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Abstract

Kinetic rate constants for the oxidation reactions of OH radicals with CH₃SH (1), C₂H₅SH (2), n-C₃H₇SH (3) and iso-C₃H₇SH (4) under inert conditions (Ar) over the temperature range 252−430 K have been studied using the CBS-QB3 composite method. Kinetic rate constants under atmospheric pressure and in the fall-off regime have been estimated using transition state theory (TST) and statistical Rice–Ramsperger–Kassel–Marcus (RRKM) theory. Comparison with experiment confirms that in the OH-addition pathways 1−4 leading to the related products, the first bimolecular reaction step has effective negative activation energies around −2.61 to 3.70 kcal mol⁻¹. Effective rate coefficients have been calculated according to a steady-state analysis of a two-step model reaction mechanism. As a result of the negative activation energies, pressures larger than 10⁴ bar would be required to restore to some extent the validity of this approximation for all the channels. By comparison with experimental data, all our calculations for both the OH-addition and H-abstraction reaction pathways indicate that from a kinetic viewpoint and in line with the computed reaction energy barriers, the most favourable process is the OH-addition pathway to n-C₃H₇SH to yield the [n-C₃H₇SH−OH]^• species, whereas under thermodynamic control of the bimolecular reactions (R−SH+OH^•), the most abundant product derived from the H-abstraction pathway will be the [n-C₃H₇ S^•+H₂O] species.

Keywords

Aliphatic thiols OH radical oxidation processes OH-addition rate constant reaction mechanism TST RRKM

Introduction

The emission of gaseous sulphur compounds into the atmosphere occurs from both natural and anthropogenic processes.¹ Despite their low concentrations, larger organic sulphur compounds may play an important role in tropospheric sulphur chemistry. Kinetic and mechanistic data for the reactions of reduced-sulphur compounds (such as aliphatic thiols, R−SH) with hydroxyl radicals are required to evaluate their residence times and their ultimate fates in the atmosphere.^2–11 Oxidation processes are thought to be the main atmospheric sink of aliphatic thiols (R−SH, R: CH₃, C₂H₅, n-C₃H₇, iso-C₃H₇), which play a dominant role in the troposphere^3,12–20 and their rate constants are, thus, needed in order to understand their involvement in photochemical air pollution. Since there are no reported theoretical data for these reactions, in this work, absolute kinetic rate constants for the reaction of OH radicals with the studied compounds have been determined over the temperature range 252−430 K.

The reaction of hydroxyl radicals with CH₃SH has been studied experimentally by Wine et al.,²¹ Atkinson et al.,² MacLeod et al.²² and Lee and Tang⁴ by the flash photolysis-resonance fluorescence technique, while Cox and Sheppard⁵ used a relative rate technique. They suggested that the kinetic rate constants obtained through this oxidation reaction were pressure-dependent. Atkinson et al.² as well as Wine et al.³ have reported a negative activation energy for the OH+CH₃SH reaction. Wine et al.²¹ concluded that addition to the sulphur atom is the dominant pathway for reactions between OH^• radicals and the studied compounds, which is in agreement with the preceding study by Hatakeyama and Akimoto.²³ The obtained rate constants for compounds 1−4 at 298 K show no significant effect of the alkyl side chain on the kinetics of these reactions. Based on the different experimental studies that have been done about reaction between OH radicals and aliphatic thiols (R−SH), there are three possible reaction pathways as follows:²¹

Hydrogen abstraction from the carbon atom $({CH}_{3} SH + {OH}^{•} \to H_{2} O + {}^{•}C H_{2} SH)$

Hydrogen abstraction from the sulphur atom $(C H_{3} SH + O H^{•} \to H_{2} O + C H_{3} S^{•})$

OH addition to the sulphur atom $(C H_{3} SH + O H^{•} \to {[C H_{3} SH - OH]}^{•})$

The kinetic rate constants obtained for the studied reactions are nearly independent of the nature of the hydrocarbon chain, which clearly indicates at 298 K that hydrogen abstraction from a carbon atom is a negligible reaction channel.²¹ Thus, reactions between R−SH and hydroxyl radicals must proceed through either hydrogen abstraction from the weak S−H bonds or by the formation of [R-SH−OH]^• adducts.^24,25

In line with our preceding article, which has been accepted for publication in this journal,²⁶ we have studied oxidation processes of aliphatic thiols containing short-chain alkyl groups (1−3 carbon atoms) by hydroxyl radicals through OH attack onto the hydrogen bonded to the sulphur atom to yield a water molecule and the related radicals. Based on several previous experiments which were carried out in this regard,^{2–4,5,21–23,27–29} we have studied in the second part of our research the involvement of an OH^•radical attack on the sulphur atom, which dominates under inert (Ar) conditions, leading to the related energized adducts [R-SH−OH]^• followed by hydrogen atom elimination, and the preceding experiment shows that the OH-addition reaction mechanism is believed to dominate. In this regard, Hatakeyama and Akimoto²³ suggested that CH₃ S^• species is produced by thermal decomposition of the [CH₃SH−OH]^• adducts under atmospheric conditions.

