Sage Journals: Discover world-class research

Abstract

Kinetic rate constants for the oxidation reaction of the hydroxyl radical with CH₃SH, C₂H₅SH, n-C₃H₇SH, and iso-C₃H₇SH under inert (Ar) conditions over the temperature range 252–430 K have been studied theoretically using density functional theory along with various exchange–correlation functionals as well as the benchmark CBS-QB3 quantum chemical approach.

Bimolecular rate constants were estimated using transition state theory and the statistical Rice–Ramsperger–Kassel–Marcus theory. Comparison with experiment confirms that in the OH addition reaction pathways leading to the related products, the first bimolecular reaction steps have effective negative activation energy barriers. Effective rate constants have been calculated according to a steady-state analysis of a two-step model reaction mechanism. As a consequence of the negative activation energies, pressures higher than 10⁴ bar are required to reach the high-pressure limit. Both from thermodynamic and kinetic viewpoints, the most favorable process here is the oxidation reaction of hydroxyl radicals with n-C₃H₇SH.

Keywords

Aliphatic thiols oxidation processes H-abstraction rate constants transition state theory reaction mechanisms Rice–Ramsperger–Kassel–Marcus theory

Introduction

The emission of gaseous sulfur compounds into the atmosphere is due to both natural and anthropogenic processes.¹ In recent years, investigation of the global atmospheric sulfur cycle has been the subject of intense scientific interest because of the need to assess the contribution of anthropogenically produced sulfur to problems such as acid rain, visibility reduction, and climate modification.² In heavily industrialized regions, anthropogenic sulfur emissions exceed natural emissions by about an order of magnitude. However, on a global scale, natural sulfur emissions are thought to equal approximately those from anthropogenic sources.^3,4 Despite their low concentrations, larger organic sulfur compounds may play an important role in tropospheric sulfur chemistry. All hydrogen-containing sulfur compounds (such as R-SH, R: CH₃, C₂H₅, n-C₃H₇, iso-C₃H₇) are probably removed from the atmosphere very rapidly by reaction with OH radicals, and some may also react rapidly with NO₃.²

The hydroxyl radical is a reactive intermediate of importance in combustion processes and in atmospheric chemistry.⁵ Hence, the kinetic rate constants and mechanisms for the reaction of hydroxyl radicals with organic sulfides (R-SH), which play a dominant role in the troposphere,^6–15 are needed in order to understand their involvement in photochemical air pollution. The products of the [R-SH···OH]· reaction chain have not been established, and the laboratory data can be interpreted either as OH addition or as H-abstraction reaction pathways.¹ Since there are no reported theoretical data for these reactions, in this article, absolute kinetic rate constants for the reactions of OH radicals with the studied compounds have been determined over the temperature range of 252–430 K.

The reaction of OH radicals with CH₃SH was studied experimentally by Wine et al.² and Atkinson et al.⁵ over the temperature range of 299–426 K with typically 50 Torr of argon as the diluent gas by using the flash photolysis-resonance fluorescence technique. The Arrhenius expression obtained was k_(MeSH) = 8.89 × 10⁻¹² exp((790 ± 300)/RT) cm³ molecule⁻¹ s⁻¹ with a rate constant at 298 K of (3.39 ± 0.34) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹. Analogous increases in kinetic rate constants have previously been observed for the reactions of O (³P) atoms with CH₃SH and C₂H₅SH at room temperature.^16,17 The observation of a negative Arrhenius activation energy for the reaction of OH radicals with CH₃SH over the studied temperature ranges probably arises from a zero or near-zero activation energy combined with a temperature-dependent preexponential factor, as has been previously observed and discussed for the reactions of OH radicals with olefins.^18–20 CH₃SH is thus as reactive as olefins toward OH radicals and can be calculated to have a half-life due to reaction with OH radicals in the lower troposphere, using an OH radical concentration of ∼3 × 10⁶ molecule cm⁻³, of ∼2 h.^21–25

The discharge flow experiments of Mac Leod et al.²⁵ and Lee and Tang,²⁶ which were carried out at total pressures 10−100 times lower than those employed in the flash photolysis studies, report kinetic rate constants for OH^•+CH₃SH and OH^•+C₂H₅SH, which are slightly lower than those obtained in the flash photolysis studies. On the other hand, Cox and Sheppard,²⁷ using a relative rate technique, obtained a 298 K rate constant for OH^•+CH₃SH in 1 atm air that is nearly a factor of three higher than that obtained in the flash photolysis studies. Cox and Sheppard suggested that the difference between their result and the flash photolysis results could be explained by assuming that the OH^•+CH₃SH rate constant was pressure-dependent. While the flash photolysis results agree with the discharge flow results within the combined experimental errors, the consistently lower rate constants obtained in the discharge flow studies suggest that OH reactions with CH₃SH and C₂H₅SH may be pressure-dependent in the low-pressure regime.²

There are three possible pathways for the reactions of OH with thiols:

Abstraction of hydrogen from a carbon atom [CH₃SH+OH^•→ H₂O+^•CH₂SH].

Abstraction of hydrogen from the sulfur atom [CH₃SH+OH^•→ H₂O+CH₃ S^•].

Addition to the sulfur atom [CH₃SH+OH^•→ CH₃SH-OH^•].

Observations show that the kinetic rate constant related to the first pathway at room temperature is nearly independent of the nature of the hydrocarbon chain, which clearly indicates that hydrogen abstraction from a carbon atom (C−H bond) is a negligible reaction channel for all reactions investigated.² Thus, these reactions must proceed via either H-abstraction from the weak S−H bonds (of bond dissociation energy 91 ± 1.5 kcal mol⁻¹)^28,29 or by the formation of an OH–thiol adduct (see Scheme 1). Since no definitive information is available concerning this issue, further experimental data are required concerning the dynamics of the reactions of the initial OH radicals with the aliphatic thiols containing short-chain alkyl groups (1 to 3 carbon atoms) and of the subsequent reaction pathways operative under atmospheric conditions.

Scheme 1.

H-abstraction reaction pathways of aliphatic thiols containing alkyl groups (1 to 3 carbon atoms) by hydroxyl radicals yielding water and the related thiol radicals.

The reactions of hydroxyl radicals with the aliphatic thiols such as methanethiol (1), ethanethiol (2), n-propanethiol (3), and isopropanethiol (4) have been studied experimentally at temperatures ranging from 252 to 430 K by means of laser flash photolysis using laser-induced fluorescence (see Figure 1). As can be seen from Figure 1, for all reported series of data, the rate constants of the reactions between hydroxyl radicals and compounds 1–4 exhibit negative temperature dependence over the studied temperature range, which are equivalent to Arrhenius activation energies of −(689.49 ± 117.23), −(786.85 ± 166.91), − (971.64 ± 194.73), and −(766.98 ± 307.98) cal mol⁻¹, respectively (see Figure 1). A least-squares analysis of the temperature dependence of the measured rate constants yields the following Arrhenius expressions² (in cm³ molecule⁻¹ s⁻¹)

\begin{matrix} k_{1} = 10^{(10.1 \pm 1.9)} \exp [\frac{(689.49 \pm 117.23 ca l^{- 1} mo l^{- 1})}{RT}]; T = 254 - 430 K \\ k_{2} = 10^{(12.3 \pm 3.3)} \exp [\frac{(786.85 \pm 166.91 ca l^{- 1} mo l^{- 1})}{RT}]; T = 252 - 425 K \\ k_{3} = 10^{(8.9 \pm 2.8)} \exp [\frac{(971.64 \pm 194.73 ca l^{- 1} mo l^{- 1})}{RT}]; T = 257 - 419 K \\ k_{4} = 10^{(11.6 \pm 5.5)} \exp [\frac{(766.98 \pm 307.98 ca l^{- 1} mo l^{- 1})}{RT}]; T = 256 - 429 K \end{matrix}

Figure 1.

Arrhenius plots of the rate constants for the reactions of OH radicals with compounds 1–4.

The Arrhenius rate constants decrease gradually with increasing temperature at temperatures ranging from 252 to 430 K, confirming negative activation energies.

