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. 2021 Jul 28;6(31):20471–20482. doi: 10.1021/acsomega.1c02155

Theoretical Study on the Unimolecular Pyrolysis of Thiophene and Modeling

Tianshuang Li †,‡, Hongliang Zhang †,‡, Yun Li †,*, Jie Li †,‡,*, Jingkun Wang §, Jin Xiao †,‡
PMCID: PMC8359137  PMID: 34395994

Abstract

graphic file with name ao1c02155_0013.jpg

Thiophenic sulfur is the most stable and abundant organic sulfur species in petroleum. Removal of thiophenes has profound significance in environmental protection. In this work, we investigate the unimolecular pyrolysis of thiophene from a kinetic perspective. High-level ab initio methods have been employed to deduce the potential energy surface. Rate coefficients of the elementary reactions are computed using variational transition-state theory at the CCSD(T)/CBS level to develop a kinetic model. By comparison with preceding experimental results, the kinetic model shows good performance in calculating the thiophene pyrolysis rate. The Arrhenius expression for thiophene unimolecular pyrolysis has been redetermined as k = 1.21 × 1013 × exp[(78.96 kcal/mol)/(RT)]. The unimolecular pyrolysis of thiophene is mainly initiated by the ring-H migrations, whereas the C–S bond rupture has limited contribution to the overall pyrolysis rate. Thioketene (SC2H2) and ethyne (C2H2) are the major pyrolysis products at all temperatures. Significant amounts of the thioformyl (HCS) radical and CS could also be yielded. By contrast, atomic sulfur and H2S are difficult to be directly produced. Possible secondary reactions in the products have also been discussed.

1. Introduction

Petroleum is the largest source of global energy consumption, supplying more than 33.1% of total world energy consumption.1 Predicted by BP p.l.c., petroleum will continue to take an important part in the global energy system for decades to come.1

Sulfur is an element commonly found in crude oil and petroleum products. In petroleum refining, sulfur is an undesirable impurity that could cause the deactivation of the catalysts and corrosion problems in pipelines and pumping and refining equipment.2,3 Moreover, combustion of sulfur in fuels leads to the emission of sulfur oxides (SOx), which are the important contributors to acid rain that can damage plants, crops, and structural surfaces.4,5 In addition, the toxic SOx released into air can interact with ozone, other gases, and particulates to form airborne sulfonated smog particles that are hazardous to human health.6 Consequently, tighter regulations to minimize the negative effects have been legislated worldwide.7−11

Several processes have been recommended for the removal of sulfur from fuel.12−18 The most common technique to remove sulfur from crude oil in the petroleum industry is hydrodesulfurization (HDS). However, HDS is less effective in treating thiophenes19−21 that are present at significant levels in most petroleum,22−26 especially alkyl dibenzothiophenes.19 Studies have shown that thiophenes have high thermal stability at even high temperatures and pressures.27,28 Hence, the knowledge on the pyrolysis mechanism of thiophenes is of significance in promoting desulfurization.

As the simplest thiophene sulfur, thiophene (C4H4S) is worthy of a detailed investigation as it could be a representative for all thiophenes. In 1959, Wynberg and Bantjes29 studied thiophene cracking in a continuous flow reactor and identified dithiophenes, carbon disulfide, free carbon, hydrogen sulfide, and hydrocarbons in the pyrolysis products. Later, Cullis and Norris30 performed thiophene pyrolysis under carbon formation conditions and commented that hydrogen sulfide was one of the major products. In 2002, Winkler et al.31 studied thiophene pyrolysis using a quartz continuous flow reactor. In addition to methane, benzene, and hydrogen sulfide, a large number of secondary condensation products were identified as the pyrolysis products of thiophene. Memon et al.32 performed thiophene thermolysis (1598–2022 K) in a shock tube. At all temperatures, acetylene was found to be the dominant product; ethene, ethanethiol, hydrogen sulfide, carbon disulfide, and several oligomers were also detected. Hore and Russell33 investigated the laser pyrolysis of thiophene and declared that acetylene was the major gas-phase product. More recent contribution was made by Vasiliou et al.,34 who carried out a thiophene decomposition experiment using a microtublar reactor and identified five groups of products. Quantum calculation methods35−37 have also been applied to study the unimolecular pyrolysis mechanism of thiophene.

Most studies on thiophene pyrolysis have been focused on identifying decomposition products. As the secondary reactions between products cannot be excluded, the primary products inevitably change in different studies. By contrast, the pyrolysis rate of thiophene is less affected by the secondary reactions. So far, only two studies34,53 involving the kinetics of thiophene pyrolysis have been reported. No kinetic model of thiophene unimolecular pyrolysis has been reported yet. Hence, the objective of this study is to investigate the unimolecular pyrolysis of thiophene and therefore develop a kinetic model. In this work, high-level ab initio methods were first used to investigate the pyrolysis reactions. Following this, rate coefficients of important elementary reactions were deduced using variational transition-state theory (VTST) at the CCSD(T)/CBS level. Based on the kinetic results, a kinetic model for the unimolecular pyrolysis of thiophene was developed.