The experimental measurements^2,21 of the kinetic rate constants for the reaction between OH radicals and compounds 1−4 reveal negative temperature dependences 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.

To explain the disparity of the kinetic data supplied in Scheme 1, chemical pathways 1−4 have been suggested for the reaction between OH radicals and compounds 1−4 in the gas phase (Figure 1). Under experimental conditions, attack of hydroxyl radicals on the studied aliphatic thiols is initiated by OH addition onto the sulphur atom to give the related energized adduct products.

Scheme 1.

OH-addition pathways of aliphatic thiols by hydroxyl radicals.

Figure 1.

Retained atom labelling for characterizing the structures of intermediates and transition states during the oxidation of the studied thiols by OH radicals.

To gain more quantitative insights into these reaction mechanisms, we calculated reaction energies and energy barriers by the CBS-QB3 composite method.^30–38 The aim of this work was to achieve comprehensive and quantitative theoretical insights of the studied pathways. Furthermore, kinetic rate constants in the high pressure limit were to be determined using transition state theory (TST),^39–45 and their falloff behaviour was to be investigated at lower pressures by means of statistical Rice–Ramsperger–Kassel–Marcus (RRKM) theory^46,47 to unravel the available experimental data at temperatures ranging from 252 to 430 K.

Theory and computational details

All the calculations reported in this study were performed using the Gaussian 09 package of programmes.⁴⁸ The high-level composite method CBS-QB3 has been used in this work. Analysis of vibrational frequencies confirmed that all transition structures have one imaginary frequency. Vibrational frequencies calculated at the CBS-QB3 theoretical level were used for characterization of stationary points as minima and transition states, for zero-point energy (ZPE) corrections. Intrinsic reaction coordinate (IRC) calculations⁴⁹ have been systematically performed at the B3LYP/6-311G(2d,d,p) level of theory to ensure that the computed transition structures connect the desired reactants and products.

The relative energies (the total energy of the reactants was set to zero for reference) of all species which were involved in the oxidation of compounds 1−4 by OH radicals into the related products were computed using the CBS-QB3 approach. In this work, we present the potential energy profile for the OH addition onto the sulphur atom in the studied compounds at the CBS-QB3 level and we calculated rate constants for the studied pathways. The five-step CBS-QB3 series of calculations started with a geometry optimization at the B3LYP/6-311G(2d,d,p) level, followed by a frequency calculation to obtain thermal corrections, zero-point vibrational energy (ZPVE) and entropic information.⁵⁰

In our study, reactions between aliphatic thiols and OH^• radicals were found to be consistent with the following scheme⁵¹ which assumed that this reaction occurs according to a two-step mechanism,⁵² involving first a fast pre-equilibrium between the isolated reactants (R−SH+OH^•) and a pre-reactive complex [R−SH….OH]^• (IM_i), and thence to the related products:

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

where k₁ and k₋₁ are the forward and reverse reactions associated with the first step, whereas k₂ is the rate constant corresponding to the second step. The overall rate constant is given by:

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

(1)

where K_c = k₁/k₋₁ is the equilibrium constant for fast pre-equilibrium between the isolated reactants and the prereactive complex (see Table S1 of the Electronic Supplementary Information (ESI)). In the high-pressure limit (TST), kinetics characterizing the unimolecular dissociation reaction are given by^39–46,53

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 the meaning of all involved parameters was illustrated in a prior paper.²⁶ Kinetic rate coefficients for the studied pathways were calculated over temperature ranges 252−430 K and in the high-pressure limit (1 atm) using TST. The overall rate constant is given by^54,55

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})

(3)

where σ is the reaction-path degeneracy, Q_R−SH, Q_OH and Q_TS_i represent the total molecular partition functions for the isolated reactants and transition state (TS_i), respectively, and κ(T) denotes the Wigner tunnelling correction factor (see Table S2 of the ESI).^56,57

Since the computed energy differences account for ZPVEs, vibrational partition functions were computed using the vibrational ground state as energy reference. TST gives an estimate of the upper-limit for rate constants as a function of temperature and is known to give reliable estimations of rate constants^47,58 in the high pressure limit, especially for cases with significant barrier heights.

The prevailing pressures were measured to be enough in order to reliably calculate kinetic rate constants by means of TST. The fall-off behaviour of canonical kinetic rate constants k(T) from the TST limit (P→∞) towards the low-pressure limit (P→0) was also calculated using RRKM theory.^59–61 The microcanonical kinetics k(E) were evaluated according to unimolecular RRKM theory⁶²

k (E) = \frac{σ N^{†} (E)}{h ρ (E)}

(4)

where ρ(E) is the density of states of the reactants and N^†(E) denotes the total number of states at the transition state.

Kinetic rate coefficients (k) of pathways 1−4 were calculated at the experimental temperatures with the KiSThelP programme⁶³ according to the TST and statistical RRKM theories. All employed Lennard-Jones potential parameters (σ and ε/k_B) of the diluent gas as well as the studied compounds as illustrated in a prior paper (see Table 1).²⁶

Table 1.

Lennard-Jones (LJ) potential parameters.