To explain the disparity of the kinetic data shown in Figure 1, pathways 1−4 have been suggested for the reactions between compounds 1−4 and OH radicals in the gas phase. To the best of our knowledge, the present theoretical study is the first one that has investigated the oxidation mechanisms of aliphatic thiols that are initiated by hydroxyl radicals. Under experimental conditions, attack of OH radicals on aliphatic thiols is initiated by addition onto the sulfur atom and onto the hydrogen bonded to the sulfur atom to give the related products (Figure 2).

Figure 2.

Retained atom labeling for characterizing the structures of intermediates and transition states.

To seek more quantitative insights into these reaction mechanisms, comparison will be made with benchmark theoretical calculations employing the high-level composite CBS-QB3 ab initio approach,^30–38 to determine which exchange–correlation functional gives the most accurate energy barriers and reaction energies. We note that density functional theory (DFT) methods alone were found to be insufficient for quantitatively investigating the potential energy surfaces of the reaction mechanisms and kinetics of oxidation processes of benzene³⁹ and naphthalene^40,41 by OH radicals, given the inability of many popular DFT functionals to describe quantitatively nonbonded interactions and barrier heights.

The aim of the present study was to achieve comprehensive and quantitative theoretical insights of the studied pathways. For this purpose, we first used DFT along with the dispersion-corrected ωB97XD⁴² and the M06-2x⁴³ exchange–correlation functionals and the aug-cc-pVTZ basis set⁴⁴ and then compared the reaction energies and energy barriers obtained with the results of benchmark theoretical calculations employing the CBS-QB3 composite method. In addition, kinetic rate constants in the high-pressure limit were obtained using transition state theory (TST),^45–51 and their falloff behavior was investigated at lower pressures using the statistical Rice–Ramsperger–Kassel–Marcus (RRKM) theory^52–54 to unravel the available experimental data^2,5 at temperatures ranging from 252 to 430 K.

Theory and computational details

All calculations reported in this study were performed using the Gaussian09 package of programs.⁵⁵ Molecular structures were visualized with GaussView.⁵⁶ The geometries and harmonic vibrational frequencies of all stationary points involved in the reactions of interest were determined using DFT⁵⁷ in conjunction with the ωB97XD and M06-2x functionals and the aug-cc-pVTZ basis set.

The energies of all the studied stationary points were reevaluated using the CBS-QB3 model.^30–38 This model includes low-level calculations using large basis sets, mid-sized basis sets for second-order correlation corrections, and small basis sets for high-level correlation corrections. It also includes an energy extrapolation up to the coupled cluster theory including single, double, and perturbative triple excitations (CCSD(T)) level⁵⁸⁻⁶⁰ in complete basis set limits in order to correct second-order Møller–Plesset correlation energies.⁵⁹

The five-step CBS-QB3 series of calculations starts with a geometry optimization at the B3LYP theoretical level,^33,38,61 followed by calculation of vibrational frequencies and thermodynamic state functions⁶² obtained from canonical partition functions that were computed for an ideal gas using Boltzmann statistical thermodynamics.⁶³⁻⁶⁶ A weakness of the B3LYP approach is that it neglects dispersion forces which may have some influence on torsional characteristics. The CBS-QB3 method amounts to an extrapolation of energies to the CCSD(T) level in conjunction with a complete basis set. The CBS-QB3 method was developed with the idea that a major source of error in quantum mechanical calculations arises from truncation of the basis set.^31,33,35,37 The CBS-QB3 method is a benchmark quantum chemical approach in order to calibrate the accuracy of DFT methods employing necessarily approximate exchange–correlation functionals.

The intrinsic reaction coordinate (IRC) analysis^67,68 was carried out in both directions (forward and backward) along the reaction path using the Hessian-based predictor corrector integrator algorithm in order to check the energy profiles connecting the identified transition state (TS) structures to the associated energy minima.^69,70

Analysis of the oxidation of aliphatic thiols by OH radicals turned out to be consistent with the scheme,⁷¹ which assumed that this reaction occurs according to a two-step mechanism,⁷² involving first a fast preequilibrium between the reactants (R−SH+OH^•) and a prereactive complex [R−SH···OH]^• (IM_i), followed by H-abstraction leading to the related products

\begin{matrix} Step 1 : R - SH + O H^{•} ⇌_{k_{- 1}}^{k_{1}} R - SH \dots O H^{•} (reversible arrows needed in step 1) \\ Step 2 : R - SH \dots O H^{•} \overset{k_{2}}{\to} R - S^{•} + H_{2} O \end{matrix}

where k₁ and k₋₁ denote the rate constants for the forward and reverse reactions associated with the first step, and k₂ is the rate constant corresponding to the second step. The overall rate constant can be rewritten as

k_{overall} = K_{c} k_{2}

(1)

where K_c = k₁/k₋₁ is the equilibrium constant for fast preequilibrium between the reactants and the prereactive complex (see Table S1 of the Supplemental Material). In the high-pressure limit (TST), the kinetic rate constant characterizing the unimolecular dissociation reaction is given by^45−52,73

k_{2} = κ (T) \times \frac{σ k_{B} T}{h} \times \frac{Q_{T S_{i}}}{Q_{I M_{i}}} \times \exp [- \frac{(E_{T S_{i}} - E_{I M_{i}})}{RT}]

(2)

where R denotes the ideal gas constant, and k_B and h represent Boltzmann’s and Planck’s constants, respectively. In the equation, Q_R−SH, Q_OH, Q_IMi, and Q_TS_i represent the total molecular partition functions for the isolated reactants, prereactive molecular complex (IM_i), and transition state (TS_i) associated with the unimolecular dissociation reaction (step 2), respectively. E_R−SH, E_OH, E_IMi, and E_TSi are the corresponding energies including B3LYP/6-311G(2d,d,p) estimates for zero-point vibrational contributions. In the above equation, σ is the reaction-path degeneracy and κ(T) denotes Wigner’s^74,75 tunneling correction factor (see Table S2 of the Supplemental Material)

κ (T) = 1 + \frac{1}{24} {(\frac{h Im (υ^{\neq})}{k_{B} T})}^{2}

(3)

where Im(υ¹) is the imaginary vibrational frequency of the relevant TS, and R is the ideal gas constant. Kinetic rate constants for the channels studied were calculated over the temperature range of 252–430 K and in the high-pressure limit (1 atm) using TST. Unimolecular kinetics are given by^76,77

k_{overall} = \frac{σ k_{B} T}{h} \times \frac{Q_{T S_{i}}}{Q_{R - SH} \times Q_{OH}} \times \frac{V_{m} (T)}{N_{Av}} \times \exp (- \frac{Δ E_{o}}{RT})

(4)

Kinetics for each pathway were evaluated in the high-pressure limit and using B3LYP/6-311G(2d,d,p) molecular partition functions that were computed using the vibrational ground state as energy reference along with the CBS-QB3 estimates for activation energies. Due to the simplicity of conventional TST, it gives the upper limit of the kinetics and enables us to provide reliable rate constants in the limiting high-pressure behavior.^54,78

According to the RRKM theory, the energy-dependent microcanonical rate constants, k(E), for the unimolecular decomposition of a molecule with internal energy E can be expressed as⁷⁹

k (E) = \frac{σ G^{†} (E - E_{o})}{h N (E)}

(5)

where G^†(E − E_o) is the sum of the densities of states of the TSs at energies ranging from 0 to E − E_o, where E_o is the critical energy for the reaction, and N(E) is the density of vibrational states in the activated molecule at an energy E. G^†(E − E_o) and N(E) were computed using the Beyer–Swinehart exact counting algorithm⁷⁹ improved by Stein and Rabinovitch.⁸⁰ Canonical (temperature-dependent) RRKM rate constants were determined from state integration and Boltzmann averaging.

TST and RRKM kinetic rate constants for the reaction pathways 1–4 were obtained using the KiSThelP program.⁸¹ In all calculations, a scaling factor of 0.99 was applied to the B3LYP/6-311G(2d,d,p) harmonic frequencies in order to account partially for anharmonic effects.⁸² The strong collision approximation has been used. It has been assumed that every collision deactivates the molecule with ω = b_c.Z_LJ[M] corresponding to the effective collision frequency, along with b_c the collisional efficiency, [M] the total gas concentration, and Z_LJ the Lennard-Jones (LJ) collision frequency. The collision frequencies (Z_LJ) were computed from the LJ parameters. The employed LJ potential parameters for argon (as diluent gas)⁷⁸ and the reactants⁸³ are listed in Table 1.

