Reaction and activation energy barriers are calculated for the H abstraction reactions (C(6)H(5)SH + X(•) → C(6)H(5)S + XH, X = H, OH and HO(2)) at the BB1K/GTLarge level of theory. The corresponding reactions with H(2)S and CH(3)SH are also investigated using the G3B3 and CBS-QB3 methods in order to demonstrate the accuracy of BB1K functional in finding activation barriers for hydrogen atom transfer reactions. Arrhenius parameters for the title reactions are fitted in the temperature range of 300 K-2000 K. The calculated reaction enthalpies are in good agreement with their corresponding experimental reaction enthalpies. It is found that H abstraction by OH radicals from the thiophenol molecule proceed in a much slower rate in reference to the analogous phenol molecule. [Formula: see text] of thiophenoxy radical is calculated to be 63.3 kcal/mol. Kinetic parameters presented herein should be useful in describing the decomposition rate of thiophenol; i.e., one of the major aromatic sulfur carriers, at high temperatures.

Introduction

Fossil fuels contain organic and inorganic sulfur. For example the sulfur content in coal varies between 0.5% and 11% depending on the location, type and origin of coal [1]. Organic sulfur in oil shale could be as high as 6% [2]. The presence of these compounds in solid or liquid fuels causes the release of large quantities of sulfur dioxide (SO2) during combustion, which contributes to air pollution and is a reason for the formation of acid rain [3]. Therefore, it is necessary to remove these sulfur compounds from oil or solid fossil fuels prior to combustion to avoid sulfur dioxide emission. During the pyrolysis or combustion, significant concentrations of organic sulfur are emitted as thiols; especially alkylthiophenes [4-6]. Thiophenol (C6H5SH) in particular is regularly utilized as a surrogate compound for thio-alcohol structural entities in coal [7,8].

A great deal of recent research has targeted reducing sulfur emission from the various types of fossil fuels; including coal, natural gas and oil shale. For instance, a number of desulphurization techniques are employed for sulfur removal from fuels, including chemical desulphurization [7-10], biological desulphurization [3,11] for solid fossil fuels, and hydrodesulphurization [12] for liquid fuels.

Central to this effort is to understand the main reactions involved in the decompositions of sulfur-containing aromatic compounds; i.e., a major entity of sulfur-bearing compounds in coal and oil shale. However, there is scarcity in experimental or theoretical measurements for reactions involving thiolic compounds in general and thiophenol in particular at temperature relevant to combustion. In particular, reactions of thiophenol with the H/O radical pools are not yet determined, neither experimentally nor theoretically. However, significant amount of experimental data are available for these reactions with hydrogen sulfide (H2S), and to a lesser extent for methyl sulfide (CH3SH) under atmospheric conditions. Particularly, the reaction of H2S with OH radicals has attracted increasing interest due its primary role in explosive and atmospheric chemistry of H2S [13]. Recently, Ellingson and Truhlar [14] studied theoretically the reaction (H2S + OH → HS + H2O) with emphasis on describing the observed unusual temperature dependence at elevated temperatures.

On the same line, the reactions of OH with aliphatic compounds have been studied theoretically with the aim of providing an explanation for a two stepwise mechanism observed experimentally under low temperatures [15]. Interestingly, experimental reaction rate constant for the reaction of the propagating radical HO2 are only available at 298.15 K for H2S and CH3SH [16]. Any attempt to satisfactorily model the low-temperature oxidation mechanism of thiol compounds would be hindered by the lack of accurate rate constant involving HO2.

To this end, we report in this study theoretical derivation of the reaction rate constants of thiophenol with H, OH and HO2 radicals. The corresponding reactions with H2S and CH3SH are also studied to fulfill two aims. Firstly to set a benchmark for the accuracy of our titled reactions with thiophenol and secondly to provide temperature-dependent rate constants for those reactions whose rate constants are only available at normal ambient temperatures. The kinetic parameters presented herein should be instrumental in building a robust kinetic model not only the decomposition of thiophenol but also for the fate of sulfur-containing at temperatures relevant to combustion conditions.