2. Results and Discussion

2.1. Major Mechanism

The major mechanism of thiophene unimolecular pyrolysis is concluded based on our preceding studies.45−48 All possible initiations, including H shifts, ring bond ruptures, isomerization (non-H-migration), and C–H fission, have been considered in this work.

2.1.1. Channel 1—Decomposition via α-Carbene

Figure 1 presents the reaction details of this channel.

Figure 1.

Figure 1

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Potential energy surface of Channel 1. The values in parentheses are Gibbs energies at 1500 K, 1 atm (unit: kcal/mol).

Thiophene converts to α-carbene via a 2,3-H shift and subsequently cracks to SC2H2 + C2H2 (thioketene + ethylene, P1) via concerted C5–S1 and C3–C4 cleavage. Song and Parish37 reported that the potential energy of TS2 is 41.06 kcal/mol above α-carbene at the CBS-QB3 level. Our CCSD(T)/CBS calculation indicates that this value is 43.80 kcal/mol. This reaction channel could be represented by eqs 1 and 2

2.1.1. 1
2.1.1. 2

2.1.2. Channel 2—Decomposition via Buta-2,3-dienethial

The potential energy surface is presented in Figure 2.

Figure 2.

Figure 2

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Potential energy surface of Channel 2. The values in parentheses are Gibbs energies at 1500 K, 1 atm (unit: kcal/mol).

In Channel 2, the ring-opening intermediate, IM3 (buta-2,3-dienethial), could be formed through two parallel pathways. One pathway starts with the isomerization of α-carbene to the four-ring intermediate IM2 and followed by ring opening at the S1–C3 bond. The transition state between IM1 and IM2 has an energy of 91.71 kcal/mol above thiophene. Additionally, thiophene could directly convert to IM3 via a 3,2-H shift, exhibiting a critical energy of 73.19 kcal/mol.

Decomposition of IM3 results in two groups of products, CS + CH3C2H (P2) and HCS* (radical) + C3H3* (P3). The former is generated via C5–H migration to C2. A barrier of 58.06 kcal/mol has been computed for this process. The later one is yielded through C4–C5 fission, which is endothermic by 64.34 kcal/mol at 0 K.

The elementary reactions in Channel 2 can be illustrated as

2.1.2. 1a
2.1.2. 3
2.1.2. 4
2.1.2. 5
2.1.2. 6
2.1.2. 7

2.1.3. Channel 3—Decomposition via But-3-ynethial

Figure 3 depicts the energy profile of Channel 3.

Figure 3.

Figure 3

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Potential energy surface of Channel 3. The values in parentheses are Gibbs energies at 1500 K, 1 atm (unit: kcal/mol).

Two independent pathways lead to the intermediate IM5, but-3-ynethial, which is the critical species for Channel 3. Intrinsic reaction coordinate (IRC) analysis verifies that thiophene could directly convert to IM5 through a 3,4-H shift. The barrier height was computed to be 86.31 kcal/mol at 0 K. Additionally, IM5 could be evolved from α-carbene via two H transfer steps, overcoming a barrier of 28.70 kcal/mol.

Decomposition of IM5 could result in three groups of products. Via C5–H transfer to C2 and C4 sites, IM5 cracks to CS + CH2CCH2 (P4) and CS + CH3C2H (P2), respectively. The corresponding energy barriers are 61.06 and 73.37 kcal/mol. However, HCS* + C3H3* (P3) is yielded through C5–C4 bond cleavage, endothermic by 72.03 kcal/mol at 0 K.

The elementary reaction of Channel 3 can be concluded as follows:

2.1.3. 1b
2.1.3. 8
2.1.3. 9
2.1.3. 10
2.1.3. 11
2.1.3. 12

2.1.4. Channel 4—Decomposition via But-3-yne-1-thiol

The potential energy surface is presented in Figure 4.

Figure 4.

Figure 4

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Potential energy surface of Channel 4. The values in parentheses are Gibbs energies at 1500 K, 1 atm. (unit: kcal/mol).

In Channel 4, IM7, but-1-en-3-yne-1-thiol is converted from thiophene through three independent pathways. The H shifts of thiophene from the C2 (via C3) to the S1 site form carbene intermediate IM6, with a maximum barrier of 93.77 kcal/mol, whereas the 1-H shift of thiophene, directly producing IM6, has a computed barrier of 84.64 kcal/mol. IM6 could readily transform to IM7, exhibiting a barrier of 11.21 kcal/mol. Besides, thiophene could first isomerize to intermediate IM8 via TS15 and subsequently convert to IM7 through the migration of C3–H to the S1 site. CCSD(T)/CBS indicated that this pathway needs to overcome an energy barrier of 102.95 kcal/mol.