Species	LJ potential parameters
	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
iso-Propanethiol (4)	5.1	418.1

Results and discussion

Structural characteristics of stationary points

The optimized molecular structures of the intermediate complexes, transition states and products in the reactions between compounds 1−4 and OH radicals along pathways 1−4 are presented in Table 2, according to the atom labels given in Figure 1. The negative barrier heights for OH additions to the isolated reactants can be accounted for by the existence of a pre-reactive complex which is structurally similar to the complex formed⁶⁴ between aliphatic thiol and hydroxyl radicals. According to Alvarez-Idaboy and colleagues,⁶⁵ such a pre-reactive complex is a common feature to reactions between radical species and unsaturated molecules, which finds its origin into long-range coulomb interactions between the reactant molecules.⁶⁶

Table 2.

Structural parameters for all stationary points which are involved in the reaction between the studied aliphatic thiols and OH radicals using the CBS-QB3 approach.

Parameter	B3LYP/6-311G(2d,d,p)
	IM1	IM2	IM3	IM4	TS1	TS2	TS3	TS4	P1	P2	P3	P4
r (H₁−O₂)	0.969	0.969	0.969	0.969	0.978	0.978	0.978	0.977	0.969	0.969	0.969	0.970
r (O₂− S₄)	2.399	2.400	2.402	2.382	3.227	3.228	3.223	3.200	2.398	2.399	2.400	2.383
r (H₃− S₄)	1.340	1.341	1.341	1.342	1.344	1.345	1.345	1.344	1.340	1.341	1.341	1.342
r (S₄− C₅)	1.823	1.835	1.833	1.854	1.834	1.845	1.843	1.863	1.823	1.835	1.833	1.854
θ (H₁−O₂− S₄)	95.4	94.7	94.6	94.9	39.9	39.4	39.0	39.1	95.3	94.6	94.5	95.0
θ (H₃−S₄−O₂)	76.6	77.0	76.5	86.4	75.9	75.3	74.9	100.3	77.0	77.1	76.5	86.7
ϕ (H₁−O₂−S₄− H₃)	150.6	−153.5	−155.1	−123.1	145.9	−147.2	−148.3	−113.5	150.0	−153.3	−155.0	−122.1

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

In line with changes in chemical bond orders, examination of Table 2 and comparison of the structures of the intermediates of pathways 1−4 show that addition of an OH radical to the sulphur atom results in a significant lengthening of the S₄−O₂ bond. For the pathways 1−4, it appears that the related transition states (TS1−TS4) are structurally much closer to the related pre-reactive intermediates than to the corresponding products (energized adducts). The related IMs intermediate complex for pathways 1−4 is located at nearly 4.3−5.4 kcal mol⁻¹ below the total energy of the isolated reactants and is characterized by S₄−O₂ bond lengths equal to ∼2.38 Å (Table 2). Proceeding further along pathways 1−4, the OH addition process via the transition states TS_i requires activation energies of about 1.58−2.36 kcal mol⁻¹ relative to the pre-reactive intermediate IM_i energies (Figure 2). With reaction energies around −4.32 to −5.27 kcal mol⁻¹, the OH attack at the sulphur atom of the studied compounds appears to be an exothermic process.

Figure 2.

Potential energy profile for the OH-addition pathways 1−4 obtained using the CBS-QB3 method.

Most significant differences are found for the O₂− S₄‘bond’ length in the IMs and TSs involved in the studied pathways (Table 2). These pre-reactive intermediates are loosely bound complexes which are held mainly by van der Waals (dispersion) forces. The extreme looseness of this complex and of the associated transition state explains the disparity of the computed bond lengths. Since van der Waals forces are weak, it is very unlikely that improvements of the geometry will strongly affect the activation and reaction energies characterizing this profile.

Prior to ending this discussion of geometric structures and parameters, it is worth noticing that for the HF/6-31+G^* wavefunction which is required for post-self-consistent field energy calculations at the coupled cluster theory along with single, double and perturbative triple electronic excitations/6-31+G^* level of theory in the CBS-QB3 procedure, the < S² > operator may reach values around 0.76 for all of the identified transition states (see Table S3 of the ESI).

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 (IM), transition states (TS) and products (P) along pathways 1−4 relative to the isolated reactants are listed in Table 3. A schematic potential energy diagram of the chemical reaction pathways 1−4 is given in Figure 2. In line with experimental Arrhenius activation energies of nearly −0.67, −0.62, −0.79 and −0.97 kcal mol⁻¹ for reaction pathways 1−4, respectively, all our calculations locate the transition states TS_i on pathway 1−4 at 2.61 to 3.70 kcal mol⁻¹ below the reactants. The CBS-QB3 results show the transition state TS3 on pathway 3 as the lowest transition state and locate it at ∼3.7 kcal mol⁻¹ below the related reactants.

Table 3.

Energy changes along the OH-addition pathways 1−4 at the CBS-QB3 level of theory (all in kcal mol⁻¹) and activation entropies (in kcal mol⁻¹ K⁻¹), and comparison with the results obtained in the H-abstraction pathways 5−8. (P = 1 atm).