Computational details

All geometrical optimizations, harmonic vibrational frequencies have been calculated using the Gaussian 03 suite of programs [17]. For the system of thiophenol, calculations are carried out using the meta hybrid density functional theory (DFT) of BB1K [18] with the GTLarge basis set [19]. The BB1K functional is found to significantly surpass the accuracy of all hybrid DFT methods including B3LYP in determination of saddle-point geometries and their associated barrier heights [20]. For hydrogen transfer reactions, BB1K method has been proven to show very comparable performance with ab initio methods such as MP2 and the chemistry models methods such as G3B3 [21]. In order to further test the accuracy of the BB1K/GTLarge methodology, reaction and activation energies for the three corresponding reactions in hydrogen sulfide (H2S) and methyl sulfide (CH3SH) systems are also calculated and compared with the corresponding results from the composite methods of G3B3 and CBS-QB3.

The transmission coefficient that accounts for the quantum tunneling corrections is calculated with the one-dimensional Eckart functional [22]. Rate constants are fitted to simple Arrhenius parameters as , where A is the pre-exponential A-factor and E≠ is the calculated energy of activation. Rate constants are calculated using TheRate code [23]. TheRate code is installed online and it is available free of charge at the CSEO resource (http://www.cseo.net).

Results and discussions

Structure and thermochemistry of thiophenol and thiophenoxy

Optimized structure of the planar thiophenol and its derived thiophenoxy radical are depicted in Fig. 1 at the BB1K/GTLarge. The calculated C–S and S–H bond lengths are 1.770 Å and 1.330 Å, i.e., in a fairly close agreement with the corresponding experimental values of 1.775 Å and 1.300 Å; respectively [24]. Our structural geometries for thiophenol and thiophenoxy are almost equivalent to those optimized at the B3LYP/6-311++G(d,p) [25] and CASPT2 [26] levels. The C–S bond in thiophenol is longer than the corresponding bond in thiophenoxy by only 3%. In comparison with the phenoxy/phenol (C6H5O/C6H5OH) system, the corresponding calculated C–O bond is significantly shortened by 9% in phenoxy radical in reference to the phenol molecule. The Mulliken charge at the S atom in thiophenoxy is determined to be −0.378 e in comparison with −0.728 e of located charge on the O atom in phenoxy. This indicates that the thiophenoxy radical exhibit less radical character at the S atom in comparison with the radical character at the O atom of the phenoxy radical.

Fig. 1

Optimized structures of thiophenol (a) and thiophenoxy (b) at the BB1K/GTLarge. Distances are in Å.

Literatures values of the bond enthalpy of dissociation (BDH) of C6H5S–H bond shows significant disparity in the range of 77.5 kcal/mol–85.9 kcal/mol [27]. Herein, BDH of C6H5S–H is reevaluated using isodesmic work reactions as:where X is considered to be one of the sulfur-centered radicals of HS, CH3S. This method is shown to provide accurate BDH values by deploying reference species with well-known enthalpies of formation (errors not greater than ±0.50 kcal/mol) while maintaining the same number of radical species on both sides of the reaction [28]. The reaction (Rx) utilizes the literature experimental enthalpy values () [29] listed in Table 1 and total electronic energies for species and as given in Table 2. The BDH value is calculated as:

Table 1

Literature enthalpies of formation () used in the estimation of BDH of C6H5S-H and the experimental values of ΔE in Table 3. Values are in kcal/mol sourced from Ref. [29].

Species	Δ_fH298o
H	52.1
OH	9.3
H2O	−57.8
HO2	2.9
H2O2	−32.4
H2S	−4.9 ± 0.1
HS	34.2 ± 0.2
CH3SH	−5.4 ± 0.1
CH3S	29.8 ± 0.4
C6H5SH	26.8
C6H5S	58.0 ± 1.1

Table 2

Electronic energies (0 K) with zero point energy (ZPE) corrections in Hartree.