Table 1.

Lennard-Jones (LJ) potential parameters.

Species	LJ potential parameters
Species	σ (Å)	ε/k _B (K)
Argon	3.465	113.5
Methanethiol (1)	4.3	377.1
Ethanethiol (2)	4.7	396.1
n-Propanethiol (3)	5.1	414.4
Isopropanethiol (4)	5.1	418.1

Results and discussion

Structural characteristics of stationary points

The optimized molecular structures of the intermediate complexes, TSs, and products along reaction pathways 1–4 are presented in Tables 2 and 3, according to the atom labels given in Figure 2. In analogy to the oxidation mechanism of benzene, as well as naphthalene, initiated by OH radicals, a prereactive molecular complex (IM_i) has been identified (Figure 3) in the reactions of reactants with OH radicals. According to Uc et al.,⁸⁴ such a prereactive complex is a feature common to reactions between radical species and unsaturated molecules, which finds its origin in long-range Coulomb interactions between the reactant molecules.⁸⁵

Table 2.

Structural parameters for all stationary points involved in the H-abstraction pathways 1 and 2 (see Figure 3) for the oxidation of methanethiol (1) and ethanethiol (2) by hydroxyl radicals to the related products (P1, P2).

Parameter	ωB97XD/aug-cc-pVTZ						M06-2x/aug-cc-pVTZ						B3LYP/6-311G(2d,d,p)
Parameter	IM1	IM2	TS1	TS2	P1	P2	IM1	IM2	TS1	TS2	P1	P2	IM1	IM2	TS1	TS2	P1	P2
r (H₁−O₂)	0.964	0.964	0.967	0.967	0.957	0.957	0.969	0.966	0.967	0.970	0.959	0.959	0.969	0.969	0.971	0.971	0.962	0.962
r (O₂−H₃)	2.573	2.554	1.595	1.612	0.957	0.957	2.555	2.553	1.576	1.586	0.959	0.959	2.468	2.471	1.635	1.658	0.962	0.962
r (H₃−S₄)	1.339	1.340	1.381	1.379	–	–	1.338	1.339	128.1	1.381	–	–	1.340	1.341	1.379	1.376	–	–
r (S₄−C₅)	1.806	1.817	1.812	1.821	1.791	1.799	1.804	1.814	1.813	1.820	1.794	1.799	1.822	1.835	1.828	1.838	1.806	1.813
∠ (H₁−O₂−H₃)	110.2	112.1	105.2	104.9	105.1	105.1	108.0	108.4	104.5	104.1	105.3	105.3	122.4	122.8	106.7	106.3	103.8	103.8
∠ (O₂−H₃−S₄)	64.6	65.4	124.5	124.1	–	–	62.0	61.9	128.1	126.1	–	–	71.2	71.1	120.9	120.3	–	–

Bond lengths are given in angstroms (Å), and angles are given in degrees (^o).

Table 3.

Structural parameters for all stationary points involved in the H-abstraction pathways 3 and 4 (see Figure 3) for the oxidation of n-propanethiol (3) and isopropanethiol (4) by hydroxyl radicals to the related products (P3, P4).

Parameter	ωB97XD/aug-cc-pVTZ						M06-2x/aug-cc-pVTZ						B3LYP/6-311G(2d,d,p)
Parameter	IM3	IM4	TS3	TS4	P3	P4	IM3	IM4	TS3	TS4	P3	P4	IM3	IM4	TS3	TS4	P3	P4
r (H₁−O₂)	0.964	0.964	0.967	0.967	0.957	0.957	0.966	0.966	0.970	0.970	0.959	0.959	0.969	0.969	0.971	0.971	0.962	0.962
r (O₂−H₃)	2.546	2.615	1.607	1.600	0.957	0.957	2.548	2.590	1.587	1.584	0.959	0.959	2.462	2.659	1.650	1.662	0.962	0.962
r (H₃−S₄)	1.340	1.340	1.379	1.380	−	−	1.339	1.340	1.381	1.381	−	−	1.341	1.342	1.377	1.375	−	−
r (S₄−C₅)	1.815	1.832	1.818	1.836	1.798	1.813	1.812	1.827	1.818	1.832	1.800	1.811	1.833	1.854	1.836	1.856	1.814	1.830
∠ (H₁−O₂−H₃)	113.3	108.0	105.0	104.7	105.1	105.1	108.9	106.5	104.1	103.8	105.3	105.3	123.1	110.4	106.6	105.9	103.8	103.8
∠ (O₂−H₃−S₄)	65.9	63.0	124.1	124.6	−	−	62.2	60.5	126.7	126.6	−	−	71.5	63.4	120.8	120.2	−	−

Bond lengths are given in angstroms (Å), and angles are given in degrees (^o).

Figure 3.

Potential energy profiles for the reaction pathways 1−4 obtained using the CBS-QB3 method.

According to our best CBS-QB3 data, this prereactive intermediate complex (IM_i) for pathways 1−4 is located at about 4.3−5.4 kcal mol⁻¹ below the total energy of the related reactants, and is characterized by H₃–O₂ bond lengths equal to around 2.46−2.66 Å (Figure 2). Proceeding further along reaction pathways 1−4, the H-abstraction processes via the transition states (TS_i) requires activation energies of about 3.1−4.0 kcal mol⁻¹ relative to the prereactive intermediate (IM_i) energies (Figure 3). With reaction energies around −30.7 to −32.9 kcal mol⁻¹, the removal of a hydrogen atom from the studied compounds by a hydroxyl radical appears to be a strongly exothermic process. Inspection of the B3LYP/6-311G(2d,d,p) geometries obtained for the transition states along pathways 1−4 shows that the breaking of the H₃−S₄ bond and the formation of the O₂−H₃ bond is a concerted process. At the level of the TSs, the breaking S−H bond is elongated by ∼2.6% (∼0.04 Å in absolute value), compared to the equilibrium structures computed for the studied compounds. In contrast, the forming O−H bond has, quite naturally, a greater length than in the isolated H₂O molecule. Compared with the latter, the elongation of the O−H bond in the TSs is of the order of about 70%−73% (∼0.67−0.70 Å in absolute value).

The fact that the relative elongation of the S−H bond is smaller than that inferred for the forming O−H bond indicates that the transition states (TS_i; i = 1−4) are structurally closer to the reactants than to the products. This is in line with Hammond’s principle⁸⁶⁻⁸⁹ and the observation that the removal of a hydrogen atom from the studied aliphatic thiol by a hydroxyl radical is an exothermic process.

Prior to ending this discussion of geometric structures and parameters, it is worth noting that, at all considered DFT levels of theory that were used to optimize the geometries of prereactive intermediates, TSs and products, the spin contamination [<S²>_obs−0.75] never exceeds 0.011 (see Table S3 of the Supplemental Material) and can thus, for all practical purposes, be regarded as negligible. For the HF/6-31+G^* wavefunction, which is required for post-self-consistent field energy calculations at the CCSD(T)/6-31+G^* theoretical level in the CBS-QB3 procedure, <S²> may reach values around 0.77 for all of the identified TSs.

Energetic and thermodynamic parameters

The total internal energies at 0 K, as well as the enthalpies and Gibbs free energies at 298 K of all identified intermediates, TSs, and products along pathways 1−4 relative to the reactants are listed in Tables 4 and 5. A schematic potential energy diagram of the pathways 1−4 is shown in Figure 3. In line with experimental Arrhenius activation energies of −0.69, −0.79, −0.97, and −0.77 kcal mol⁻¹ for pathways 1−4, respectively, all our calculations locate the TSs (TS_i) on pathways 1−4 at 0.65–4.58 kcal mol⁻¹ below the isolated reactants. The results show the transition state TS3 on pathway 3 as the lowest TS, located at 2.13–4.58 kcal mol⁻¹ below the reactants.

Table 4.

Internal energies, standard enthalpies, and Gibbs free energies (in kcal mol⁻¹) of prereactive intermediates, and products relative to the reactants along H-abstraction pathways 1−4 at different levels of theory (P = 1 atm).

