Quantum mechanical studies of the kinetics, mechanisms and thermodynamics of gas-phase thermal decomposition of ethyl dithiocarbonate (xanthate)

Peer review under responsibility of Taibah University.

Abstract

Theoretical studies were carried out to investigate the thermal decomposition of ethyl dithiocarbonates (xanthate) using Hartree–Fock at the HF/321-G* level and the density functional method with Becke 3 Lee Yang pair DFT/(B3LYP), 6-31G*, 6-31G**, 6-31+G*, MP2 and CCSD in the ab initio method of calculation using Spartan 10. Geometric parameters, such as the bond length, bond angles, dihedral angles, heat of formation, atomic charges and vibrational frequencies, were obtained. The data were used to calculate the thermodynamics parameters, change in entropy ΔS, enthalpy change ΔH, free energy G, pre-exponential factor A, rate k at 623 K, and variation of rate k with temperatures from 498–623 K at temperature intervals of 25 K. It was observed that the values obtained are in good agreement with the experimental values for the ab initio methods, and according to Arrhenius theory, the calculated rate k increases with increasing temperature.

Keywords:

• Kinetics
• Ethyl dithiocarbonate
• Semi-empirical
• Ab-initio
• Transition state
• Xanthates

1 Introduction

Pyrolysis of dithiocarbonates (xanthates) and carbonate related compounds are valuable routes to synthesizing alkenes without rearranging the carbon skeleton. Pyrolysis of xanthate precursors was first reported by Chugaev in 1899 in studies on the optical properties of xanthates [1].

Table 2 Selected bond angles in degrees for the pyrolysis of O-ethyl, S-methyl xanthate (dithiocarbonates).

Bond angle (°)	State	DFT/6-31+G*	DFT/6-31G**	HF/3-12G*	DFT/MP2	DFT/CCSD
H1–C2–H3	GS	108.539	108.519	108.672	108.539	108.539
	TS	103.52	104.910	93.940	103.52	103.52
	PROD	–	–	–	–	–
H1–C2–C5	GS	110.868	110.752	109.743	110.868	110.868
	TS	103.980	103.980	99.94	103.980	103.980
	PROD	–	–	–	–	–
C2–C5–C6	GS	111.616	111.616	1110.829	111.616	111.616
	TS	121.046	120.963	122.260	121.046	121.046
	PROD	121.791	121.871	121.896	121.791	121.791
C2–C5–O8	GS	106.951	106.823	105.017	106.951	106.951
	TS	109.830	109.830	110.750	109.830	109.830
	PROD	–	–	–	–	–
C5–O8–C9	GS	123.054	122.770	125.709	123.054	123.054
	TS	119.080	119.080	118.030	119.080	119.080
	PROD	–	–	–	–	–
H6–C5–O8	GS	108.804	109.049	109.530	108.804	108.804
	TS	86.110	86.110	80.530	86.110	86.110
	PROD	–	–	–	–	–
O8–C9=S10	GS	119.933	120.013	120.270	119.933	119.933
	TS	124.530	125.018	124.230	124.530	124.530
	PROD	124.526	124.474	123.611	124.526	124.526
O8–C9–S11	GS	114.453	114.547	114.097	114.453	114.453
	TS	120.221	119.949	122.180	120.221	120.221
	PROD	123.818	123.987	123.468	123.818	123.818
C9–S11–C12	GS	102.198	101.938	103.143	102.198	102.198
	TS	102.913	102.517	99.160	102.913	102.913
	PROD	93.218	98.140	93.937	93.218	93.218
S10=C9–S11	GS	125.613	125.440	125.639	125.613	125.613
	TS	115.219	115.015	113.590	115.219	115.219
	PROD	111.656	111.539	112.921	111.656	111.656

Table 3 Selected dihedral angles in degrees for the pyrolysis of O-ethyl S-methyl xanthate (dithiocarbonate).