MethodSpecies	CBS-QB3
	ΔE_0K	ΔH°_298K	ΔG°_298K	ΔE_0K^†	ΔH°_298K^†	ΔG°_298K^†	literatureΔE_act (kcal mol⁻¹)
R−SH+OH^•	0.000	0.000	0.000
R: methyl, ethyl, n-propyl, iso-propyl
IM1 [CH₃SH….OH]^•	−4.300	−4.892	3.198
IM2 [ C₂H₅SH ….OH]^•	−4.843	−5.412	2.847
IM3 [ n-C₃H₇SH ….OH]^•	−5.274	−5.811	2.571
IM4 [ iso-C₃H₇SH ….OH]^•	−5.406	−5.912	2.559
OH-addition pathway R−SH+OH^•→[R-SH−OH]^•
P1 [CH₃SH−OH]^•	−4.319	−4.910	3.176
P2 [C₂H₅SH−OH]^•	−4.851	−5.421	2.845
P3 [ n-C₃H₇SH−OH]^•	−5.269	−5.806	2.575
P4 [ iso-C₃H₇SH−OH]^•	−5.417	−5.921	2.550
TS1 [CH₃SH−OH]^•				−2.613	−3.257	4.589	(−0.689 ± 0.117)²¹(−0.791 ± 0.301)²(−0.672 ± 0.199)²
TS2 [C₂H₅SH−OH]^•				−3.209	−3.842	4.187	(−0.788 ± 0.167)²¹
TS3 [ n-C₃H₇SH−OH]^•				−3.698	−4.308	3.895	(−0.972 ± 0.195)²¹
TS4 [ iso-C₃H₇SH−OH]^•				−3.042	−3.526	4.262	(−0.767 ± 0.308)²¹
H-abstraction pathway* R−SH+OH^•→ [R-S]^•+ H₂O
P5 [H₂O+CH₃ S^• ]	−32.106	−32.058	−32.594
P6 [H₂O+C₂H₅ S^• ]	−32.373	−32.383	−32.857
P7 [H₂O+n-C₃H₇ S^• ]	−32.853	−32.984	−33.108
P8 [H₂O+iso-C₃H₇ S^• ]	−31.254	−31.825	−31.878
TS5 [TS-CH₃ S^•]				−0.653	−1.408	6.793
TS6 [TS-C₂H₅ S^•]				−1.707	−2.415	5.565
TS7 [TS-n-C₃H₇ S^•]				−2.134	−2.829	5.505
TS8 [TS-iso-C₃H₇ S^•]				−1.418	−2.077	6.231

The values have been obtained at the CBS-QB3 level.²⁶

According to experiment,^2,21 this difference in activation energies for the bimolecular reactions R_i→P_i (i = 1−4) indicates that the formation of product P3 species is kinetically favoured over the formation of the other products (P1, P2, P4). The activation barrier for pathway 3 is, therefore, lower by 1.09, 0.49 and 0.66 kcal mol⁻¹ than the barrier height for chemical pathways 1, 2 and 4, respectively (Table 4). Reaction energies, enthalpies, entropies and Gibbs free energies for the oxidation of compounds 1−4 by OH radicals are supplied in Table 3. In line with the structural characteristics of the transition states discussed previously, the CBS-QB3 results show that all studied pathways are found to be exothermic (ΔH_r < 0) and endoergic (ΔG_r > 0) processes at a pressure of 1 atm and T = 298 K. From the energy profiles supplied in Figure 2, it is clear that the formation of product P4 species will also be thermodynamically fairly favoured, since the reaction is strongly exothermic (ΔH_r = −5.92 kcal mol⁻¹) and endoergic (ΔG_r = 2.55 kcal mol⁻¹).

Table 4.

Rate constants (units: unimolecular reactions in s⁻¹; bimolecular reactions in cm³ molecule⁻¹ s⁻¹) for the reaction of OH radicals with CH₃SH (compound 1). These data were obtained at P = 1 bar using TST and RRKM theories.

T(K)	Rate constant [Pathway 1]				Effective rate constant		k_exp×10¹¹(cm³ molecule⁻¹ s⁻¹)^2,21
	TST		RRKM		TST	RRKM
	IM1 → R1k₋₁ (s⁻¹)	IM1 → P1k₂ (s⁻¹)	IM1 → R1k₋₁ (s⁻¹)	IM1 → P1k₂ (s⁻¹)	R1 → P1k_tot (1)	R1 → P1k_tot (1)
254	2.89×10¹⁵	3.23×10¹²	2.89×10¹⁵	1.63×10⁹	1.27×10⁻¹¹	6.42×10⁻¹⁵	(4.08 ± 0.42)
298	1.34×10¹⁵	4.32×10¹²	1.34×10¹⁵	1.49×10⁹	9.02×10⁻¹²	3.11×10⁻¹⁵	(3.04 ± 0.19)
322	9.67×10¹⁴	4.92×10¹²	9.67×10¹⁴	1.41×10⁹	8.01×10⁻¹²	2.30×10⁻¹⁵	(3.03 ± 0.26)
375	5.58×10¹⁴	6.25×10¹²	5.58×10¹⁴	1.26×10⁹	6.67×10⁻¹²	1.34×10⁻¹⁵	(2.80 ± 0.28)
403	4.46×10¹⁴	6.93×10¹²	4.46×10¹⁴	1.20×10⁹	6.26×10⁻¹²	1.08×10⁻¹⁵	(2.39 ± 0.13)
430	3.71×10¹⁴	7.58×10¹²	3.71×10¹⁴	1.14×10⁹	6.01×10⁻¹²	9.05×10⁻¹⁶	(2.25 ± 0.14)