Method	ωB97XD/aug-cc-pVTZ			M06-2x/aug-cc-pVTZ			CBS-QB3
Species	ΔE_0K	ΔH°_298K	ΔG°_298K	ΔE_0K	ΔH°_298K	ΔG°_298K	ΔE_0K	ΔH°_298K	ΔG°_298K
R−SH+OH^•	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
(R: methyl, ethyl, n-propyl, iso-propyl)
IM1 [CH₃SH…OH]^•	−6.064	−6.706	1.477	−5.031	−5.841	2.921	−4.316	−4.906	3.180
IM2 [C₂H₅SH …OH]^•	−6.625	−7.232	1.160	−5.461	−5.703	1.873	−4.843	−5.414	2.846
IM3 [n-C₃H₇SH …OH]^•	−7.201	−7.712	0.622	−6.497	−6.858	0.145	−5.274	−5.811	2.571
IM4 [iso-C₃H₇SH …OH]^•	−6.795	−7.334	1.140	−6.207	−6.799	1.923	−5.407	−5.912	2.555
P1 [H₂O+CH₃ S^• ]	−32.544	−32.630	−32.952	−31.497	−31.624	−31.802	−32.106	−32.058	−32.594
P2 [H₂O+C₂H₅ S^• ]	−32.156	−32.055	−32.774	−31.024	−30.772	−31.817	−32.373	−32.383	−32.857
P3 [H₂O+n-C₃H₇ S^• ]	−32.644	−32.673	−33.121	−32.329	−32.418	−32.865	−32.853	−32.984	−33.108
P4 [H₂O+iso-C₃H₇ S^• ]	−30.662	−30.567	−31.396	−31.095	−31.186	−31.606	−31.254	−31.825	−31.878

Table 5.

Internal energies, standard enthalpies, and Gibbs free energies (in kcal mol⁻¹) of transition states relative to the reactants along H-abstraction pathways 1−4 at different levels of theory (P = 1 atm).

Method	ωB97XD/aug-cc-pVTZ			M06-2x/aug-cc-pVTZ			CBS-QB3			literature^2,5ΔE_act (cal mol⁻¹)
Species	ΔE_0K^≠	ΔH°_298K^≠	ΔG°_298K^≠	ΔE_0K^≠	ΔH°_298K^≠	ΔG°_298K^≠	ΔE_0K^≠	ΔH°_298K^≠	ΔG°_298K^≠
R−SH+OH^•	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
(R: methyl, ethyl, n-propyl, iso-propyl)
TS1 [TS-CH₃ S^•]	−3.125	−3.864	4.243	−1.583	−2.385	5.871	−0.653	−1.408	6.793	−(689.49 ± 117.23)
TS2 [TS-C₂H₅ S^•]	−3.891	−4.656	3.710	−2.178	−2.583	5.228	−1.707	−2.415	5.565	−(786.85 ± 166.91)
TS3 [TS-n-C₃H₇ S^•]	−4.579	−5.289	3.301	−3.303	−3.821	3.916	−2.134	−2.829	5.505	−(971.64 ± 194.73)
TS4 [TS-iso-C₃H₇ S^•]	−3.397	−4.087	4.395	−2.139	−2.802	5.662	−1.418	−2.077	6.231	−(766.98 ± 307.98)

Our best (CBS-QB3) estimated value for the corresponding activation energy of these reactions is 0.65–2.13 kcal mol⁻¹ below the reactants. According to experiment,^2,5 this difference in activation energies for the bimolecular reactions R_i+OH^•→P_i (i = 1−4) indicates that the formation of products P3 (H₂O+n-C₃H₇ S^•) is kinetically favored over the formation of the other products. The activation barrier for pathway 3 is therefore lower by 1.48, 0.43, and 0.72 kcal mol⁻¹ than the barrier height for pathways 1, 2, and 4, respectively (Table 4).

Reaction energies, enthalpies, entropies, and Gibbs free reaction energies for the oxidation of compounds 1−4 by hydroxyl radicals are supplied in Table 4. In line with the structural characteristics of the TSs discussed previously, CBS-QB3 results show that all studied pathways are found to be extremely exothermic (ΔH^o < 0) as well as extremely exoergic (ΔG^o < 0) processes at ambient temperature and pressure. From the energy profiles shown in Figure 3, it is clear that the formation of products P3 (H₂O+n-C₃H₇ S^•) will also be thermodynamically fairly favored, since the reaction is strongly exothermic (ΔH^o =−32.98 kcal mol⁻¹) and exoergic (ΔG^o =−33.11 kcal mol⁻¹).

Comparison of the CBS-QB3 results with data obtained using ωB97XD and M06-2x exchange–correlation functionals (Tables 4 and 5) shows that the standard and widely used ωB97XD functional performs rather poorly in calculating reaction and activation energies. A much better agreement with the benchmark CBS-QB3 results is obtained with the M06-2x functional. Nevertheless, differences in activation energies of the order of 1.35 kcal mol⁻¹ or more are still noted when comparing the ωB97XD and M06-2x results with the CBS-QB3 estimates. This, along with the extreme variability of the DFT results with respect to the employed exchange–correlation functional, shows that DFT still remains unsuited for highly quantitative studies of kinetic rate constants.⁴⁰

As can be seen in Tables 3 and 4, the newly supplied CBS-QB3 data differ sensitively from those reported by Wine et al.² and Atkinson et al.⁵ Among all supplied data, energy values obtained with the M06-2x functional appear on average to be in closest agreement with the benchmark CBS-QB3 results. From the data provided in Table 4, we characterize in detail (Table 5) the energy barriers associated with the conversion of the prereactive intermediates IM_i into the related products (see also Figure 3). The CBS-QB3 results show that the energy barriers (IM_i→TS_i; i = 1−4) encountered along the pathways 1−4 amount to ∼2.94, ∼2.73, ∼2.62, and ∼3.40 kcal mol⁻¹, respectively.

According to Hammond’s postulate, the structure of the TSs would resemble the products more than the reactants.⁸⁶ This type of comparison is especially useful because most TSs cannot be characterized experimentally.⁸⁷ Hammond’s postulate explains this observation by describing how varying the enthalpy of a reaction would also change the structure of the TS. In turn, this change in geometric structure would alter the energy of the TS and therefore also the activation energy and reaction rate.⁸⁸ This can be quantified in terms of a parameter L, defined as the ratio of the elongation of the S₄−H₃ bond length to the shrinkage of the H₃−O₂ bond distance⁸⁹

L = \frac{δ r (S_{4} - H_{3})}{δ r (H_{3} - O_{2})}

(6)

L > 1 indicates that the TS lies closer to the products, whereas L < 1 indicates that the TS lies closer to the reactants.⁹⁰ The values obtained for the parameter L for pathways 1−4 are equal to 0.052, 0.033, 0.049, and 0.044, respectively, which confirms that the TSs are structurally closer to the reactants than to the products. These reaction pathways, being characterized by very early TSs, are expected to be extremely exoergic.

Prior to ending this discussion of reaction energies and energy barriers, it is worth noting that, at all employed levels of DFT, the spin contamination [<S²>_obs− 0.75] never exceeds 0.011 (see Table S3 of the Supplemental Material) and can thus, for all practical purposes, be regarded as insignificant. As is readily apparent from Table S3 of the Supplemental Material, spin contamination of the unrestricted Hartree-Fock electronic wave functions used at the start of all CBS-QB3 computations never exceeds 0.02 in this study and can thus, for all practical purposes, be regarded as negligible. The obtained CBS-QB3 results may therefore safely be regarded as benchmark results.

Kinetic parameters

TST and RRKM estimates for individual rate constants of the studied compounds calculated in the gas phase at a pressure of 1 bar and at the considered temperatures in line with the original experiments^2,5 are listed in Tables 6 −9 and compared with experimental data. Further RRKM data computed at lower and higher pressures are provided for the same temperatures in Table S4a−S4i of the Supplemental Material. Theoretical values obtained using TST at a pressure of 1 bar do not differ by more than two orders of magnitude from the experimental data.

Table 6.