	BB1K/GTLarge	G3B3	CBS-QB3
H	−0.49844	−0.50109	−0.49982
H2	−1.15754	−1.16748	−1.16608
OH	−75.72107	−75.69637	−75.64972
H2O	−76.40079	−76.38373	−76.33748
HO2	−150.88321	−150.82995	−150.74110
H2O2	−151.50890	−151.46671	−151.37774
C6H5SH	−630.35081	−630.10670	−629.53673
C6H5S	−629.72880	−629.46783	−628.89749
CH3SH	−438.69954	−438.50368	−438.15282
CH3S	−438.06880	−437.86753	−437.51622
H2S	−399.43493	−399.23984	−398.93490
HS	−398.79430	−398.59664	−398.29066
TS (H2S + H → HS + H2)	−399.92832	−399.73669	−399.43023
TS (CH3SH + H → CH3S + H2)	−439.19582	−439.00236	−438.64982
TS (C6H5SH + H → C6H5S + H2)	−630.84522
TS (H2S + OH → HS + H2O)	−475.13605	−474.91367	−474.56336
TS (CH3SH + OH → CH3S + H2O)	−514.40594	−514.18009	−513.78405
TS (C6H5SH + OH → C6H5S + H2O)	−706.06061
TS (H2S + HO2 → HS + H2O2)	−550.29244	−550.04316	−549.65049
TS (CH3SH + HO2 → CH3S + H2O2)	−589.56314	−589.31270	−588.87424
TS (C6H5SH + HO2 → C6H5S + H2O2)	−781.21825

The calculated values for and are listed in Table 3 using the two campsite methods of G3B3 and CBS-QB3. These two methods yield a BDH value of 88.0–98.0 kcal/mol. The value calculated herein is significantly higher than any other literature value by at least 2.1 kcal/mol. Accordingly; H expulsion from the thiol group in thiophenol is as endoergic as H expulsion from the hydroxyl group in phenol [28]. Utilizing the values for H atom (52.1 kcal/mol) and the thiophenol (57.96 kcal/mol); in addition to the calculated BDH of C6H5S–H as 88.5 kcal/mol, for thiophenoxy radical is calculated to be 63.3 kcal/mol. This value is higher than the available corresponding experimental [27] value by 3.3 kcal/mol. The difference between the experimental and the calculated for thiophenoxy can be partially attributed to the uncertainty in for reference species (±1.1 kcal/mol)and the small margin errors in the theoretical predictions (±1.0 kcal/mol).

Table 3

Reaction enthalpies () used in the estimation of the S–H bond in thiophenol and the calculated bond enthalpy of dissociation (BDH). All values are in kcal/mol.

Reaction	Δ_rxnH298o		BDH
	G3B3	CBS-QB3	G3B3	CBS-QB3
C6H5SH + HS → C6H5S + H2S	−2.7	−3.1	88.5	88.0
C6H5SH + CH3S → C6H5S + CH3SH	1.7	1.7	89.0	89.0

In the calculations of So(298.15 K) for thiophenol, torsional frequency corresponding to the rotation of H about the C–S bond in thiophenol was treated as a hindered rotor and its thermochemical contribution is replaced by its corresponding rotational barrier, symmetry numbers and moment of inertia. The calculated internal barrier of rotation about the C–S bond is calculated to be 0.67 kcal/mol, in good agreement with the reported experimental value of 0.76 kcal/mol measured by microwave spectroscopy [30]. The calculated So(298.15 K) values for thiophenol and thiophenoxy are 81.13 cal/K mol and 76.76 cal/K mol, respectively in a satisfactorily agreement with the corresponding experimental values, i.e., 80.48 cal/K mol and 76.66 cal/K mol, respectively [31].

Energies and activation barriers for H abstraction by H, OH and HO2 radicals

Formation of complexes of products and reactants is expected in case of the reactions of thiols with OH and HO2 radicals, however, it is very likely that these complexes will reside in a very shallow well depth in reference to the entrance channel. Accordingly, these complexes are expected to be very short-lived species at elevated temperatures. Since these complexes will have a very minor effect on the calculated rate constants at high temperatures, the formation of these complexes is not investigated herein.

Table 4 gives the calculated reaction (ΔE) and activation energies (ΔE≠) calculated for H abstraction from the thiol group in H2S, CH3SH and C6H5SH by H (R1–R3), OH (R4–R6) and HO2 (R7–R9) radicals. Optimized geometries for transition structures at the BB1K/GTLarge level of theory are presented in Fig. 2. As it is shown in Table 4, ΔE≠ values calculated at the BB1K/GTLarge for the systems of H2S and CH3SH are very close to the corresponding values calculated using the two composite methods of G3B3 and CBS-QB3. This finding confirms the accuracy of the BB1K methodology in calculating reaction barriers for hydrogen transfer reactions. The experimental enthalpies of reactions are also calculated based on the () values for reactants and products given in Table 2.