As can be seen in Table 3, the newly supplied CBS-QB3 data differ sensitively from those reported by Wine et al.²¹ as well as Atkinson et al.² From the data summarized in Table 3, we have characterized in detail the energy barriers associated with the conversion of the pre-reactive intermediate IM_i into the related products (P1−P4). The CBS-QB3 results show that the activation barriers (IMi→TS_i; i = 1−4) encountered along pathways 1−4 amount to nearly 1.69, 1.63, 1.58 and 2.36 kcal mol⁻¹, respectively.

The difference in reaction energies for both oxidation reactions (OH-addition and H-abstraction pathways) indicates that formation of products (P5−P8) related to the H-abstraction pathways 5−8 will be thermodynamically favoured (Table 3). Among the products P5−P8, it is clear that the formation of product P7 species [H₂O+n-C₃H₇S^•] is the most favoured process among all other products, since the pathway 7 [n-propyl+OH^•→ H₂O+n-C₃H₇S^•] is strongly exothermic (ΔH = −32.98 kcal mol⁻¹) and strongly exoergic (ΔG = −33.11 kcal mol⁻¹). With reaction energies around −31.25 to −32.85 kcal mol⁻¹, the H-abstraction pathway 5−8 appears to be the rather strongly exothermic processes, whereas pathways 1−4 related to the OH-addition pathway appear to be exothermic (around −4.91 to −5.92 kcal mol⁻¹), with reaction energies around −4.32 to −5.42 kcal mol⁻¹ at the CBS-QB3 level.

Furthermore, as can be seen in Table 3, the difference in activation energies for both the bimolecular reactions indicates that the formation of products P1−P4 will be kinetically favoured over the formation of the products P5−P8. Consider that the most favourable process is OH addition at the sulphur atom in the studied compounds. Among the reactions 1−4 leading to products P1−P4 related to the OH-addition pathway, the supplied data indicate that from a kinetic viewpoint, the most favourable process is reaction between n-C₃H₇SH and OH^• radicals via the OH-addition pathway yielding the [n-C₃H₇SH−OH]^• species (OH attack at the sulphur atom).

Based on Hammond’s postulate, the location of the transition state structure along the reaction coordinate is given by n_T parameter defined as follows:^67,68

n_{T} = \frac{1}{2 - (Δ G^{o} / Δ G^{†})}

(5)

where n_T represents the degree of similarity between the transition state and the product. If n_T < 0.5, the TS structure is similar to that of the reactants (early TS), and if n_T > 0.5, it is similar to the products (late TS). Based on the CBS-QB3 estimates, for the IMi→Pi (i = 1−4) reaction steps, n_T is found to be equal to 0.496, 0.5, 0.499 and 0.498, respectively, which implies that the TS structures are located almost halfway between the pre-reactive complexes and the products.

Kinetic parameters

TST and RRKM estimates for individual rate constants of the studied compounds were calculated in the gas-phase and at a pressure of 1 bar and over the considered temperatures in line with the original experiments^2,21 which are listed in Tables 4 −7 and compared with experimental data. Furthermore, RRKM data computed at lower and higher pressures are provided for the same temperatures in Table S4(a)−(i) of the ESI. Theoretical values obtained using the TST at a pressure of 1.0 bar do not differ by more than one order of magnitude from the experimental data.

Table 5.

Rate constants (units: unimolecular reactions in s⁻¹; bimolecular reactions in cm³ molecule⁻¹ s⁻¹) for the reaction of OH radicals with C₂H₅SH (compound 2). These data were obtained at P = 1 bar using TST and RRKM theories.

T(K)	Rate constant [Pathway 2]				Effective rate constant		k_exp×10¹¹(cm³ molecule⁻¹ s⁻¹)^2,22
	TST		RRKM		TST	RRKM
	IM2 → R2k₋₁ (s⁻¹)	IM2 → P2k₂ (s⁻¹)	IM2 → R2k₋₁ (s⁻¹)	IM2 → P2k₂ (s⁻¹)	R2 → P2k_tot (2)	R2 → P2k_tot (2)
252	1.55×10¹⁵	3.54×10¹²	1.55×10¹⁵	1.94×10⁹	3.08×10⁻¹¹	1.69×10⁻¹⁴	(6.55 ± 0.51)
278	1.00×10¹⁵	4.21×10¹²	1.00×10¹⁵	1.81×10⁹	2.20×10⁻¹¹	9.47×10⁻¹⁵	(5.15 ± 0.35)
298	7.60×10¹⁴	4.73×10¹²	7.60×10¹⁴	1.72×10⁹	1.79×10⁻¹¹	6.51×10⁻¹⁵	(4.21 ± 0.32)
343	4.65×10¹⁴	5.88×10¹²	4.65×10¹⁴	1.55×10⁹	1.28×10⁻¹¹	3.38×10⁻¹⁵	(4.02 ± 0.14)
397	3.05×10¹⁴	7.24×10¹²	3.05×10¹⁴	1.38×10⁹	9.84×10⁻¹²	1.88×10⁻¹⁵	(3.41 ± 0.31)
425	2.58×10¹⁴	7.92×10¹²	2.58×10¹⁴	1.31×10⁹	8.96×10⁻¹²	1.48×10⁻¹⁵	(3.32 ± 0.27)

Table 6.