Rate constants (units: unimolecular reactions in s⁻¹; bimolecular reactions in cm³ molecule⁻¹ s⁻¹) for the H-abstraction of methanethiol (compound 1). These data were obtained at P = 1 bar using TST and RRKM theories with the CBS-QB3 composite method.

T(K)	Rate constant (pathway 1)				Effective rate constant		k_exp × 10¹¹(cm³ molecule⁻¹ s⁻¹)^2,5
	TST		RRKM		TST	RRKM
	IM1→R1+OH^•k₋₁ (s⁻¹)	IM1→P1k₂ (s⁻¹)	IM1→R1+OH^•k₋₁ (s⁻¹)	IM1→P1k₂ (s⁻¹)	R1+OH^•→P1k_eff (1)	R1+OH^•→P1k_eff (1)
254	2.89 × 10¹⁵	6.92 × 10¹⁰	2.89 × 10¹⁵	4.79 × 10⁸	3.53 × 10⁻¹³	2.44 × 10⁻¹⁵	(4.08 ± 0.42)
298	1.34 × 10¹⁵	1.46 × 10¹¹	1.34 × 10¹⁵	6.72 × 10⁸	3.72 × 10⁻¹³	1.71 × 10⁻¹⁵	(3.04 ± 0.19)
322	9.67 × 10¹⁴	2.03 × 10¹¹	9.67 × 10¹⁴	7.55 × 10⁸	3.91 × 10⁻¹³	1.45 × 10⁻¹⁵	(3.03 ± 0.26)
375	5.58 × 10¹⁴	3.64 × 10¹¹	5.58 × 10¹⁴	8.78 × 10⁸	4.41 × 10⁻¹³	1.06 × 10⁻¹⁵	(2.80 ± 0.28)
403	4.46 × 10¹⁴	4.66 × 10¹¹	4.46 × 10¹⁴	9.14 × 10⁸	4.73 × 10⁻¹³	9.28 × 10⁻¹⁶	(2.39 ± 0.13)
430	3.71 × 10¹⁴	5.76 × 10¹¹	3.71 × 10¹⁴	9.33 × 10⁸	5.06 × 10⁻¹³	8.20 × 10⁻¹⁶	(2.25 ± 0.14)

TST: transition state theory; RRKM: Rice–Ramsperger–Kassel–Marcus theory.

Table 7.

Rate constants (units: unimolecular reactions in s⁻¹; bimolecular reactions in cm³ molecule⁻¹ s⁻¹) for the H-abstraction of ethanethiol (compound 2). These data were obtained at P = 1 bar using TST and RRKM theories with the CBS-QB3 composite method.

T(K)	Rate constant (pathway 2)				Effective rate constant		k _exp × 10¹¹(cm³ molecule⁻¹ s⁻¹)^2,5
	TST		RRKM		TST	RRKM
	IM2→R2+OH^•k₋₁ (s⁻¹)	IM2→P2k₂ (s⁻¹)	IM2→R2+OH^•k₋₁ (s⁻¹)	IM2→P2k₂ (s⁻¹)	R2+OH^•→P2k_eff (2)	R2+OH^•→P2k_eff (2)
252	1.55 × 10¹⁵	3.28 × 10¹¹	1.55 × 10¹⁵	1.05 × 10⁹	2.71 × 10⁻¹²	1.12 × 10⁻¹⁴	(6.55 ± 0.51)
278	1.00 × 10¹⁵	4.85 × 10¹¹	1.00 × 10¹⁵	1.16 × 10⁹	2.44 × 10⁻¹²	7.22 × 10⁻¹⁵	(5.15 ± 0.35)
298	7.60 × 10¹⁴	6.28 × 10¹¹	7.60 × 10¹⁴	1.22 × 10⁹	2.31 × 10⁻¹²	5.41 × 10⁻¹⁵	(4.21 ± 0.32)
343	4.65 × 10¹⁴	1.01 × 10¹²	4.65 × 10¹⁴	1.27 × 10⁹	2.14 × 10⁻¹²	3.11 × 10⁻¹⁵	(4.02 ± 0.14)
397	3.05 × 10¹⁴	1.57 × 10¹²	3.05 × 10¹⁴	1.25 × 10⁹	2.09 × 10⁻¹²	1.86 × 10⁻¹⁵	(3.41 ± 0.31)
425	2.58 × 10¹⁴	1.89 × 10¹²	2.58 × 10¹⁴	1.22 × 10⁹	2.11 × 10⁻¹²	1.49 × 10⁻¹⁵	(3.32 ± 0.27)

TST: transition state theory; RRKM: Rice–Ramsperger–Kassel–Marcus.

Table 8.

Rate constants (units: unimolecular reactions in s⁻¹; bimolecular reactions in cm³ molecule⁻¹ s⁻¹) for the H-abstraction of n-propanethiol (compound 3). These data were obtained at P = 1 bar using TST and RRKM theories with the CBS-QB3 composite method.

T(K)	Rate constant (pathway 3)				Effective rate constant		k_exp × 10¹¹(cm³ molecule⁻¹ s⁻¹)^2,5
	TST		RRKM		TST	RRKM
	IM3→R3+OH^•k₋₁ (s⁻¹)	IM3→P3k₂ (s⁻¹)	IM3→R3+OH^•k₋₁ (s⁻¹)	IM3→P3k₂ (s⁻¹)	R3+OH^•→P3k_eff (3)	R3+OH^•→P3k_eff (3)
257	8.23 × 10¹⁴	2.58 × 10¹¹	8.23 × 10¹⁴	1.48 × 10⁹	3.35 × 10⁻¹²	2.89 × 10⁻¹⁴	(6.31 ± 0.20)
298	4.77 × 10¹⁴	4.50 × 10¹¹	4.77 × 10¹⁴	1.56 × 10⁹	2.59 × 10⁻¹²	1.71 × 10⁻¹⁴	(4.56 ± 0.18)
353	2.87 × 10¹⁴	7.87 × 10¹¹	2.87 × 10¹⁴	1.52 × 10⁹	2.14 × 10⁻¹²	1.21 × 10⁻¹⁴	(3.63 ± 0.16)
419	1.91 × 10¹⁴	1.28 × 10¹²	1.91 × 10¹⁴	1.39 × 10⁹	1.92 × 10⁻¹²	5.78 × 10⁻¹⁵	(2.91 ± 0.09)

TST: transition state theory; RRKM: Rice–Ramsperger–Kassel–Marcus theory.

Table 9.

Rate constants (units: unimolecular reactions in s⁻¹; bimolecular reactions in cm³ molecule⁻¹ s⁻¹) for the H-abstraction of isopropanethiol (compound 4). These data were obtained at P = 1 bar using TST and RRKM theories with the CBS-QB3 composite method.

T(K)	Rate constant (pathway 4)				Effective rate constant		k_exp × 10¹¹(cm³ molecule⁻¹ s⁻¹)^2,5
	TST		RRKM		TST	RRKM
	IM4→R4+OH^•k₋₁ (s⁻¹)	IM4→P4k₂ (s⁻¹)	IM4→R4+OH^•k₋₁ (s⁻¹)	IM4→P4k₂ (s⁻¹)	R4+OH^•→P4k_eff (4)	R4+OH^•→P4k_eff (4)
256	8.10 × 10¹⁴	2.56 × 10¹⁰	8.10 × 10¹⁴	9.24 × 10⁸	4.70 × 10⁻¹³	1.69 × 10⁻¹⁴	(5.69 ± 0.90)
299	4.60 × 10¹⁴	5.97 × 10¹⁰	4.60 × 10¹⁴	1.19 × 10⁹	4.28 × 10⁻¹³	8.53 × 10⁻¹⁵	(4.22 ± 0.71)
358	2.71 × 10¹⁴	1.39 × 10¹¹	2.71 × 10¹⁴	1.34 × 10⁹	4.14 × 10⁻¹³	3.99 × 10⁻¹⁵	(3.12 ± 0.09)
380	2.34 × 10¹⁴	1.78 × 10¹¹	2.34 × 10¹⁴	1.34 × 10⁹	4.16 × 10⁻¹³	3.13 × 10⁻¹⁵	(3.30 ± 0.34)
429	1.79 × 10¹⁴	2.85 × 10¹¹	1.79 × 10¹⁴	1.31 × 10⁹	4.33 × 10⁻¹³	1.99 × 10⁻¹⁵	(2.51 ± 0.23)

TST: transition state theory; RRKM: Rice–Ramsperger–Kassel–Marcus theory.