Decomposition of IM7 could proceed via two routes. SC2H2 + C2H2 (P1) is yielded from IM7 through S1–H shifts to C3 accompanied by C5–H transfer to C4. The transition state has been located at 83.80 kcal/mol above IM7, whereas H2S + C4H2 (P5) is formed through C4–H migration to S1 via the C5 site. The energy barrier is determined to be 85.76 kcal/mol.

The pathway of Channel 4 can be represented by

2.1.4. 1c
2.1.4. 13
2.1.4. 14
2.1.4. 15
2.1.4. 16
2.1.4. 17
2.1.4. 18

It has been noticed that Channel 2, Channel 3, and Channel 4 are connected by the H migration process, as shown in Figure 5.

Figure 5.

Figure 5

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Conversion between IM3, IM5, and IM7. The values in parentheses are Gibbs energies at 1500 K, 1 atm (unit: kcal/mol).

It is indicated by the energy barrier and Gibbs energy that the processes of IM3–IM7 and IM5–IM7 are more important than IM3–IM5

2.1.4. 19
2.1.4. 20

2.1.5. Channel 5—Decomposition via Buta-1,3-diene-1-thione

Details of this channel are illustrated in Figure 6.

Figure 6.

Figure 6

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Potential energy surface of Channel 5. The values in parentheses are Gibbs energies at 1500 K, 1 atm (unit: kcal/mol).

Starting with the 2,3-H shift, thiophene first converts to α-carbene and thus undergoes a C3–H shift to C5, forming another carbene intermediate IM9. The overall barrier height of this process is 86.88 kcal/mol, located at the IM1 → IM9 step. The subsequent ring opening of IM9 gives IM10, exhibiting a barrier of 18.02 kcal/mol. IM10 undergoes C3–H migration to C2, giving the C–S–C three-ring intermediate IM11. The following cleavage of the S1–C3 bond leads to the triplet intermediate IM12(3A). Atomic sulfur (P6) is produced through the elimination of sulfur via the transition state TS25(3A), of which the energy is 56.17 kcal/mol above IM11.

The important reactions in Channel 5 can be concluded as

2.1.5. 1d
2.1.5. 21
2.1.5. 22

2.1.6. Channel 6—Decomposition via Bond Rupture

Ring bond rupture has been proposed as the initiation of thiophene pyrolysis in preceding. However, the relative importance of this channel has not been reported yet. In this work, this pathway has also been investigated. The potential energy surface is presented in Figure 7.

Figure 7.

Figure 7

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Potential energy surface of Channel 6. The values in parentheses are Gibbs energies at 1500 K, 1 atm (unit: kcal/mol).

The cleavage of the S–C bond, forming triplet intermediate IM13(3A), endothermic by 90.86 kcal/mol at 0 K. IM15(3A) is converted via C5–C4 bond rotation and subsequent C5–H migration. Decomposition of IM15(3A) proceeds via two steps. The first step is the H transfer from C4 to C5, giving the triplet intermediate of IM12(3A). The following step is the elimination of sulfur via transition state TS23(3A). Judging from the Gibbs free energy, the process of IM15(3A) → IM12(3A) is supposed to be the rate-limiting step of Channel 6. The overall reaction of this channel is given by eq 23

2.1.6. 23

2.1.7. Channel 7—Decomposition via Simple Ring-H Fission

The fission of the C–H bond could either be a possible initiation for thiophene pyrolysis. In previous study, we have compared the C–H bonds of thiophene, furan, and benzene. It is indicated that the C–H bond of thiophene is stronger than that of benzene, however energetically similar to furan. We assumed that the recombination rate constant of H + 2-/3-thienyl → thiophene is identical to that of H + 2-/3-furyl → furan and thus estimated the dissociation rate constant through the equilibrium constant and microscopic reversibility

2.1.7. 24
2.1.7. 25

To check the reliability of the CCSD(T)/CBS calculation, we have computed (including optimization) all stationary points at M062x/def2-QZVP, CBS-QB3, G4, and W1BD levels. Table 1 presents the relative energies of IMs and TSs at different levels.