Rate constants (units: unimolecular reactions in s⁻¹; bimolecular reactions in cm³ molecule⁻¹ s⁻¹) for the reaction of OH radicals with n-C₃H₇SH (compound 3). These data were obtained at P = 1 bar using TST and RRKM theories.

T(K)	Rate constant [Pathway 3]				Effective rate constant		k_exp×10¹¹(cm³ molecule⁻¹s⁻¹)^2,21
	TST		RRKM		TST	RRKM
	IM3 → R3k₋₁ (s⁻¹)	IM3 → P3k₂ (s⁻¹)	IM3 → R3k₋₁ (s⁻¹)	IM3 → P3k₂ (s⁻¹)	R3 → P3k_tot (3)	R3 → P3k_tot (3)
257	8.23×10¹⁴	1.89×10¹²	8.23×10¹⁴	2.13×10⁹	2.96×10⁻¹¹	3.33×10⁻¹⁴	(6.31 ± 0.20)
298	4.77×10¹⁴	2.39×10¹²	4.77×10¹⁴	1.90×10⁹	2.21×10⁻¹¹	1.76×10⁻¹⁴	(4.56 ± 0.18)(4.18 ± 0.57)(4.55 ± 0.25)
353	2.87×10¹⁴	3.06×10¹²	2.87×10¹⁴	1.65×10⁹	2.15×10⁻¹¹	1.16×10⁻¹⁴	(3.63 ± 0.16)
419	1.91×10¹⁴	3.82×10¹²	1.91×10¹⁴	1.44×10⁹	1.46×10⁻¹¹	5.52×10⁻¹⁵	(2.91 ± 0.09)

Table 7.

Rate constants (units: unimolecular reactions in s⁻¹; bimolecular reactions in cm³molecule⁻¹s⁻¹) for the reaction of OH radicals with iso-C₃H₇SH (compound 4). These data were obtained at P = 1 bar using TST and RRKM theories.

T(K)	Rate constant [Pathway 4]				Effective rate constant		k_exp×10¹¹(cm³molecule⁻¹s⁻¹)^2,21
	TST		RRKM		TST	RRKM
	IM4 → R4k₋₁ (s⁻¹)	IM4 → P4k₂ (s⁻¹)	IM4 → R4k₋₁ (s⁻¹)	IM4 → P4k₂ (s⁻¹)	R4 → P4k_tot (2)	R4 → P4k_tot (2)
256	8.10×10¹⁴	9.47×10¹¹	8.10×10¹⁴	1.91×10⁹	1.48×10⁻¹¹	2.98×10⁻¹⁴	(5.69 ± 0.90)
299	4.60×10¹⁴	1.51×10¹²	4.60×10¹⁴	1.78×10⁹	9.58×10⁻¹²	1.13×10⁻¹⁴	(4.22 ± 0.71)
358	2.71×10¹⁴	2.42×10¹²	2.71×10¹⁴	1.59×10⁹	6.59×10⁻¹²	4.33×10⁻¹⁵	(3.12 ± 0.09)
380	2.34×10¹⁴	2.79×10¹²	2.34×10¹⁴	1.52×10⁹	6.05×10⁻¹²	3.29×10⁻¹⁵	(3.30 ± 0.34)
429	1.79×10¹⁴	3.66×10¹²	1.79×10¹⁴	1.38×10⁹	5.23×10⁻¹²	1.97×10⁻¹⁵	(2.51 ± 0.23)

Effective rate constants for pathways 1−4 have been computed assuming a two-step mechanism, involving first a fast and reversible pre-eq7 between the isolated reactants (R−SH and OH^• radical) and a pre-reactive complex [R−SH…OH]^• (IMz 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 kinetics characterizing the studied chemical pathways:

k_{eff} (i) = \frac{k_{R i \to IM i} k_{IM i \to P i}}{k_{R i \to IM i} + k_{IM i \to P i}} \approx {K_{c}}_{(R i ⇌ IM i)} k_{IM i \to P i} = (RT) {K_{p}}_{(R i ⇌ IM i)} k_{IM i \to P i} i = 1 - 4

(6)

k_[R→IMz,(z ₌ _1−4)] represent the kinetics characterizing the forward bimolecular reaction step (in cm³molecule⁻¹s⁻¹), whereas k_IMz→P and k_IMz→R are the forward and backward unimolecular kinetics (in s⁻¹), respectively. RRKM estimates for unimolecular (k₂) and effective bimolecular kinetics (k_eff) are listed in Tables 4 −7 (at P = 1 bar) and Tables 8 and 9 (at P = 75 Torr). These data were obtained from the computed CBS-QB3 energy profiles and B3LYP/6-311G(2d,d,p) microcanonical rovibrational densities of states. In these tables, theoretical kinetics can also be compared with available experimental data.^2,21

Table 8.