Dihedral angle (°)	State	DFT/6-31G*	DFT/6-31G**	HF/3-21G*	DFT/6-31+G*	DFT/MP2	DFT/CCSD
H1–C2–C5–O8	GS	59.918	59.948	59.675	60.063	59.948	59.675
	TS	5.770	6.180	13.050	6.200	6.180	13.050
	PROD	–	–	–	–	–	–
C2–C5–O8–C9	GS	179.026	178.960	−179.957	178.908	178.960	−179.957
	TS	15.600	15.110	13.050	15.880	15.110	13.050
	PROD	–	–	–	–	–	–
H5–O8–C9–S10	GS	179.817	179.827	179.949	179.898	179.827	179.949
	TS	−42.990	−43.140	−101.30	−45.160	−43.140	−101.30
	PROD	–	–	–	–	–	–
C5–O8–C9–S11	GS	−60.226	−0.211	−0.062	−0.136	−0.211	−0.062
	TS	−106.380	135.270	139.460	132.730	135.270	139.460
	PROD	–		–	–		–
H6–C5–O8–C9	GS	−60.226	−60.272	−59.863	−60.392	−60.272	−59.863
	TS	−106.380	−106.920	−101.300	−106.070	−106.920	−101.300
	PROD	–	–	–	–	–	–
H7–C5–O8–C9	GS	58.347	58.262	59.949	58.285	58.262	59.949
	TS	137.700	137.280	139.460	137.86	137.280	139.460
	PROD	–	–	–	–	–	–
O8–C9–S11–C12	GS	−179.899	−179.912	180.000	−179.859	−179.912	180.000
	TS	5.150	5.141	1.600	6.487	5.141	1.600
	PROD	−0.000	−0.000	−0.000	−0.000	−0.000	−0.000
C9–S11–C12–H13	GS	−61.093	−61.078	−60.771	−60.209	−61.078	−60.771
	TS	−122.220	−122.766	−119.51	−125.035	−122.766	−119.51
	PROD	−60.751	−60.781	−60.561	−61.307	−60.781	−60.561
S10=C9–S11–C12	GS	0.056	0.047	−0.011	0.104	0.047	−0.011
	TS	−176.270	−176.294	−177.910	−175.430	−176.294	−177.910
	PROD	180.000	180.000	180.000	180.000	180.000	180.000
H3–C2–C5–O8	GS	−60.485	−60.482	−59.674	−60.535	−60.482	−59.674
	TS	−108.420	−108.190	−88.040	−108.260	−108.190	−88.040
	PROD	–	–	–	–	–	–
O8=C9–S10–H1	GS	–	–	–	–	–	–
	TS	–	–	–	–	–	–
	PROD	−0.000	−0.000	−0.000	−0.000	−0.000	−0.000
H1–S10–C9–S11	GS	–	–	–	–	–	–
	TS	–	–	–	–	–	–
	PROD	180.000	180.000	180.000	180.000	180.000	180.000

The preparation of xanthates was carried out by reacting the corresponding alcohol with a base and carbon disulphide, accompanied by an alkyl iodide (usually methyl iodide) [14]. For pyrolysis to produce alkenes, together with the elimination of by-products (carbonyl sulphide and a thiol), β-hydrogen is required, and when more than one β-hydrogen is present, regioselectivity has to be considered, which limits the Chugaev reaction. Xanthates with no β-hydrogen will undergo thione-to-thiol rearrangements, giving S,S-dialkyl dithiocarbonates. The mechanism of the Chugaev reaction was proposed to involve two possible pathways. The first pathway reacts in a one-step mechanism, yielding an alkene, carbonyl sulphide and thiol. In the second mechanism, a thione group attacking a β-hydrogen yields an alkene and an unstable S-alkyl dithiocarbonate intermediate, which will decompose to carbonyl sulphide and a thiol (Scheme 1).

Scheme 1 Two proposed pathways for the pyrolysis of xanthates.