Table 1. Relative Energy (0 K) of All Intermediates, Transition States, and Products at M062x/def2-QZVP, CBS-QB3, G4, W1BD, and CCSD(T)/CBS Levelsa.
species M062x/def2-QZVP CBS-QB3 G4 W1BD CCSD(T)/CBS
IM1 58.85 58.31 57.31 57.73 57.35
IM2 39.67 39.20 38.62 39.16 38.78
IM3 46.39 46.91 46.48 47.90 47.21
IM4 77.27 76.21 74.97 75.64 75.44
IM5 52.70 52.28 51.61 52.87 52.17
IM6 81.34 81.11 80.09 80.00 79.79
IM7 43.48 45.63 45.10 45.35 44.76
IM9 56.18 56.21 54.55 54.91 54.48
IM10 36.22 36.84 36.19 38.00 37.57
IM11 59.00 61.59 60.84 61.82 61.44
IM12 79.83 81.88 82.78 83.64 83.43
IM13 86.62 88.41 90.92 90.50 90.86
IM14 86.86 89.23 90.53 90.91 90.83
IM15 72.56 72.96 73.64 74.52 74.36
TS1 65.24 66.83 66.06 66.05 65.59
TS2 102.69 99.40 99.74 101.87 101.15
TS3 92.52 91.49 91.21 92.42 91.71
TS4 69.07 67.17 67.14 68.99 68.10
TS5 73.08 74.58 73.88 73.78 73.19
TS6 110.82 105.50 103.94 106.79 105.26
TS7 86.20 85.91 85.98 86.34 86.05
TS8 95.65 96.89 95.58 97.14 95.91
TS9 86.83 86.73 86.36 86.68 86.31
TS10 130.17 124.82 124.03 126.48 125.54
TS11 117.69 112.43 112.10 114.50 113.23
TS12 94.94 94.41 93.83 93.86 93.77
TS13 85.47 85.82 85.25 84.93 84.64
TS14 91.86 93.86 92.85 92.14 91.00
TS15 91.86 99.76 99.23 101.96 100.49
TS16 101.61 103.83 103.55 104.08 102.95
TS17 128.01 129.45 128.34 129.77 128.56
TS18 131.65 129.80 128.99 131.62 130.52
TS19 115.64 111.22 110.23 113.32 112.30
TS20 75.02 73.66 73.03 74.12 73.20
TS21 100.63 97.40 96.18 99.99 98.42
TS22 86.75 87.78 87.00 87.28 86.88
TS23 75.59 70.69 71.22 73.00 72.50
TS24 90.64 92.99 92.23 93.86 92.90
TS25b 115.74       117.61
TS26 101.55 103.69 102.39 104.28 103.56
TS27 104.10 103.52 106.32 105.83 106.18
TS28 123.96 127.30 127.43 128.73 128.42
P1 62.12 62.44 61.31 63.29 62.84
P2 74.31 71.93 70.49 72.79 71.79
P3 111.38 110.14 109.32 111.43 111.54
P4 74.44 72.90 72.65 73.88 72.96
P5 69.11 69.40 68.97 68.60 67.85
P6 98.37 99.29 97.67 98.47 97.56
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a

Unit: kcal/mol.

b

Transition state TS25 could be located only at the M062x/def2-QZVP level. The geometry optimized at the M062x/def2-QZVP level was further used to obtain CCSD(T)/CBS energy of TS25.

All of these calculation methods give comparable results. The mean absolute energy deviation between CCSD(T)/CBS and W1BD is only 0.64 kcal/mol. This comparison led us to conclude that our CCSD(T)/CBS calculation is reliable in studying the kinetic behavior of thiophene.

2.2. Thermodynamic

To ensure the accuracy of thermodynamic calculations, the standard enthalpy change, ΔfHΘ at 298 K, of the involved pyrolysis reaction has been calculated at various levels and compared to available experimental values in Table 2. Besides, we have contrasted the calculated thermodynamic properties (SΘ and Cp at 298 K) with literature data for some species.

Table 2. Standard Enthalpy Change (ΔfHΘ, 298 K) of the Thiophene Pyrolysis Reactiona.

  M062x/def2-QZVP CBS-QB3 G4 W1BD CCSD(T)/CBS reference
thiophene → P1 74.94 75.29 74.22 76.13 75.69  
thiophene → P2 87.33 84.95 83.56 85.80 84.81 83.01b
thiophene → P3 126.42 125.22 124.51 126.51 126.62 123.75b
thiophene → P4 87.36 85.75 84.44 86.74 85.83 84.45b
thiophene → P5 77.85 78.55 78.21 78.01 77.27 77.35b
thiophene → P6 109.39 110.28 108.69 109.47 108.56 107.28b
thiophene → H + 2-thienyl 116.44 118.40 116.99 118.44 119.04 119.2c, 118.39d
thiophene → H + 3-thienyl 114.06 115.95 114.65 116.05 116.65 117.0c, 115.93d
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a

Unit: kcal/mol.

b

Experimental results, calculated based on the thermodynamic data of Goos et al.49

c

By Barckholtz et al.50 at the CBS-Q level.

d

By Song and Parish37 at the CBS-QB3 level.

As can be seen in Table 2, the ΔfHΘ values at 298 K of thiophene pyrolysis derived from different methods are in accordance with the experimental values within chemical accuracy. The calculated C2–H and C3–H bond strengths are also identical to our CCSD(T)/CBS results. The comparison of SΘ and Cp at 298 K (in Table S4) shows that our calculations are in good agreement with the literature values within the uncertainties. These discussions further convinced us that CCSD(T)/CBS is accurate in describing the kinetics of thiophene pyrolysis.

To deduce the thermodynamic product, the Gibbs free energy change ΔG of thiophene pyrolysis has been computed. For comparison purposes, the ΔG was either obtained using M062x/def2-QZVP, CBS-QB3, G4, and W1BD methods. Results are shown in Figure 8.