Table 4

Reaction energies (ΔE) and activation energies (ΔE≠) for the abstraction reactions from the three considered molecules. All values are in kcal/mol.

	Reaction	ΔE≠			ΔE
		BB1K	G3B3	CBS	BB1K	G3B3	CBS	Exptl
R1	H2S + H → HS + H2	3.2	2.7	2.8	−11.6	−14.6	−13.8	−13.0
R2	CH3SH + H → CH3S + H2	1.4	1.5	1.8	−17.8	−19.0	−18.6	−16.9
R3	C6H5SH + H → C6H5S + H2	2.5			−23.3	−17.3	−17.0	−21.0
R4	H2S + OH → HS + H2O	12.5	14.1	13.3	−24.5	−27.7	−27.3	−28.0
R5	CH3SH + OH → CH3S + H2O	9.2	12.5	11.6	−30.7	−32.1	−32.1	−31.9
R6	C6H5SH + OH → C6H5S + H2O	7.1			−36.2	−30.4	−30.4	−36.0
R7	H2S + HO2 → HS + H2O2	16.1	16.7	16.0	9.4	11.0	4.8	3.7
R8	CH3SH + HO2 → CH3S + H2O2	12.3	13.1	12.4	3.2	−0.4	0.0	−0.1
R9	C6H5SH + HO2 → C6H5S + H2O2	9.9			−2.3	1.3	1.6	−4.2

Fig. 2

Optimized structures for transition structures at the BB1K/GTLarge. Distances are in Å.

As it is given in Table 4, the three abstraction reactions for thiophenol (R3, R6 and R9) are more thermodynamically and kinetically preferred in reference to the corresponding abstraction reactions of H2S (R1, R4 and R7), and CH3SH (R2, R5, R8). This finding is in accord with the fact that the bond rupture of S–H in thiophenol (83.4 kcal/mol) is less endoergic in comparison with the S–H bond cleavages in H2S (91.0 kcal/mol), and CH3SH (87.3 kcal/mol). In general, calculated ΔE values are in relative consensus with the corresponding experimental reaction enthalpies values. Despite the similar BDH of S–H in thiophenol and O–H in phenol, the calculated ΔE≠ values for the two systems differ substantially. For instance, the calculated ΔE≠ for H abstraction from phenol by H, OH and HO2 radical are reported to be 10.3 kcal/mol, 3.0 kcal/mol and 13.6 kcal/mol; respectively, whereas the three corresponding values for the thiophenol system amount to 2.5 kcal/mol, 7.1 kcal/mol and 9.9 kcal/mol; respectively.

In order to further test the performance of the B3LYP functional in predicting activation barriers, barriers estimated by the B3LYP/CBSB7 method (the level of optimization and frequency calculations in the CBS-QB3 composite method) are compared with the corresponding values obtained by the BB1K/GTLarge level of theory. It is found that the B3LYP/CBSB7 method significantly underestimate reactions barriers in reference to the BB1K/GTLarge method. For instance, the calculated barriers reactions R2, R5 and R8 (H abstraction from the SH group in CH3SH) by the B3LYP/CBSB7 are found to be 0.1 kcal/mol, 1.0 kcal/mol and 7.3 kcal/mol, while the corresponding BB1K/GTLarge values are estimated to be 1.4 kcal/mol, 9.2 kcal/mol and 12.3 kcal/mol; respectively. In the H2S system (R1, R4 and R7), the B3LYP/CBSB7 are calculated to be 0.6 kcal/mol, 2.7 kcal/mol and 10.0 kcal/mol; respectively. These three values are noticeably lower from the corresponding values obtained by the BB1K/GTLarge method; i.e., 3.2 kcal/mol, 12.5 kcal/mol and 16.1 kcal/mol; respectively.

Reaction rate constants

Reaction rate constants are calculated for the nine considered hydrogen atom transfer reactions based on energies and optimized structures at the BB1K/GTLarge with the inclusion for corrections of tunneling as implemented in the “TheRate” code. Simple Arrhenius parameters are given in Table 5. The contributions from compensation for tunneling effects are rather very modest at elevated temperatures. For instance, the one-dimensional Eckart functional are in the range of 2.32–1.37 in the temperature interval of 600–1200 K for the reaction of C6H5SH + HO2 → C6H5S + H2O2.