Kinetic and effective rate constants for the OH-addition pathways of compounds 1 and 2. These data were calculated at P = 75 Torr using RRKM theory.

T(K)	Rate constant (s⁻¹)				Effective rate constant(cm³ molecule⁻¹ s⁻¹)
	[Pathway 1]		[Pathway 2]
	IM1 → R1k₋₁	IM1 → P1k₂	IM2 → R2k₋₁	IM2 → P2k₂	R1 → P1k_eff (1)	R2 → P2k_eff (2)
252			1.55×10¹⁵	1.94×10⁸		1.69×10⁻¹⁵[1.14×10⁻¹⁵]
254	2.89×10¹⁵	1.63×10⁸			6.42×10⁻¹⁶[2.50×10⁻¹⁶]
278			1.00×10¹⁵	1.81×10⁸		9.47×10⁻¹⁶[7.35×10⁻¹⁶]
298	1.34×10¹⁵	1.49×10⁸	7.60×10¹⁴	1.72×10⁸	3.11×10⁻¹⁶[1.74×10⁻¹⁶]	6.51×10⁻¹⁶[5.46×10⁻¹⁶]
322	9.67×10¹⁴	1.41×10⁸			2.30×10⁻¹⁶[1.48×10⁻¹⁶]
343			4.65×10¹⁴	1.55×10⁸		3.38×10⁻¹⁶[3.13×10⁻¹⁶]
375	5.58×10¹⁴	1.26×10⁸			1.34×10⁻¹⁶[1.07×10⁻¹⁶]
397			3.05×10¹⁴	1.38×10⁸		1.98×10⁻¹⁶[1.89×10⁻¹⁶]
403	4.46×10¹⁴	1.20×10⁸			1.08×10⁻¹⁶[9.34×10⁻¹⁷]
425			2.58×10¹⁴	1.31×10⁸		1.58×10⁻¹⁶[1.49×10⁻¹⁶]
430	3.71×10¹⁴	1.14×10⁸			9.05×10⁻¹⁷[8.24×10⁻¹⁷]

The values in bracket obtained via H-abstraction pathway at the CBS-QB3 level of theory.²⁶

Table 9.

Kinetic and effective rate constants for the OH-addition pathways of compounds 3 and 4. These data were calculated at the P = 75 Torr using RRKM theory.

T(K)	Rate constant (s⁻¹)				Effective rate constant(cm³ molecule⁻¹ s⁻¹)
	[Pathway 3]		[Pathway 4]
	IM3 → R3k₋₁	IM3 → P3k₂	IM4 → R4k₋₁	IM4 → P4k₂	R3 → P3k_eff (3)	R4 → P4k_eff (4)
256			8.10×10¹⁴	1.91×10⁸		2.98×10⁻¹⁵[1.90×10⁻¹⁵]
257	8.23×10¹⁴	2.14×10⁸			3.35×10⁻¹⁵[3.01×10⁻¹⁵]
298	4.77×10¹⁴	1.90×10⁸			1.86×10⁻¹⁵[1.74×10⁻¹⁵]
299			4.60×10¹⁴	1.79×10⁸		1.14×10⁻¹⁵[9.15×10⁻¹⁶]
353	2.87×10¹⁴	1.65×10⁸			1.26×10⁻¹⁵[1.22×10⁻¹⁵]
358			2.71×10¹⁴	1.59×10⁸		4.33×10⁻¹⁶[4.12×10⁻¹⁶]
380			2.34×10¹⁴	1.52×10⁸		3.29×10⁻¹⁶[3.22×10⁻¹⁶]
419	1.91×10¹⁴	1.44×10⁸			5.52×10⁻¹⁶[5.82×10⁻¹⁶]
429			1.79×10¹⁴	1.38×10⁸		1.97×10⁻¹⁶[2.02×10⁻¹⁶]

The values in bracket obtained via H-abstraction pathway at the CBS-QB3 level of theory.²⁶

Kinetic rate constants are the results of TST and RRKM calculations performed upon 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 S4(a)−(i) of the ESI. The reader is referred further to Table S4(a)−(i) of the ESI for a detailed evaluation of the temperature dependence of the equilibrium constants (K_p) characterizing the first reversible reaction step. In line with the computed energy profiles and rate constants, the formation of the P3 species (via pathway 3) clearly predominates over the formation of the other products at 298 K. The supplied RRKM data (see Table S4(a)−(i) of the ESI) indicate that over the temperatures ranging from 252 to 430 K, the production of the P3 species will dominate the overall reaction mechanism and this down to extremely low pressures, larger than 10⁴ bar.