Figure 8.

Figure 8

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Gibbs free energy change ΔG of thiophene pyrolysis. Solid line, CCSD(T)/CBS; short dash line, M062x/def2-QZVP; dash line, CBS-QB3; dot line, G4; dash dot line, W1BD.

From Figure 8, it can be seen that the results given by these methods are approximate. Compared with other methods, the G4 method may underestimate the Gibbs free energy of products for most cases. However, the results of CBS-QB3 are more close to those of CCSD(T)/CBS and W1BD that are theoretically more accurate.

The decomposition of thiophene to SC2H2 + C2H2 (P1) is thermodynamically preferred to other products at all temperatures. P1 is the most stable product that could be directly produced from thiophene. The spontaneous temperature (ΔG = 0) is around 1695 K. Thermolysis of thiophene to CS + CH3C2H (P2) and CS + CH2CCH2 (P3) has a similar thermodynamic character. The spontaneous temperatures for P2 and P4 are around 1930 and 1980 K, respectively. The importance of P2 and P4 is only secondary to P1.

By contrast, the formation of HCS* + C3H3* (P3) and H2S + C4H2 (P5) is highly endergonic. The favored temperatures for P3 and P5 are above 2425 and 2300 K at the CCSD(T)/CBS level, respectively. The group of atomic sulfur + C4H4 is the most endothermic product among these products. The spontaneous temperature, i.e., 2825 K, indicates that atomic sulfur is less likely to be a major product of thiophene.

Based on the discussion above, it is concluded that SC2H2 + C2H2 (P1), CS + CH3C2H (P2), and CS + CH2CCH2 (P4) are the principal products of thiophene, whereas the appearance of HCS* + C3H3* (P3), H2S + C4H2 (P5), and atomic sulfur + C4H4 (P6) needs higher temperatures. All of these of products, except P4, have been detected by Vasiliou et al.34 in the microtublar reactor pyrolysis experiment. The absence of CH2CCH2 may be caused by the kinetic competition between P2 and P4. On the contrary, the detection of HCS*, as well as SC2H2, at the beginning temperature of pyrolysis (1300 K) indicates that HCS* is likely a kinetic product.

2.3. Kinetics and Modeling

The high-pressure limit rate constant, k, of elementary reactions was calculated using the VTST-CCSD(T)/CBS method and subsequently fitted to the modified three-parameter Arrhenius expression k = A × Tn × exp[−Ea/(RT)]. For the four barrierless reactions, namely, IM3 → P3 (7), IM5 → P3 (11), TRE → H + 2-thienyl (24), and TRE → H + 3-thienyl (25), we estimated the rate constants by analogy to the similar reaction in furan pyrolysis. Particularly, the rate constants of IM3 → P3 (7) and IM5 → P3 (11) are estimated from the reaction of buta-2,3-dienal → formyl radical + propargyl radical.51 The C2–H and C3–H loss rates of thiophene were estimated by analogy to that of furan.52 Rate coefficients of the elementary reactions in the kinetic model are presented in Table 3.

Table 3. Rate Coefficients k = A × Tn × exp[−Ea/(RT)] of the Elementary Reactions Involved in the Unimolecular Decomposition of Thiophene for 1300–1700 Ka.

    k(T) = A × Tn × exp[−Ea/(RT)]
no. reaction A T Ea
R1 TRE → IM1 4.49 × 1013 0.16 67.08
  reverse 7.39 × 1012 0.13 8.73
R2 IM1 → P1 1.23 × 1016 –0.31 47.71
  reverse 4.44 × 103 2.23 26.20
R3 IM2 → IM1 9.63 × 1012 0.05 53.50
  reverse 3.27 × 1013 0.00 35.24
R4 IM3 → IM2 7.43 × 1012 0.04 21.30
  reverse 5.51 × 1013 0.05 30.42
R5 TRE → IM3 6.53 × 1013 0.14 74.92
  reverse 2.38 × 1011 0.14 25.80
R6 IM3 → P2 1.20 × 1013 0.21 62.89
  reverse 8.00 × 102 2.61 19.80
R7b IM3=P3 4.00 × 1024 –3.00 70.26
R8 IM1 → IM5 5.17 × 1017 –0.88 40.92
  reverse 8.19 × 1015 –0.82 44.90
R9 TRE → IM5 2.28 × 1013 0.29 87.65
  reverse 1.82 × 1011 0.19 34.00
R10 IM5 → P2 1.65 × 1015 0.10 76.38
  reverse 5.37 × 104 2.60 42.90
R11b IM5=P3 3.29 × 1024 –3.00 70.47
R12 IM5 → P4 1.08 × 1013 0.23 62.11
  reverse 0.21 3.13 –15.40
R13 IM6 → IM1 9.75 × 1011 0.14 48.36
  reverse 7.63 × 1013 0.12 37.78
R14 IM6 → IM7 5.92 × 1014 0.09 13.39
  reverse 2.17 × 1013 0.09 47.48
R15 TRE → IM6 1.50 × 1014 0.19 86.91
  reverse 1.82 × 1013 0.10 5.48
R16 TRE → IM7 2.60 × 1013 0.56 104.65
  reverse 4.22 × 1012 0.14 59.10
R17 IM7 → P1 1.74 × 1014 0.02 84.24
  reverse 2.68 × 107 1.65 56.90
R18 IM7 → P5 1.02 × 1015 0.22 88.71
  reverse 2.68 × 105 3.07 54.10
R19 IM7 → IM3 1.18 × 1012 0.13 28.70
  reverse 1.50 × 1012 0.18 27.18
R20 IM7 → IM5 6.05 × 1013 –0.07 55.10
  reverse 7.30 × 1013 –0.03 48.49
R21 IM1 → IM10 1.95 × 1013 0.12 30.29
  reverse 3.88 × 1011 0.17 49.40
R22 IM10=P6 1.55 × 1014 –0.37 71.35
R23 TRE → P6 1.98 × 1012 1.39 126.30
  reverse 2.70 × 108 1.74 22.10
R24c TRE → H + 2-thienyl 1.55 × 1013 0.52 112.61
R25c TRE → H + 3-thienyl 1.18 × 1013 0.55 110.14
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a