The first pathway was supported by Huckel et al. [2], while Barton and Cram [3,4] preferred the second mechanism. Experimental studies were also applied to investigate the Chugaev mechanisms. Alexander and Mudrak [5,6] demonstrated the cis-elimination mechanism; Bader and Bourns [7] conducted isotope effect studies for the pyrolysis of trans-2-methyl-1-indanyl xanthate and found solid evidence for the second pathway; further kinetic and thermodynamic studies concluded that the Chugaev reactions were homogenous and unimolecular.

Erickson and Kahn [8] first calculated the activation energies of HSC(S)OEt with MP2 and Hartree–Fock at the 6-31G(d) level. Velez et al. [9] investigated the Ei reaction of EtSC(S)OMe and its substituent effects (such as α-CN, β-CN, trans-stilbene and cis-stilbene) at different theoretical levels (HF, B3LYP, MPW1K, MP2, MP3, MP4, CCSD, CCSD(T)) with different basis sets (6-31G*, 6-31G**, 6-311G**,6-311++G**, cc-pVDZ). Wu et al. [10] investigated the computational study of regioselectivity for the pyrolysis of xanthates.

However, previous studies have focused on various computational methods or different transition states, but no studies have been considered regarding the quantum mechanical studies of the kinetics and thermodynamics of gas phase thermal decomposition of ethyl dithiocarbonates through a procedure devised by Adejoro and Bamkole [11] using a semi-empirical method in Mopac.

2 Computational procedure

2.1 Conformational search

A conformational search was performed on the molecule to locate the structure with the lowest energy. The conformational search was carried out using a molecular mechanics force field (MMFF), which is quite successful at assigning low energy conformers and providing quantitative estimates of conformational energy differences [15]. Using ab initio methods, the geometry of the lowest conformer of the reactant was optimized. Five different conformers were obtained, as shown in Scheme 2.

Scheme 2 Different conformers of O-ethyl, S-methyl xanthates (dithiocarbonates).

In Scheme 3, H₁ is the β-hydrogen atom to be eliminated from the alkyl part and the dihedral is acute negative (−11.35°).

Scheme 3 Reactant, transition and product state.

2.2 Reaction path study

Reaction path calculations were performed on the optimized geometry of ethyl (dithiocarbonates) xanthate using H₁–S₁₀ as the reaction coordinate. The internal coordinate was varied from its initial distance in the stable reactant form to its distance in the product molecule. For instance, for ethyl xanthates, the initial distance between H₁–C₂ is 4.7342 Å. The inter-atomic distance is slowly altered throughout the reaction path, varying from 4.723 (initial distance) to 1.200 Å, its approximate distance in the stable product molecule, over 20 steps. Reports in previous works [16] show that instead of the energy passing smoothly through a maximum, it rose to a very high value and then the geometry suddenly dropped to that of the product with a drop in the heat of formation to a value that was approximately the same as the sum of the expected products (methyl dithiocarbonates) and ethylene, as shown in Scheme 4.

Scheme 4 Reaction path coordinate of O-ethyl, S-methyl xanthates (dithiocarbonates).

2.3 Transition state structure

Transition states correspond to energy maxima. However, the underlying principle is that stable molecules (energy minima) will be interconnected by a smooth pathway passing through a well-defined transition state with the product. Using the guess-transition state in Spartan on the suggested mechanism of the transition state, the structure was optimized and was subjected to two tests to verify that their practical geometry corresponds to a saddle point (transition structure) and that this saddle point corresponds to the reactants and products. It is shown that the Hessian matrix of second energy derivations with respect to the coordinates yields one and only one imaginary IR frequency, which will be in the range of 400–2000 cm⁻¹, and that the normal coordinates corresponding to the imaginary frequency smoothly connect the reactants and products. The intrinsic reaction coordinates (IRC) method was also used, which was obtained by optimizing the molecule subject to a fixed position along the reaction coordinates [12]. The transition state was confirmed using the IRC method. Two IRC calculations were performed. The first calculation, a positive perturbation, evaluated the initial perturbation on the atomic coordinates in the direction of the single negative frequency, while the calculation evaluated a negative perturbation along the same normal coordinates.