Effective rate constants for the reaction pathways 1−4 have been computed on the assumption of a two-step mechanism, involving first a fast and reversible preequilibrium between the reactants (R−SH and OH^• radicals) and a prereactive complex [R−SH···OH]^• (IM_z with z = 1−4), followed by an irreversible dissociation step leading to the products

\begin{matrix} Step 1 : R - SH + O H^{•} ⇌_{k_{IM z} \to R}^{k_{R} \to {IM}_{z}} {[R - SH . . . OH]}^{•} \\ Step 2 : {[R - SH . . . OH]}^{•} \overset{k_{IM z \to P z}}{\to} {[R - SH - OH]}^{•} \end{matrix}

A steady-state analysis of the above sequence of reactions leads to the following easily tractable expressions for the effective rate constants characterizing the studied reaction pathways:

k_{eff} (1) = \frac{k_{R 1 \to IM 1} k_{IM 1 \to P 1}}{k_{IM 1 \to R 1} + k_{IM 1 \to P 1}} \approx {K_{c}}_{(R 1 ⇌ IM 1)} k_{IM 1 \to P 1} = (RT) {K_{p}}_{(R 1 ⇌ IM 1)} k_{IM 1 \to P 1}

(7)

k_{eff} (2) = \frac{k_{R 2 \to IM 2} k_{IM 2 \to P 2}}{k_{IM 2 \to R 2} + k_{IM 2 \to P 2}} \approx {K_{c}}_{(R 2 ⇌ IM 2)} k_{IM 2 \to P 2} = (RT) {K_{p}}_{(R 2 ⇌ IM 2)} k_{IM 2 \to P 2}

(8)

k_{eff} (3) = \frac{k_{R 3 \to IM 3} k_{IM 3 \to P 3}}{k_{IM 3 \to R 3} + k_{IM 3 \to P 3}} \approx {K_{c}}_{(R 3 ⇌ IM 3)} k_{IM 3 \to P 3} = (RT) {K_{p}}_{(R 3 ⇌ IM 3)} k_{IM 3 \to P 3}

(9)

k_{eff} (4) = \frac{k_{R 4 \to IM 4} k_{IM 4 \to P 4}}{k_{IM 4 \to R 4} + k_{IM 4 \to P 4}} \approx {K_{c}}_{(R 4 ⇌ IM 4)} k_{IM 4 \to P 4} = (RT) {K_{p}}_{(R 4 ⇌ IM 4)} k_{IM 4 \to P 4}

(10)

k _(R→IMz,(z ₌ ₁₋₄₎₎ represent the rate constants characterizing the forward bimolecular reaction steps (in cm³ molecule⁻¹ s⁻¹), whereas k_IMz→P and k_IMz→R are the forward and backward unimolecular reaction rate constants (in s⁻¹), respectively.

RRKM estimates for unimolecular (k₂) and effective bimolecular rate constants (k_eff) are listed in Tables 6 −9 (at P = 1 bar) and Tables 10 and 11 (at P = 75 Torr), respectively. These data were obtained from the computed CBS-QB3 energy profiles and B3LYP/6-311G(2d,d,p) microcanonical rovibrational densities of states. In Tables 6 −9, theoretical rate constants can also be compared with available experimental data.^2,5 These rate constants are the results of TST and RRKM calculations performed on the CBS-QB3 energy barriers and densities of states. Further RRKM data obtained at lower and higher pressures are given at the same temperatures in Table S4a−S4i in the Supplemental Material. The reader is referred further to Table S4a−S4i of the Supplemental Material for a detailed evaluation of the temperature dependence of the equilibrium constants (K_p) characterizing the first reversible reaction step.

Table 10.

Rate constants (units: unimolecular reactions in s⁻¹; bimolecular reactions in cm³ molecule⁻¹ s⁻¹) for the H-abstraction of methanethiol (pathway 1) and ethanethiol (pathway 2). These data were obtained at P = 75 Torr using RRKM theory with the CBS-QB3 energy profiles.

T(K)	Rate constant				Effective rate constant
	(Pathway 1)		(Pathway 2)		Effective rate constant
	IM1→ R1+OH^·k₋₁ (s⁻¹)	IM1→ P1k₂ (s⁻¹)	IM2→R2+OH^·k₋₁ (s⁻¹)	IM2 → P2k₂ (s⁻¹)	R1+OH^·→ P1k_eff (1)	R2+OH^·→ P2k_eff (2)
252			1.55 × 10¹⁵	1.07 × 10⁸		1.14 × 10⁻¹⁵
254	2.89 × 10¹⁵	4.91 × 10⁷			2.50 × 10⁻¹⁶
278			1.00 × 10¹⁵	1.18 × 10⁸		7.35 × 10⁻¹⁶
298	1.34 × 10¹⁵	6.84 × 10⁷	7.60 × 10¹⁴	1.23 × 10⁸	1.74 × 10⁻¹⁶	5.46 × 10⁻¹⁶
322	9.67 × 10¹⁴	7.66 × 10⁷			1.48 × 10⁻¹⁶
343			4.65 × 10¹⁴	1.28 × 10⁸		3.13 × 10⁻¹⁶
375	5.58 × 10¹⁴	8.86 × 10⁷			1.07 × 10⁻¹⁶
397			3.05 × 10¹⁴	1.27 × 10⁸		1.89 × 10⁻¹⁶
403	4.46 × 10¹⁴	9.20 × 10⁷			9.34 × 10⁻¹⁷
425			2.58 × 10¹⁴	1.22 × 10⁸		1.49 × 10⁻¹⁶
430	3.71 × 10¹⁴	9.38 × 10⁷			8.24 × 10⁻¹⁷

Table 11.

Rate constants (units: unimolecular reactions in s⁻¹; bimolecular reactions in cm³ molecule⁻¹ s⁻¹) for the H-abstraction of n-propanethiol (pathway 3) and isopropanethiol (pathway 4). These data were obtained at P = 75 Torr using RRKM theory with the CBS-QB3 energy profiles.

T(K)	Rate constant				Effective rate constant
	(Pathway 3)		(Pathway 4)		Effective rate constant
	IM3 → R3+OH^·k₋₁ (s⁻¹)	IM3→ P3k₂ (s⁻¹)	IM4 → R4+OH^·k₋₁ (s⁻¹)	IM4 → P4k₂ (s⁻¹)	R3+OH^·→ P3k_eff (3)	R4+OH^·→ P4k_eff (4)
256			8.10 × 10¹⁴	1.04 × 10⁸		1.90 × 10⁻¹⁵
257	8.23 × 10¹⁴	1.54 × 10⁸			3.01 × 10⁻¹⁵
298	4.77 × 10¹⁴	1.59 × 10⁸			1.74 × 10⁻¹⁵
299			4.60 × 10¹⁴	1.28 × 10⁸		9.15 × 10⁻¹⁶
353	2.87 × 10¹⁴	1.54 × 10⁸			1.22 × 10⁻¹⁵
358			2.71 × 10¹⁴	1.38 × 10⁸		4.12 × 10⁻¹⁶
380			2.34 × 10¹⁴	1.38 × 10⁸		3.22 × 10⁻¹⁶
419	1.91 × 10¹⁴	1.40 × 10⁸			5.82 × 10⁻¹⁶
429			1.79 × 10¹⁴	1.33 × 10⁸		2.02 × 10⁻¹⁶

In line with the computed energy profiles and kinetic rate constants, the formation of P3 (H₂O+n-C₃H₇ S^•) via pathway 3 clearly predominates over the formation of the other products at room temperature. The supplied RRKM data (see Table S4a−S4i of the Supplemental Material) indicate that at temperatures ranging from 252 to 430 K, the production of the products P3 will dominate the overall reaction mechanism down to extremely low pressures, higher than 10⁻⁸ bar.