Units: s, cm, mol, and kcal.

b

Estimated from a similar reaction of furan.51

c

Estimated from a similar reaction of furan.52

To verify the model, the unimolecular pyrolysis rate of thiophene in the 1300–1800 K range has been computed. A small residence time of 100 μs was used in the modeling to avoid the effect of secondary reactions. The results are demonstrated in Figure 9.

Figure 9.

Figure 9

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Comparison of the Arrhenius plot of thiophene decomposition. The data of Memon et al. and Hurley et al. were taken from refs (32) and (53), respectively.

From Figure 9, it can be seen that all of the Arrhenius plots are located on a straight line. Least-squares regression analysis implies that the pyrolysis rate of thiophene could be given by eq 26

2.3. 26

The square of the correlation coefficient, r2 (i.e., 0.9973), indicates that our results in 1300–1700 K are in good agreement with the results of the higher-temperature range and lower-temperature range. However, we also noticed that the decomposition of thiophene to C2H2 + SC2H2 is proceeding at a rather high rate above 2000 K. At such a high temperature, the secondary reactions may play a more significant role in thiophene pyrolysis. Hence, the suggested temperature range for this model is 1300–1700 K.

We further applied this model to study thiophene pyrolysis. The unimolecular pyrolysis of thiophene was modeled at 1300, 1400, 1500, and 1600 K. The product distribution of thiophene unimolecular pyrolysis at different temperatures is shown in Figure 10.

Figure 10.

Figure 10

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Product distribution of thiophene unimolecular pyrolysis at different temperatures. C0 is the initial concentration of thiophene. Modeling conditions: 3 atm, thiophene 0.5%, Ar 99.5%.

As can be seen from Figure 10, the amount of SC2H2 + C2H2 (P1) in the product is significant at all modeling temperatures. Both the kinetics and thermodynamics indicate that SC2H2 + C2H2 is the principal pyrolysis product of thiophene. The reaction of α-carbene → P1 is concluded to be the principal formation route for SC2H2 + C2H2. In previous study, the feasibility of SC2H2 + C2H2 formation during thiophene pyrolysis has been discussed. Song and Parish37 proposed SC2H2 + C2H2 as a major product of thiophene based on their CBS-QB3 calculation. Vasiliou et al.34 detected SC2H2 + C2H2 at the beginning pyrolysis temperature (i.e., 1300 K) in the microtublar reactor pyrolysis experiment. Memon et al.32 identified C2H2 as the principal hydrocarbon product at 1559–2022 K. However, no SC2H2 was found in their experiment. It seems that SC2H2 is first produced accompanied by C2H2 and subsequently consumed rapidly. This could be partly explained by the reaction of eq 27

2.3. 27

The ΔG of eq 26 is barely effected by temperature, −30.64 kcal/mol at 298 K and −24.75 kcal/mol at 1500 K. CS2 could be converted indirectly in thiophene pyrolysis by consuming CS and SC2H2. This is in accordance with the experimental result that CS2 is one of the major sulfur-containing compound of thiophene pyrolysis.34 Besides, the decomposition of SC2H2 through eq 28 is favored at higher temperatures

2.3. 28

The ΔGR27 is −0.85 kcal/mol at 1500 K. We concluded that SC2H2 + C2H2 is the major primary product of thiophene pyrolysis. Its behavior in the products is important in understanding the mechanism of final stable product formation.