2.4 Mechanism of decomposition of alkyl dithiocarbonates (xanthates)

The Chugaev reaction is analogous to the thermal decomposition of carboxylic esters of alcohols and of other related derivatives of alcohols, such as carbamates and carbonates. The mechanism of dithiocarbonate (xanthate) pyrolysis is concerted fragmentation, but products could conceivably arise from β-hydrogen abstraction to either thiol or thione sulphur atoms in mechanisms A and B, respectively, in Scheme 1.

In mechanism (A), the reaction occurs in one step, giving the products of reaction (1); in mechanism (B), the initial products are an alkene and unstable dithiocarbonate derivative that subsequently decompose to carbonyl sulphide and a thiol respectively. Huckel et al. [2] postulated the first mechanism (A); Barton and Cram [3,4] proposed the second mechanism. Experimental evidence showing that a thione, rather than a thiol, sulphur atom attacks the β-hydrogen was obtained by Bader and Bourns, who performed a study of ³⁴C and ¹³C isotope effects in the pyrolysis of trans-2-methyl-1-indanyl xanthate of natural isotopic abundance.

3 Calculation

Thermodynamic calculations were obtained for ethyl xanthate by calculating the ground state, GS; transition state, TS; and product. The mechanically calculated enthalpy and entropy were used, which is not a true representation of the total energy of the molecule, knowing that the major portion of enthalpy in a molecule is contained in its bonds and physical conformation; hence, the sum of the ground state energy (GSE) and mechanically calculated enthalpy are used to arrive at a closer approximation of the energy of the molecule. With the modified version of the heat of reaction, the equation is given as shown below (Spartan guide). The enthalpy of a species is defined as(1) $H_i={\text{GSE}}_i+H_i^{\text{sm}}$(1) where the superscript “sm” is the mechanically calculated enthalpy; substituting this into the initial definition of the heat reaction we have(2) $\Delta H_{\text{Rxn}}=({\text{GSE}}_{\text{product}}+H_{\text{product}}^{\text{sm}})-({\text{GSE}}_{\text{Reactant}}+H_{\text{reactant}}^{\text{sm}})$(2) The enthalpy of reaction was calculated as 623 K.

The activation energy (E_a) was calculated according to the transition state theory for a unimolecular reaction at 623 K.(3) $E_{\text{a}}=\Delta H+RT$(3) The entropy of the reaction was calculated by taking the difference of the product and reactant entropies, that is$\Delta S_{\text{Reaction}}=S_{\text{Product}}-S_{\text{Reactant}}$and$\Delta S_{\text{Activated}}=S_{\text{Transition}}-S_{\text{Reactant}}\text{.}$The Gibbs free energy was calculated using the modified version of the heat of reaction equation knowing that G = H − TS.(4) $\Delta G^{*}=\Delta H^{*}-T\Delta S$(4) Classic transition-state theory (TST) was selected to calculate the rate constant, k(T) for the rate-determining steps, as shown in Eqs. (4)(4) $\Delta G^{*}=\Delta H^{*}-T\Delta S$(4) and (5)(5) $k(T)=\frac{k_{\text{B}}T}{h}{e}^{-\Delta G^{*}(T)/RT}$(5) , which assumes that the transmission coefficient is equal to unity:(5) $k(T)=\frac{k_{\text{B}}T}{h}{e}^{-\Delta G^{*}(T)/RT}$(5) (6) $k(T)=A{\text{exp}}^{(-E_{\text{a}}/RT)}$(6) where k_B, h and R are the Boltzmann constant, Planck’s constant and universal gas constant, respectively, and ΔG*(T) is the standard free energy of activation at the absolute temperature T.

