder. For Channel 15, starting from ¹CH₃CH₂SOH complex, the isomerization process (¹CH₃CH₂SOH → TS15 → CH₃CH₂SHO) takes place by the S atom abstracts hydrogen atom from OH site in ¹CH₃CH₂SOH. This reaction channel includes the O(4)–H(10) dissociation and S(3)–H(O(4)) bond formation. The O(4)–H(10), and S(3)–H(O(4)) bond lengths in TS15 is 1.479 and 1.394 Å, respectively. The transition states TS15 show three-member-ring structures (H(10)–O(4)–S(3)) and has a barrier of 58.02 kcal mol⁻¹, which is only higher by 1.48 kcal mol⁻¹ than that of Channel 12. This indicates that Channel R15 also occurs easily.

In summary, addition–elimination channels R6, R12, R13 and R15 are the major channels. Other channels may be negligible due to the high barrier heights. Furthermore, the lowest barrier for the channel CH₃CHS + H₂O is ∼ 5 kcal mol⁻¹ lower than that of the addition–elimination channel CH₂CH₂ + HSOH, which is similar with the reactions of ethanol⁴⁵ (the lowest energy channel is the H₂O-formation reaction).

3.2. Rate constant calculation for major channels

The rate constant calculations of the selected channels were shown in Scheme 1, where “TS” and “K_eq” denote the transition state and equilibrium constant of the corresponding reaction pathway, respectively. k denotes the rate constant of the corresponding reaction pathway. We neglect the rate constant calculation of channel R1–R5, R7–R11, R14 and R16 because of their high barriers. Reaction channels R6, R12, R13 and R15 all began with the formation of a prereactive complex before progressing through the transition state, which is depicted in eqn (1).

Scheme 1 The selected reaction channels in rate constant calculations.

Assuming that the prereactive complex ¹C₂H₅SOH was in equilibrium with the reactants and was at steady state, the overall rate constant was expressed as.

If k₂ « k₋₁, the rate constant was rewritten as

where K_eq and k₂ were given by eqn (4) and the VKLab program,³⁵ respectively.

The various Q values denoted the partition functions of the intermediates, reactants C₂H₅S and OH. E_R, E_CR are the total energies of the reactants and the post-reactant complex CR; σ is the symmetry number.

In the rate constant calculation, the overall rate constant k_total are calculated within the temperature range of 200–3000 K, which was given by k_total = K_eq × (k_6a + k_6b + k₁₂ + k₁₃ + k₁₅). Fig. 7 and Table S3† lists the temperature dependence of k_R6(k_R1 = K_eq × (k_6a + k_6b)), k_R12(k_R12 = K_eq × k₁₂), k₁₃(k₁₃ = K_eq × k₁₃), k₁₅ (k_R15 = K_eq × k₁₅) and k_total within the temperature range of 200–3000 K. In the calculated temperature range, k_R6, k_R12, k₁₃, k₁₅ and k_total all decrease slowly at low temperature, and increase at high temperature range. Such as, as the temperature increases, k_total decreases slowly in the temperature range of 200–298 K (k²⁹⁸_total/k²⁰⁰_total = 0.88), and increases within the temperature range of 298–3000 K (k³⁰⁰⁰_total/k²⁹⁵_total = 13.1). The branching ratios of channel R6, R12, R13 and R15 are described in Fig. 8 and Table S4.† It can be seen in Fig. 8 and Table S4† that the overall rate constant in the temperature of 200–3000 K is main dependent on the R6, R12 and R15. At 200 K, the contribution of R1(k₆k_total), R12(k₁₅/k_total) and R15((k₁₅/k_total)) to the total rate constant is 50.0%, 25.0%, 18.0%, respectively. As the temperature increases, R6 and R12 become significant (k₆/k_total, 66.0%, k₁₂/k_total, 28.0%, k₁₅/k_total, 5.0% at 3000 K). The contribution of R13 to the overall rate constant over the temperature of 200–3000 K is small within 7%.

Fig. 7 Rate constants calculated in this work are plotted as a function of temperature (200–3000 K). k_R6 (k_R6 = K_eq × (k_6a + k_6b)) is rate constant for channel R6. k_R12 is rate constant of channel R12, k_R13(k_R13 = K_eq × k₁₃) is rate constant of channel R13, k_R15 is rate constant of channel R15, k_total is the sum of k_R6, k_R12, k_R13 and k_R15.

Fig. 8 The predicted branching ratios over the temperature range of 200–3000 K. The k_R6/k_total, k_R12/k_total, k_R13/k_total and k_R15/k_total represent the branching ratios of channel R6, R12, R13 and R15, respectively.

For kinetic modeling applications, the calculated TST rate constant k₆, k₁₂, k₁₃, k₁₅ and k_total in the temperature range of 200–3000 K have been fitted to the three-parameter expressions (unit in cm³ molecule⁻¹ s⁻¹):

k₆ = 2.77 × 10⁻²¹T^2.71 exp(−751.02/T)

k₁₂ = 3.00 × 10⁻²¹T^2.60 exp(−714.11/T)

k₁₃ = 7.13 × 10⁻²²T^2.35 exp(−1054.81/T)

k₁₅ = 4.97 × 10⁻²⁰T^2.02 exp(−711.46/T)

k_total = 7.42 × 10⁻²¹T^2.63 exp(−772.43/T)

4. Conclusions

Theoretical method CBS-QB3 is applied to study the reaction mechanism of CH₃CH₂S with OH. The rate constants of major channels are evaluated over the temperature range of 200–3000 K. The main conclusions are summarized as follows:

(1) Two mechanisms are investigated for the title reaction, namely, substitution and addition–elimination. Addition–elimination channels CH₃CHS + H₂O, CH₂CH₂ + HSOH, CH₃CHSO + H₂ and CH₃CH₂SH + O are the major channels.

(2) The overall rate constant in the temperature of 200–3000 K is main dependent on the channels CH₃CHS + H₂O, CH₂CH₂ + HSOH and CH₃CH₂SH + O. The contribution of channel CH₃CHSO + H₂ to the overall rate constant over the calculated temperature is small within 7%.

Acknowledgements

The project was supported by the National Natural Science Foundation of China (21473108), Education department of shaanxi provincial government research project (14JK1154), the Funds of Research Programs of Shaanxi University of Technology (SLGQD13(2)-3, SLGQD13(2)-4).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra07780f

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