In addition to SC2H2 + C2H2, HCS* + C3H3* (P3) is also yielded in an significant amount. HCS* may be of similar importance to SC2H2 in thiophene pyrolysis. Vasiliou et al.34 confirmed that HCS*, as well as SC2H2, is formed at the beginning pyrolysis temperature of 1300 K. However, in the shock tube experiment of Memon et al.,32 HCS* was traceless over the temperature of 1559–2022 K. This may be accounted for by the reactions of eqs 29 and 30

2.3. 29
2.3. 30

The ΔGR28 and ΔGR29 are −32.42 and −48.79 kcal/mol at 1500 K (−7.17 and −52.18 kcal/mol at 298 K), respectively. As the rate coefficient for HCS* formation is estimated from a similar reaction in this modeling, certain uncertainties of the HCS* content may exist. Combining previous experimental results and our kinetic modeling results, HCS* + C3H3* is expected to be a significant product of thiophene unimolecular thiophene pyrolysis.

CS is another sulfur-containing product of thiophene pyrolysis. The corresponding hydrocarbon products are CH3C2H and CH2CCH2. In modeling, CH2CCH2 is present at a much lower level compared with CH3C2H, which is consistent with the results of the pyrolysis experiment.36 The modeling results also manifest that the formation of CS is promoted at higher temperatures. The mole ratio of CS/SC2H2 in the product is merely 1:10 at 1300 K, whereas this value have exceeded to 1:3 at 1600 K. Production of CS has been confirmed in the microtublar reactor experiment at 1400 K and above.34 However, none CS was detected in the pyrolysis experiment of the shock tube.32 Based on the discussion above, we suppose CS as an important direct product of thiophene pyrolysis.

The amount of atomic sulfur + C4H4 in the product is negligible for its high formation barrier. Vasiliou et al.34 detected atomic sulfur during thiophene pyrolysis at 1500 K. However, the source of atomic sulfur from other sulfur-containing products cannot be excluded. In the shock tube experiment by Memon et al.,32 no atomic sulfur was detected over the temperature range of 1598–2022 K. Atomic sulfur is less likely to be important. However, the atomic sulfur evolved from other sulfur-containing products could promote the variation of sulfur-containing hydrocarbon compounds.

Similar to atomic sulfur, the amount of H2S is also ignorable even at highly elevated temperatures. Our results are basically consistent with the experimental result that H2S was detected only at a higher temperature (1500 K) than SC2H2, HCS*, and CS.34 Surprisingly, Memon et al.32 found that H2S is present at a significant level in products, which is much higher than its corresponding hydrocarbon compound C4H2. As the atomic hydrogen that is produced directly from ring-H fission is negligible, the explanation that H2S is produced through secondary reactions (eqs 31–37) is preferred by this work. The ΔG values of R30–R36 have been calculated at the CCSD(T)/CBS level and are presented in Table 4.

Table 4. ΔG of the Reactions Related to H2S Formationa.

reaction ΔG(T)
graphic file with name ao1c02155_m048.jpg 31
–0.0323 × T + 93.26
graphic file with name ao1c02155_m049.jpg 32
–0.0328 × T + 92.33
graphic file with name ao1c02155_m050.jpg 33
–0.0238 × T + 52.10
graphic file with name ao1c02155_m051.jpg 34
0.0213 × T – 103.95
graphic file with name ao1c02155_m052.jpg 35
0.0485 × T – 178.01
graphic file with name ao1c02155_m053.jpg 36
0.0164 × T – 71.43
graphic file with name ao1c02155_m054.jpg 37
0.0845 × T – 292.67
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a

Unit: kcal/mol, K.

In studying furan thermal decomposition, Sendt et al.51 proposed the mechanism of eq 31 as an important path for atomic hydrogen. Considering that the pyrolysis temperature of thiophene is much higher than that of furan, the H loss reaction of CH3C2H is supposed to be an important source of atomic hydrogen in thiophene pyrolysis and further leads to the formation of H2S.

Based on the discussion above, we conclude that the unimolecular pyrolysis of thiophene mainly starts with ring-H migration, namely, C2–H migrations and C3–H migrations. By contrast, the cleavage of the C–S bond has limited contribution to the overall pyrolysis rate. The major mechanism of thiophene unimolecular pyrolysis is the conversion and decomposition of α-carbene (IM1), buta-2,3-dienethial (IM3), and but-3-ynethial (IM5). SC2H2 + C2H2 (P1), CS + CH3C2H (P2), and HCS* + C3H3* (P3) are concluded to be the principal direct products. However, these direct products could be further converted to more stable sulfur species through the secondary relations.

Compared with the unimolecular pyrolysis mechanism, the secondary reactions between products may be more complicated. The high temperature promotes the condensation and decomposition of hydrocarbon products, leading to various hydrocarbon species and sulfur-containing species. In this work, we mainly concentrated on the unimolecular thermolysis mechanism of thiophene. However, these secondary reactions have an important significance in understanding the complete mechanism of thiophene pyrolysis. In the following study, we will focus on the secondary reactions to develop a more comprehensive kinetic model.