Arrhenius plots (Figure 4) of the effective rate constants, which were obtained using RRKM theory for reactions 1–4 at the experimental pressure P = 75 Torr (Tables 10 and 11), clearly confirm that the formation of the products P3 will be the most efficient process at upper atmospheric pressure and at the studied temperatures. The same observation can be made for pressures ranging from 10⁻⁸ to 10⁸ bar (Table S4a−S4i in the Supplemental Material). In line with the experimental data,^2,5 regardless of the pressure, the RRKM effective rate constants of pathways 1−4 decrease gradually with increasing temperatures. The same observation holds for pressures ranging from 10⁻⁸ to 10⁸ bar (Table S4a−S4i in the Supplemental Material).

Figure 4.

Arrhenius plots of the obtained RRKM bimolecular rate constants using the CBS-QB3 approach (P = 75 Torr).

As is to be expected, because of the negative energy barriers involved at the experimental pressure of 75 Torr,^2,5 RRKM effective rate constants obtained from the CBS-QB3 energy for the fastest reaction pathway (R3+OH^•→ P3) overestimate the experiments, which at the investigated temperatures (252−430 K) correspond to errors of the order of 0.04–1.16 kcal mol⁻¹ on the computed activation energies. In view of the known performances of the CBS-QB3 approach, this semiquantitative agreement between theory and experiment is quite satisfactory, considering that hindered rotations of the OH group and anharmonic effects in the intermediates and TSs have been neglected. Furthermore, it appears quite clearly that pressures higher than ∼10⁴ bar are required for ensuring a saturation of the computed bimolecular rate constants compared with the high-pressure limit (TST) of the RRKM bimolecular rate constants (see Figure 5). Consequently, the comparison with the RRKM data nevertheless indicates that the TST approximation breaks down at pressures higher than 10⁴ bar for the kinetic rate constant characterizing pathway 3 (k(3)). With reaction enthalpies and Gibbs free reaction energies below −31.3 and −31.8 kcal mol⁻¹, respectively, the second unimolecular reaction steps in pathways 1–4 are highly exothermic and exoergic, and, therefore, most clearly irreversible.

Figure 5.

Pressure dependence of kinetic rate constants for R_i→P_i (i = 1−4) reaction pathways at different temperatures; results obtained with CBS-QB3 quantum chemical data.

The pressure dependence of the computed RRKM rate constants is depicted at 254, 322, and 397 K in Figure 5. Upon inspecting this figure, it is immediately apparent that rather high pressures (> ∼10⁴ bar) are enough to ensure a saturation of the RRKM rate constants, in comparison with the high-pressure limit. This observation is most obviously the consequence of negative activation energies, which makes standard TST invalid at atmospheric pressure (1 bar). Pressure effects need therefore to be taken into account on RRKM grounds for consistent insights (Tables 10 and 11) into the experimental rate constants,^2,5 which were obtained at a pressure of 75 Torr. Compared with the high-pressure limit, the pressure effects result, indeed, in this case in a most significant decrease of the computed rate constants, by approximately four orders of magnitude. These differences are due to the applied tunneling corrections.

Conclusion

The oxidation mechanisms of alkyl-substituted aliphatic thiols initiated by hydroxyl radicals in the gas phase have been studied for the first time on computational grounds using DFT along with various exchange–correlation functionals (ωB97XD and M06-2x) and the aug-cc-pVTZ basis set. The obtained reaction energies and activation barriers incorporate zero-point vibrational energy differences and counterpoise corrections for basis set superposition errors. Comparison has been made with benchmark computational results obtained at the composite CBS-QB3 level of theory. The best agreement with the computed energy barriers is obtained with the M06-2x exchange–correlation functional. Kinetic rate constants for unimolecular and bimolecular reaction steps were estimated by means of TST and statistical RRKM theory.

These first reaction steps for OH addition in pathways 1−4 are exoergic (ΔG < 0) at ambient temperature and pressure. In line with experiment, due to the formation of a prereactive van der Waals molecular complex [R−SH…OH]^•, the energies of the corresponding TSs lie below those of the reactants, with effective negative activation energies around −0.65, −1.71, −2.13, and −1.42 kcal mol⁻¹ for pathways 1−4, respectively.

Effective rate constants have been calculated according to a steady-state analysis of a two-step model reaction mechanism, assuming reversibility of the first bimolecular addition reaction step, and irreversibility of the second unimolecular dissociation step. In line with the experimental observations,^2,5 results indicate that the kinetically most efficient process at temperatures ranging from 252 to 430 K corresponds to OH addition onto n-propanethiol (3). These results show that the reaction rate decreases with increasing temperatures and decreasing pressures.

In line with negative activation energies,⁹¹ it was found that the standard TST approximation breaks down at ambient pressure (1 bar) for the first bimolecular reaction steps. RRKM calculations show in particular that overwhelmingly high pressures, higher than 10⁴ bar, are required for restoring of this approximation for all reaction channels involved in the oxidation of the studied pathways, in particular for the conversion of the prereactive van der Waals complex [R−SH^…OH]^• into the molecular energized adduct [R−SH-OH]^•.

A comparison with TST results seems to validate RRKM theory for all studied reaction pathways. The RRKM theory appears to be sufficient for achieving semiquantitative insights into the experimentally kinetic rate constants, with discrepancies in the range of three to four orders of magnitude between theory and experiment.

Note that the oxidation reaction mechanisms of the alkyl-substituted aliphatic thiols involved in the so-called OH addition pathways (the OH radical attacks the sulfur atom) were the subject of the separate theoretical study using a similar DFT and CBS-QB3 quantum chemical approach that has been published.⁹²

Supplemental Material

Electronic_Supplementary_Information – Supplemental material for Oxidation reaction mechanism and kinetics between OH radicals and alkyl-substituted aliphatic thiols: H-abstraction pathways

Supplemental material, Electronic_Supplementary_Information for Oxidation reaction mechanism and kinetics between OH radicals and alkyl-substituted aliphatic thiols: H-abstraction pathways by Arezoo Tahan and Abolfazl Shiroudi in Progress in Reaction Kinetics and Mechanism

Footnotes

Acknowledgements

This article has been derived from the research project entitled “Theoretical study on mechanisms and kinetics of the gas phase reactions of the hydroxyl radicals with aliphatic thiols containing short chain alkyl groups (1 to 3 carbon atoms).” The authors thank the anonymous referees for their highly relevant comments.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was financially supported by the Semnan Branch, Islamic Azad University, through Grant No. 17752.

Supplemental material

The Supplemental Material (Tables S1–S4) for this article can be found in the online version. Table S1: Temperature dependence of the equilibrium constants for the first bimolecular reaction step [R_i+_OH^•.→IM_i; i = 1–4] along the pathways 1–4 at different temperatures; Table S2: Wigner tunneling factor for the final unimolecular dissociation reaction step at temperatures ranging from 252 to 430 K; Table S3: Expectation value of the <S²> operator at the reported theoretical levels; Table S4: Kinetic rate constants for all reaction steps involved in the reaction pathways 1–4 at different pressures and temperatures, using the RRKM theory, according to the computed CBS-QB3 energy profiles.

References

Graedel

. Geophys Res Lett 1979; 6: 329.

Wine

Thompson

Semmes

. Int J Chem Kinet 1984; 16: 1623.

Cullis

Hirscher

. Atmos Environ (1967–1989) 1980; 14: 1263.

Granat

Rodhe

Hallberg

. In: Svensson

Soderlund

(eds) Nitrogen, phosphorous, and sulfur-global cycles. (SCOPE Report 7). Stockholm: Swedish Natural Science Research Council, 1976, pp. 89–134.

Atkinson

Perry

Pitts

Jr.

J Chem Phys 1977; 66: 1578.

Calvert

Bottenheim

Strausz

. Atmos Environ. (1967–1989) 1978; 12: 197.

Kurylo

. Chem Phys Lett 1978; 58: 238.

Sze

MKW

. Nature 1979; 280: 308.

Levy

. Planet Space Sci 1973; 21: 575.

10.

Levy

. Adv Photochem. 1974; 9: 369.

11.

McElroy

Wofsy

Penner

, et al. J Atmos Sci 1974; 31: 287.

12.

Nicolet

. Can J Chem 1974; 52: 1381.

13.

Wofsy

McElroy

. Can J Chem 1974; 52: 1582.

14.

Wofsy

. Annu Rev Earth Planet Sci 1976; 4: 441.