An Arrhenius plot (Figure 3) of the effective rate constants which were obtained using RRKM theory for the chemical reactions 1−4 at the experimental pressure P = 75 Torr (Tables 8 and 9) clearly confirms that the production of the P3 species will be the most efficient process at upper atmospheric pressure and at the studied temperatures. In line with the experimental data,²¹ whatever the pressure (see also Table S4(a)−(i) of the ESI), the RRKM effective rate constants of the pathways 1−4 decrease gradually with increasing temperatures. The same observation holds for pressures ranging from 10⁻⁸ to 10⁸ bars (Table S4(a)−(i) in the ESI).

Figure 3.

Arrhenius plot of the obtained RRKM bimolecular rate constants for the reactions of OH radicals with the studied aliphatic thiols using the CBS-QB3 approach (P = 75 Torr). Symbols:

As is to be expected, because of the involved negative energy barriers at the experimental pressure of 75 Torr,²¹ RRKM effective rate constants obtained from the CBS-QB3 energy for the fastest reaction pathway (R3→P3) overestimate the experimental ones by ∼4 orders of magnitude at the investigated temperatures. In view of the known performances of the CBS-QB3 approach, this semi-quantitative agreement between theory and experimental is quite satisfactory, considering that hindered rotations of the OH group and anharmonic effects in the intermediate and transition states have been neglected. Furthermore, it appears quite clearly that pressures larger 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 4).

Figure 4.

Plot of the bimolecular rate constants for R_i→P_i (i = 1−4) reaction pathways at a pressure of 75 Torr and the studied temperatures.

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 enthalpy and Gibbs free energy below −5.81 and −2.58 kcal mol⁻¹, respectively, the second unimolecular reaction steps in pathways 1−4 are exothermic and endoergic, and, therefore, clearly irreversible.

The pressure dependence of the computed RRKM rate constants is depicted at 254, 322 and 397 K in Figure 4. From this figure, it is immediately apparent that rather high pressures (>10⁴ bar) are large enough to ensure a saturation of the RRKM rate constants, in comparison with the high-pressure limit (TST). This observation is most obviously the consequence of the 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 8 and 9) into the experimental rate constants,^2,21 which were obtained at a pressure of 75 Torr. Compared with the high pressure limit, the pressure effects result, indeed, in this case into a most significant decrease of the computed rate constants, by ∼4 orders of magnitude.

As a result of the differences in energy barriers between the OH-addition and H-abstraction reaction pathways (Table 3), and also lower barrier height levels for the OH attack onto sulphur atom in the studied compounds 1−4 to the removal of hydrogen atom bonded to the sulphur atom by a OH^• radical, it is clear that rate constants for the OH-addition pathways are higher than that for the H-abstraction pathways under the experimental conditions (Tables 8 and 9).

Conclusion

The reactions between alkyl-substituted aliphatic thiol and hydroxyl radicals in the gas phase have been studied for the first time on computational grounds using at the composite CBS-QB3 level of theory. Kinetic rate constants for unimolecular and bimolecular reaction steps were estimated by means of TST and statistical RRKM theory.

This first reaction steps for OH addition via pathways 1−4 are exergonic (ΔG < 0) at ambient temperature and pressure. In line with experiments^2,21 due to the formation of a pre-reactive van der Waals (vdW) molecular complex [R−SH…OH]^•, the corresponding transition state lies below the isolated reactants; hence, effective negative activation energies around −2.61, −3.21, −3.70 and −3.04 kcal mol⁻¹ in pathways 1−4, respectively, were found.

Effective rate coefficients have been calculated according to a steady state analysis upon 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,^2,21 this indicates that the kinetically most efficient process at temperatures ranging from 252 to 430 K corresponds to OH addition to n-C₃H₇SH. The results show that the kinetic rate constants decrease with increasing temperatures and decreasing pressure.

In line with negative activation energies, it was found that the standard transition-state-approximation breaks down at ambient pressure (1 bar) for the first bimolecular reaction steps. RRKM calculations show in particular that overwhelmingly high pressures, larger 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 pre-reactive vdW 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 pathways. RRKM theory appears to be sufficient for achieving semi-quantitative insights into the experimentally kinetic rate constants, with discrepancies in about ∼4 orders of magnitude between theory and experiment.

The supplied data indicate that, from a kinetic viewpoint, the most favourable process is reaction between n-C₃H₇SH and hydroxyl radicals through OH-addition pathway into the [n-C₃H₇SH−OH]^• species, whereas under thermodynamic control of the bimolecular reactions (OH-addition and H-abstraction), the most abundant product derived from the oxidation of n-C₃H₇SH by hydroxyl radical via H-abstraction pathway will be the P7 [H₂O+n-C₃H₇S^•] species.

Supplemental Material

PRK1800760_Supp_ – Supplemental material for Oxidation reaction mechanism and kinetics between OH radicals and alkyl-substituted aliphatic thiols: OH-addition pathways

Supplemental material, PRK1800760_Supp_ for Oxidation reaction mechanism and kinetics between OH radicals and alkyl-substituted aliphatic thiols: OH-addition pathways by Arezoo Tahan and Abolfazl Shiroudi in Progress in Reaction Kinetics and Mechanism

Footnotes

Acknowledgements

This paper 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 would like to thank Prof. M.S. Deleuze for helpful discussions during the course of this investigation.

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) received 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

Supplemental material for this article is available online.

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