Derived from TST, the activation energy, E_a, and Arrhenius factor, A, could also be obtained from Eqs. (3)(3) $E_{\text{a}}=\Delta H+RT$(3) and (4)(4) $\Delta G^{*}=\Delta H^{*}-T\Delta S$(4) (7) $E_{\text{a}}=\Delta H^{*}(T)+RT$(7) (8) $A=\frac{e{k}_{\text{B}}T}{h}{e}^{-\Delta S^{*}(T)/RT}$(8)

4 Results and discussion

Pyrolysis of ethyl xanthates (dithiocarbonates) gives ethane and methyl dithiocarbonates, CH₃SCOSH, which subsequently decompose to give methyl sulphide and thiol. In the structure (Fig. 1), H₁ is the hydrogen attached to the β-carbon that is hydrogen eliminated from the alkyl group. The bond between C₂ and H₁ is stretched with bond lengths of 1.2970 (AM1) and 1.3390 (PM3) for semi-empirical, and pyrolysis of ethyl xanthates gives methyl dithiocarbonates (CH₃SCOH) and ethylene C₂H₄. The decomposition proceeds through a concerted _{fragmentation} in which the product could conceivably be from β-hydrogen abstraction through a six-membered cyclic transition state that involves S–H bond formation plus C–H and C–O bond breaking, as shown in Fig. 1.

Fig. 1 Reaction path calculation.

In the transition state, there is a stretch between the C₂–H₁ bond with bond lengths of 1.2970 (AM1), 1.3390 (PM3), (HF321G), 1.5860 (DFT/B3LYP/631G*) 1.2490 (DFT/631G**), and 1.1980 (DFT/631+G*), and against bond lengths of 1.1162 (AM1), 1.0979 (PM3), 1.108, 1.0812 (HF/321-G*), 1.0941 (DFT/631G*), 1.0930 (DFT/6-31G**), and 1.0947 (DFT/6-31+G) at the ground state. Table 1 shows that both the semi-empirical and ab initio methods could effectively predict the bond length except for DFT, which has values lower compared with others from the table. Dotted lines show the point at which cleavage occurs, between C₅–O₈, which also has a long stretch in bond length in the transition state for all of the methods, and between C₂–H₁, while a new bond is formed between S₁₀–H₁. At the ground state, the bond length is in the range of 4.7–4.9; in the transition state, the bond length is in the range of 1.0–1.4 compared to a stable product bond length in the range of 1.07–1.09. The bond angles and dihedrals are shown in Tables 2 and 3.

Table 1 Selected bond lengths (Å) for the pyrolysis of O-ethyl, S-methyl xanthate (dithiocarbonate). Δd = (TS − GS).

Bond length (Å)	State	DFT/631G*	DFT/6-31G**	DFT/6-31+G*	HF/3-21G*	DFT/MP2	DFT/CCSD
H1–C2	GS	1.09	1.09	1.09	1.08	1.09	1.09
	TS	1.25	1.20	1.20	1.59	1.24	1.20
	PROD	–	–	–	–	–	–
	Δd	+0.79	+0.10	+0.10	+0.50	+0.15	+0.10
C2–C5	GS	1.52	1.52	1.52	1.52	1.53	1.52
	TS	1.42	1.42	1.42	1.31	1.43	1.42
	PROD	1.33	1.33	1.33	1.32	1.33	1.34
	Δd	−0.10	−0.10	−0.10	−0.21	−0.10	−0.10
C5–O8	GS	1.45	1.45	1.45	1.47	1.46	1.45
	TS	2.10	2.10	2.10	2.42	2.12	2.10
	PROD	–	–	–	–	–	–
	Δd	+0.65	+0.63	+0.64	+0.95	+0.66	+0.64
O8–C9	GS	1.34	1.34	1.33	1.35	1.33	1.33
	TS	1.26	1.26	1.26	1.21	1.26	1.27
	PROD	1.20	1.20	1.21	1.21	1.21	1.21
	Δd	−0.08	−0.08	−0.08	−0.13	−0.07	−0.08
C9=S10	GS	1.65	1.65	1.65	1.63	1.65	1.65
	TS	1.73	1.72	1.72	1.78	1.74	1.72
	PROD	1.79	1.79	1.79	1.76	1.77	1.79
	Δd	+0.08	+0.08	+0.08	+0.15	+0.09	+0.08
C9–S11	GS	1.79	1.79	1.79	1.76	1.77	1.79
	TS	1.80	1.80	1.80	1.76	1.81	1.81
	PROD	1.79	1.79	1.81	1.78	1.77	1.84
	Δd	+0.01	+0.01	+0.01	−0.00	+0.04	+0.01
S10–H1	GS	4.99	5.00	5.00	4.90	5.00	5.00
	TS	1.88	1.88	1.89	1.31	1.87	1.89
	PROD	1.35	1.35	1.34	1.33	1.34	1.34
	Δd	−3.11	−3.12	−3.11	−3.59	−3.13	−3.11