Table 5

Arrhenius parameters for reactions rate constants.

Reaction	A (molecule/cm3 s)	Ea/R (K)
H2S + H → HS + H2	2.32 × 10−10	1900
CH3SH + H → CH3S + H2	3.40 × 10−9	1800
C6H5SH + H → C6H5S + H2	6.34 × 10−10	1900
H2S + OH → HS + H2O	9.8 × 10−12	4500
CH3SH + OH → CH3S + H2O	1.80 × 10−10	4600
C6H5SH + OH → C6H5S + H2O	4.23 × 10−11	3400
H2S + HO2 → HS + H2O2	5.25 × 10−12	8500
CH3SH + HO2 → CH3S + H2O2	1.51 × 10−11	7200
C6H5SH + HO2 → C6H5S + H2O2	3.78 × 10−12	5800

Fig. 3 gives Arrhenius plots for the calculated rate constants for the abstraction reactions by H atoms for the three considered systems. The good agreement among the calculated and experimental values for H abstraction from H2S [32] and CH3SH by an H atom [33], provide a satisfactory benchmark of accuracy for our calculated rate constants for the reaction C6H5SH + H → C6H5S + H2 (R3). The calculated rate constant for thiophenol is faster than the corresponding experimental rate constant for phenol by about two orders of magnitude at 1000 K.

Fig. 3

Arrhenius plots for H abstraction by H atoms Ref. [32], bRef. [33].

Due to its central role in the atmospheric fate of thiol compounds, several studies focused on the reactions of thiols with OH radicals. Consensus of opinions in the literature point out that all thiols react with the OH radicals with similar reaction rate constants via H abstraction from the thiol group. For instance, Tyndall and Ravishankara [34] show that the CH3S radical is the sole initial product from the reaction CH3SH + OH via the use of via laser-induced fluorescence. Cruz-Torres and Galano [15] provided mechanistic pathways for the reactions of OH with C1–C3 aliphatic thiols. In an analogy to the reaction of OH with phenol, abstraction of the thiolic H dominates addition at temperatures relevant to combustion. The rate constant expression for the reaction C6H5SH + OH → C6H5S + H2O (R8) represents the first estimate of rate constant for the reaction of OH with aromatic thiols. Due to the unexpected reaction barrier for this reaction in comparison with other H abstraction by OH radicals, H abstraction of the thiolic H is very slow than the corresponding process of the phenolic H.

Reactions of thiols with HO2 radicals are investigated experimentally for H2S and CH3SH. Through the use of flash photolysis technique, an upper limit for the overall reaction of HO2 radicals with H2S and CH3SH are reported to be 3–4 × 10−15 cm3 molecule−1 s−1 at 298.15 K [16]. The aim was to clarify the efficiency of HO2 as a sink pathway for sulfur-containing compounds in the atmosphere. The rate constants for H abstraction from the thiol group in H2S and CH3SH and C6H5SH at 298.15 K are calculated to be 5.71 × 10−24 cm3 molecule−1 s−1, 5.71 × 10−21 cm3 molecule−1 s−1 and 7.25 × 10−20 cm3 molecule−1 s−1; respectively. The calculated values herein agree with the interpretation of Mellouki and Ravishankara [16] who observed that no apparent reactions between H2S and CH3SH with the HO2 radicals. Arrhenius plots for the reactions of the three thiols are presented in Fig. 4.

Fig. 4

Arrhenius plots for H abstraction by HO2 radicals.

Conclusions

The bond dissociation enthalpy of C6H5S–H are found to be 88.5 kcal/mol; i.e., very close to the C6H5O–H bond (89.0 kcal/mol). Reaction of thiophenol with H and OH radicals are found to be exoergic with modest reactions barriers. Despite the similarity in the calculated BDH of S–H in thiophenol and O–H in phenol, it is found that the reaction of H/O radicals with thiophenol and phenol have different reaction barriers. The reason is attributed to the nature of the phenoxy radical as a very strong oxygen-centered radical while the thiophenoxy is rather a weak sulfur-centered radical. Reactions of H2S, CH3SH and C6H5SH with hydrogen atoms are found to occur in a similar rate coefficients. Reactions with HO2 radicals are found to be rather very slow in accord with the experimental finding with regard to the observation that no reactions occur between H2S and CH3SH with HO2 radicals.