15.

Wine

Kreutter

Gump

, et al. J Phys Chem 1981; 85: 2660.

16.

Slagle

Baiocchi

Gutman

. 12th international symposium on free radicals, Laguna Beach, CA, 4–9 January 1976.

17.

Slagle

Graham

Gutman

. Int J Chem Kinet 1976; 8: 451.

18.

Atkinson

Pitts

Jr . J Chem Phys 1975; 63: 3591.

19.

Atkinson

Perry

Pitts

Jr . Chem Phys Lett 1976; 38: 607.

20.

Atkinson

Perry

Pitts

Jr . J Chem Phys 1977; 66: 1197.

21.

Wang

Davis

Jr Wu

, et al. Science 1975; 189: 797.

22.

Perner

Ehhalt

Patz

, et al. Geophys Res Lett 1976; 3: 466.

23.

Davis

Heaps

McGee

. Geophys Res Lett 1976; 3: 331.

24.

Calvert

. Environ Sci Technol 1976; 10: 256.

25.

Mac Leod

Poulet

Le Bras

. J Chim Phys Phys: Chim Biol 1983; 80: 287.

26.

Lee

Tang

. J Chem Phys 1983; 78: 6646.

27.

Cox

Sheppard

. Nature 1980; 284: 330.

28.

McMillen

Golden

. Annu Rev Phys Chem 1982; 33: 493.

29.

Benson

. Chem Rev 1978; 78: 23.

30.

Montgomery

Jr Ochterski

Petersson

. J Chem Phys 1994; 101: 5900.

31.

Montgomery

Jr Frisch

Ochterski

, et al. J Chem Phys 1999; 110: 2822.

32.

Ochterski

Petersson

Montgomery

Jr . J Chem Phys 1996; 104: 2598.

33.

Nyden

Petersson

. J Chem Phys 1981; 75: 1843.

34.

Petersson

Bennett

Tensfeldt

, et al. J Chem Phys 1988; 89: 2193.

35.

Petersson

Al-Laham

. J Chem Phys 1991; 94: 6081.

36.

Petersson

Yee

Bennett

. J Chem Phys 1985; 83: 5105.

37.

Montgomery

Jr Frisch

Ochterski

, et al. J Chem Phys 2000; 112: 6532.

38.

Casasnovas

Frau

Ortega-castro

, et al. Int J Quantum Chem 2010; 110: 323.

39.

Hollman

Simmonett

Schaefer

. Phys Chem Chem Phys 2011; 13: 2214.

40.

Shiroudi

Deleuze

. J Phys Chem A 2014; 118: 3625.

41.

Shiroudi

Deleuze

Canneaux

. J Phys Chem A 2014; 118: 4593.

42.

Chai

J-D

Head-Gordon

. Phys Chem Chem Phys 2008; 10: 6615.

43.

Zhao

Truhlar

. Theor Chem Acc 2008; 120: 215.

44.

Dunning

Jr . J Chem Phys 1989; 90: 1007.

45.

Eyring

. J Chem Phys 1935; 3: 107.

46.

Johnston

. Gas phase reaction rate theory. New York: Roland Press, 1966.

47.

Laidler

. Theories of chemical reaction rates. New York: McGraw-Hill, 1969.

48.

Weston

Schwarz

. Chemical kinetics. Englewood Cliffs, NJ: Prentice Hall, 1972.

49.

Rapp

. Statistical mechanics. New York: Holt, Rinehart and Winston, 1972.

50.

Nikitin

. Theory of elementary atomic and molecular processes in gases. Oxford: Clarendon Press, 1974.

51.

Smith

IWM

. Kinetics and dynamics of elementary gas reactions. London: Butterworths, 1980.

52.

Steinfeld

Francisco

Hase

. Chemical kinetics and dynamics. Englewood Cliffs, NJ: Prentice Hall, 1989.

53.

Steinfeld

Francisco

Hase

. Chemical kinetics and dynamics. Englewood Cliffs, NJ: Prentice Hall, 1999.

54.

Eyring

Lin

. Basic chemical kinetics. New York: Wiley, 1980.

55.

Frisch

Trucks

Schlegel

, et al. Gaussian 09, revision B.01. Wallingford, CT: Gaussian, Inc., 2009.

56.

Dennington

IIR

Keith

Millam

, et al. GaussView, version 3.09. Shawnee Mission, KS: Semichem, Inc., 2003.

57.

Parr

Yang

. Density functional theory of atoms and molecules. New York: Oxford University Press, 1989.

58.

Bartlett

Watts

Kucharski

, et al. Chem Phys Lett 1990: 165: 513.

59.

Stanton

. Chem Phys Lett 1997; 281: 130.

60.

Szabo

. and Ostlund NS. Modern quantum chemistry: introduction to advanced electronic structure theory. New York: McGraw-Hill, 1989.

61.

Lee

Yang

Parr

. Phys Rev B: Condens Matter 1988; 37: 785.

62.

Sousa

Silva

Machado

AEH

, et al. Braz J Chem Eng 2013; 30: 83.

63.

McQuarrie

. Statistical mechanics. New York: Harper and Row, 1976.

64.

Herzberg

. Molecular spectra and molecular structure. II. Infrared and Raman spectra of polyatomic molecules. New York: Van Nostrand Reinhold, 1945.

65.

Martin

JML

El-Yazal

François

J-P

. Mol Phys 1995; 86: 1437.

66.

Martin

JML

de Oliveira

. J Chem Phys 1999; 111: 1843.

67.

Gonzalez

Schlegel

. J Chem Phys 1989; 90: 2154.

68.

Gonzalez

Schlegel

. J Phys Chem 1990; 94: 5523.

69.

McIver

Jr . Acc Chem Res 1974; 7: 72.

70.

Fukui

. J Phys Chem 1970; 74: 4161.

71.

Singleton

Cvetanovic

. J Am Chem Soc 1976; 98: 6812.

72.

Alvarez-Idaboy

Diez

Vivier-Bunge

. J Am Chem Soc 2000; 122: 3715.

73.

Gilbert

Smith

. Theory of unimolecular and recombination reactions. Oxford: Blackwell Scientific, 1990.

74.

Wigner

. J Chem Phys 1937; 5: 720.

75.

Wigner

. Z Phys Chem B 1932; 19: 203.

76.

Moore

VJW

Pearson

. Kinetics and mechanism. A study of homogeneous chemical reactions. Chichester: Wiley-Interscience, 1981.

77.

Carstensen

H-H

Dean

Deutschmann

. Proc Combust Inst 2007; 31: 149.

78.

Mourits

Rummens

. Can J Chem 1977; 55: 3007.

79.

Beyer

Swinehart

. Commun ACM 1973; 16: 379.

80.

Stein

Rabinovitch

. J Chem Phys 1973; 58: 2438.

81.

Canneaux

Bohr

Henon

. J Comput Chem 2014; 35: 82.

82.

Johnson

III (ed.). NIST Computational Chemistry Comparison and Benchmark Database, NIST Standard References Database Number 101, section XIII.B.4a: precomputed vibrational scaling factors, http://cccbdb.nist.gov/vibscalejust.asp

83.

Kee

Rupley

Miller

, et al. Chemkin. San Diego, CA: Reaction Design, 2010.

84.

Alvarez-Idaboy

Galano

, et al. J Phys Chem A 2008; 112: 7608.

85.

Zhou

C-W

Mebel

X-Y

. J Phys Chem A 2009; 113: 10667.

86.

Carey

Sundberg

. Advanced organic chemistry part A: structure and mechanisms. Norwell, MA: Springer, 2007.

87.

Anslyn

Dougherty

. Modern physical organic chemistry. Sausalito, CA: University Science, 2006.

88.

McMurry

Organic chemistry. 3rd ed. Pacific Grove, CA: Brooks/Cole, 1994.

89.

Hammond

. J Am Chem Soc 1955; 77: 334.

90.

Rayez

M-T

Rayez

J-C

Sawerysyn

J-P

. J Phys Chem 1994; 98: 11342.

91.

Garrett

Truhlar

. J Phys Chem 1979; 83: 1052.

92.

Tahan

Shiroudi

. Prog React Kinet Mec 2019; 44: 157.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.31 MB