The charges in the transition state TS (Table 4) show that H₁ has the largest charge development, while C₅ has the smallest charge development [17]. Polarization of the C₅–O₈ and C₂–H₁ bond causes an increasing positive charge on carbon atoms C₅ and C₉ and causes the S₁₀ atom to become more negative (Table 4). The greater increase of the negative charge on S₁₀ causes increased polarization of the C₂–H₁ bond and places considerable positive charge on the H₁ atom, such that the positive charge is delocalized over the entire O₈–C₅–C₂ frame in the TS; C₉–C₁₀–H₁ is the electron demand and supply within the GS of ethyl xanthates; the vinyl carbon becomes (S₁₀) quite highly negative, and the β-hydrogen, H₁, becomes quite acidic, so that a fast proton transfer equilibrium takes place. Formation of an intermediate by an attack from the ethyl carbon on the β-hydrogen, H₁, takes place as a fast step followed by the rate-determining step (Table 5).

Table 4 Selected atomic charges (Mulliken). Δq = (TS − GS) for the pyrolysis of O-ethyl-S-methyl xanthate.

Molecule	state	DFT/6-3IG*	DFT/6-3IG**	DFT/6-3I+G*	HF/3-2IG*	DFT/MP2	DFT/CCSD
H1	GS	+0.174	+0.221	+0.221	+0.237	+0.056	+0.221
	TS	+0.140	+0.207	+0.207	+0.168	+0.247	+0.207
	PROD	+0.129	+0.134	+0.134	+0.1669	+0.015	+0.134
	Δq	−0.034	−0.014	−0.014	−0.069	+0.191	−0.014
C1	GS	−0.458	−0.785	−0.785	−0.600	−0.121	−0.785
	TS	−0.480	−0.524	−0.524	−0.429	−0.415	−0.524
	PROD	−0.285	−0.395	−0.395	−0.425	−0.153	−0.395
	Δq	−0.938	+0.261	+0.261	+0.171	−0.294	+0.261
C2	GS	−0.071	−0.031	−0.031	−0.124	+0.026	−0.031
	TS	−0.123	−0.194	−0.194	−0.454	+0.224	−0.194
	PROD	−0.285	−0.395	−0.395	−0.425	−0.153	−0.395
	Δq	−0.011	−0.163	−0.163	−0.328	+0.198	−0.163
O1	GS	−0.387	−0.267	−0.267	−0.664	−0.132	−0.267
	TS	−0.437	−0.498	−0.498	−0.564	−0.346	−0.498
	PROD	+0.389	−0.432	−0.432	−0.561	−0.280	−0.432
	Δq	−0.050	−0.231	−0.281	+0.100	−0.214	−0.281
C3	GS	+0.064	+0.159	−0.100	+0.124	−0.040	−0.100
	TS	+0.082	+0.184	+0.217	+0.172	+0.094	+0.217
	PRD	+0.098	+0.179	+0.167	+0.167	+0.134	+0.167
	Δq	+0.018	+0.025	+0.317	+0.048	+0.054	+0.317
S1	GS	−0.186	−0.216	−0.193	−0.132	−0.160	−0.193
	TS	−0.116	−0.245	−0.369	+0.024	−0.245	−0.369
	PROD	+0.158	+0.167	+0.190	+0.229	+0.038	+0.190
	Δq	+0.07	−0.229	−0.1759	+0.156	−0.085	−0.1759
C4	GS	−0.594	−0.505	−0.810	−0.789	−0.217	−0.810
	TS	−0.618	−0.526	−0.734	−0.779	+0.271	−0.734
	PROD	−0.587	−0.492	−0.718	−0.778	−0.196	−0.718
	Δq	−0.024	−0.021	−0.076	−0.010	−0.054	−0.076

Table 5 Heat of formation for the pyrolysis of O-ethyl, S-methyl xanthate (dithiocarbonates).