3. Conclusions

In this work, high-level ab initio methods were adopted to investigate the unimolecular pyrolysis of thiophene. All possible initiation reactions, including ring-H migration, C–S bond fission, non-H-migration isomerization, and simple ring-H fission, have been considered. The mechanisms are shown in Figure 11.

Figure 11.

Figure 11

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Sketch of the mechanism of thiophene unimolecular pyrolysis.

Rate coefficients of the elementary reactions have been computed using variational transition state theory at the CCSD(T)/CBS level to develop a kinetic model for thiophene unimolecular pyrolysis. The calculated pyrolysis rate of thiophene is in good agreement with preceding experimental results, which could be given by eq 38

3. 38

Further applying this kinetic modeling in studying the pyrolysis product distribution, we found that the unimolecular pyrolysis of thiophene is mainly initiated by the ring-H migrations, whereas the C–S bond rupture and other initial steps have limited contribution to the overall pyrolysis rate. SC2H2 + C2H2 is found to be the major pyrolysis product at all temperatures. Significant amounts of HCS radical and CS are yielded. By contrast, the atomic sulfur and H2S are present in negligible levels and likely to be produced through secondary reactions. The major principal products could be converted to other forms via secondary reactions.

4. Computational Details

4.1. Potential Energy Surface

All calculations were performed using the Gaussian 09 package.38 The harmonic vibrational frequencies of stationary points were computed to verify the nature of intermediates and transition states. IRC calculations39 were also carried out to validate the connection between the transition state and designed reactant/product.

To improve the accuracy of relative energy, the CCSD(T) single point energy was calculated using cc-pVTZ and cc-pVQZ basis sets in the well-optimized geometry at the B3LYP/cc-pVTZ level. The spin eigenvalue of T1 diagnostic for the Hartree–Fock wave function40 has been checked to ensure the reliability of the CCSD(T) calculation. The zero-point vibrational energy (ZPE) and thermodynamic correction energy were obtained from the result of the B3LYP/cc-pVTZ frequency using software Shermo 2.0.8.41 To accurately determine the Gibbs free energy, the quasi-RRHO method proposed by Grimme et al.42 has been adopted to treat the low frequencies of IMs and TSs. All energies reported in the figure of potential energy surface are CCSD(T)/CBS energies including the ZPE energy.

4.2. CBS Extrapolation

To obtain the CCSD(T)/CBS energy, the extrapolation method proposed by Helgaker et al.43 has been employed. The CCSD(T)/CBS energy Inline graphic could be expressed as the sum of the Hartree–Fock CBS energy Inline graphic and the correlation CBS energy Inline graphic, as illustrated by eq 39

4.2. 39

For the reason that the Hartree–Fock energy Inline graphic and the correlation energy Inline graphic have apparently different converging characters, extrapolation of the Hartree–Fock energy and the correlation energy was carried out independently. The extrapolation of Hartree–Fock energy Inline graphic can be given by eq 40

4.2. 40

where X denotes the cardinality of the basis set and A is the constant needed to be parameterized during extrapolation. The recommended α is 5.46 for TZ/QZ extrapolations.44Equation 41 presents the extrapolation of the correlation energy Inline graphic.

4.2. 41

where X and Y are the cardinal numbers. The proposed value of β is 3 for TZ/QZ extrapolation.

4.3. Rate Coefficient Calculation

Rate coefficients of elementary reactions were calculated using VTST at the CCSD(T)/CBS level. The VTST rate constant kVTST is given by eq 42

4.3. 42

where σ is the symmetry factor of reaction pathway. kB and h are Boltzmann’s constant and Planck’s constant, respectively. Na is the Avogadro number. ΔE0 is the maximum energy barrier along IRC excluding ZPE. QTS and Qreac denote the total partition functions of the transition state and reactant with the translational partition functions expressed in per unit volume, respectively. In this work, the thermodynamic equivalent of eq 43 was employed

4.3. 43

where R is the gas constant and ΔGmax is the maximum Gibbs free energy barrier along the IRC path at the CCSD(T)/CBS level. Detailed procedure of the VTST-CCSD(T)/CBS calculation can be found in our previous work.45

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (nos. 51974373 and 51874365), the Major Scientific and Technological Innovation Projects of Shandong Province (no. 2019JZZY020123), the China National Postdoctoral Program for Innovation Talents (no. BX20200391), and the Natural Science Foundation of Hunan Province, China (no. 2018JJ2521).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.1c02155.

  • Geometries in the xyz format; only imaginary frequency of transition states; Gibbs free energies of all transition states and intermediates at B3LYP/cc-pVTZ, M062x/def2-QZVP, CBS-QB3, G4, W1BD, and CCSD(T)/CBS levels; T1 diagnostic for CCSD(T) calculations; comparison of the calculated thermodynamic property with available experiment data; and CCSD(T)/CBS-VTST calculation procedure (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao1c02155_si_001.pdf (208.1KB, pdf)

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