	GS (kJ/mol)	TS (kJ/mol	PROD (kJ/mol)
DFT/6-31G*	−2,700,810.370	−2,700,530.990	−2,700,634.640
DFT/6-31G**	−2,700,797.560	−2,700,564.825	−2,700,670.875
DFT/6-31+G*	−2,700,804.320	−2,700,560.625	−2,700,676.125
HF/3-21G*	−2,690,184.325	−2,680,127.321	−2,680,117.094
DFT/MP2	−2,700,797.560	−2,700,564.825	−2,700,670.875
DFT/CCSD	−2,700,797.560	−2,700,564.825	−2,700,670.875

There is an assumption that the interaction and charge transmission of C₂–C₅ is not efficient so that the sizable charge on S₁₀ is not efficiently transmitted to the electron deficient C₉; hence, a double bond slowly forms between C₂–C₅ [17].

The calculated Arrhenius parameters are as shown in Table 6 and are in good agreement with the experimental values, for instance, H calculated for DFT/B3LYP/6-31G* (162.808) DFT/6-31G** (113.720) DFT/6-31+G* (115.281), and HF/3-21G*(157.817) at 623 K compares well with the experimental data. The activation energy E_a, A and rate k as calculated are in good agreement with the experimental data.

Table 6 Arrhenius parameters for O-ethyl S-methyl xanthate (dithiocarbonates).

	ΔS (J/mol/K)	ΔG (kJ/mol)	ΔH (kJ/mol)	Ea (kJ/mol)	A	k (S^−1)
EXPERIMENTAL	−28.000	143.560	161.000	166.200	4.70 × 10^11	1.4 × 10^−2
DFT/6-31G*	−29.842	181.491	162.808	167.988	3.56 × 10^11	2.93 × 10^−3
DFT/6-31G**	−28.480	131.164	113.720	118.897	4.20 × 10^11	4.45 × 10^1
DFT/6-31+G*	−31.013	135.217	115.281	120.457	3.09 × 10^11	2.43 × 10^1
HF/3-21G*	−36.308	177.491	157.817	158.994	1.64 × 10^11	7.61 × 10^−3
DFT/MP2	−30.014	142.217	151.481	160.457	4.09 × 10^11	1.43 × 10^1
CCSD	−29.590	161.164	163.720	164.567	2.90 × 10^11	3.43 × 10^1

As stated by Moyano et al. [13]. Relative variation of the bond index for the transition state for every bond i involved in the reaction in Eq. (9)(9) $\delta B_i=\left(\frac{B_i^{\text{TS}}-B_i^{\text{R}}}{B_i^{\text{P}}-B_i^{\text{R}}}\right)$(9) (9) $\delta B_i=\left(\frac{B_i^{\text{TS}}-B_i^{\text{R}}}{B_i^{\text{P}}-B_i^{\text{R}}}\right)$(9) where the superscripts R, TS and P refer to the reactant, transition state and products, respectively. Additionally, %Ev is the percentage of evolution of the bond order during the calculated mechanism, as obtained from(10) $\%\text{Ev}=100\delta B_i$(10) The calculated values for the percentage of evolution are listed in Table 7 for O-ethyl S-methyl dithiocarbonates. The extent of the breaking of O₈–C₅ is 66%, while the extent of new formation of H₁–S₁₀ bonds is 45%; this implies that breaking of bonds comes before bond formation (Table 8).

Table 7 Variation of rate of reaction (S⁻¹) with temperature (K).

Temp (K)	DFT/6-31G*	DFT/6-31G**	DFT/6-31+G**	HF/3-21G*
373	1.56 × 10^−10	1.23 × 10^−6	4.56 × 10^−7	6.78 × 10^−10
398	2.37 × 10^−9	3.45 × 10^−5	3.56 × 10^−6	4.34 × 10^−9
423	8.11 × 10^−9	4.51 × 10^−4	9.57 × 10^−4	8.23 × 10^−9
448	1.11 × 10^−8	2.99 × 10^−3	6.167 × 10^−3	6.56 × 10^−8
498	9.16 × 10^−7	7.39 × 10^−2	1.46 × 10^−1	2.46 × 10^−7
523	6.24 × 10^−6	2.93 × 10^−1	5.72 × 10^−1	6.00 × 10^−6
548	3.54 × 10^−5	1.034	1.966	1.23 × 10^−5
573	1.74 × 10^−4	3.257	6.130	3.17 × 10^−4
598	7.57 × 10^−4	9.371	17.400	2.15 × 10^−3
623	2.93 × 10^−3	24.30	44.5	3.46 × 10^−2

Table 8 B3LYP/6-31G* calculated Wiberg bond indices, B_i, for the reactants, transition states and products: percentage of evolution through the chemical process of the bond indices at the transition states %Ev, degrees of advancement of the transition states δB_av, and absolute synchronicities Sy for pathway A for the pyrolysis of O-ethyl, S-methyl dithiocarbonates.

Compound	State	C2–C5	C2–H1	H1–S10	S10–C5	C9–O8	O8–C5
O-ethyl S-methyl Xanthate	$B_i^{\text{R}}$	1.026	0.944	0.000	1.663	1.081	0.830
	$B_i^{\text{TS}}$	1.348	0.534	0.422	1.258	1.505	0.279
	$B_i^{\text{P}}$	2.042	0.000	0.928	1.006	1.807	0.000
	δBi	0.317	0.444	0.454	0.616	0.584	0.664
	%Ev	31.7	44.4	45.4	61.6	58.4	66.4
	δBav	0.5132
	A	0.00039
	Sy	0.9912

The average relative bond indices δB_av were also calculated as a measurement of the degree of advancement of the transition state along the reaction path, i.e., the early or advanced nature of the transition state, from equation(11) $\delta B_{av}=\frac{1}{n}\sum \delta B_i$(11) where n is the number of bonds involved in the reaction. For O-ethyl S-methyl dithiocarbonates, the δB_av values were higher than 0.500, indicating a late character for the transition states. These observations were consistent with the energy profile in which all three intermediates were energetically higher than their corresponding reactants and the transition states were closer to the intermediates than the reactants. The synchronous or asynchronous nature of the concerted mechanism was also considered by the synchronicity, Sy, as calculated from Eq. (12)(12) $\text{Sy}=1-A$(12) (12) $\text{Sy}=1-A$(12) where A is the asynchronicity defined from Eq. (13)(13) $A=\frac{1}{2(n-1)}\sum \frac{\left|\delta B_i-\delta B_{\text{av}}\right|}{\delta B_{\text{av}}}$(13) by Moyano et al. [13].(13) $A=\frac{1}{2(n-1)}\sum \frac{\left|\delta B_i-\delta B_{\text{av}}\right|}{\delta B_{\text{av}}}$(13)

The synchronicity values vary from zero to one, indicating completely asynchronous and synchronous, respectively.

5 Conclusion

In conclusion, it is observed that both the ab initio and DFT methods in Spartan could be used effectively to study the kinetics, mechanism and thermodynamic and vibrational spectroscopy of O-ethyl, S-methyl dithiocarbonates. The following conclusions can be drawn from the present study. The ab initio and DFT levels predict that the thermal decomposition of O-ethyl S-methyl dithiocarbonates is a concerted yet asynchronous process.

Notes

Peer review under responsibility of Taibah University.

Appendix A

Supplementary data

Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.jtusci.2016.08.001.

Appendix A

Supplementary data

The following are the supplementary data to this article: