Study on the mechanism of the effect of temperature on the decomposition reaction of SFn (n = 1–6) under discharge conditions

The study on the mechanism of the effect of temperature on the decomposition reaction of SFn (n = 1–6) under discharge conditions is very important in studying the potential fault of SF6 high voltage switch equipment and perfecting the chemical kinetic model of SFn discharge. In this paper, structural optimizations, thermal correction to Gibbs free energy for the reactants, and products were performed at the B3LYP/6–311 +  + G(d,p) theory level. The single-point energies of all species were collected at the CCSD(T)/aug-cc-PVTZ level. The electric and thermal decomposition mechanism of SFn under discharge conditions of 298–10,000 K were studied, respectively. The conclusion drawn was that in the temperature range of 298–10,000 K, the thermal decomposition homopolytic reaction △G began to decline from 200 kJ/mol, while the △G of the other two heterogenous reactions began to decrease from 1000 kJ/mol and 2000 kJ/mol, showing a downward trend of an almost similar slope. The electrolysis of SFn is related to electron energy. When the electron energy is low, SFn + e → SFn− series reactions occur, and △G of R12, R20, R28, R36, and R44 increases with temperature rise, while △G of R4 decreases with temperature. When the electron energy is high, one of SFn−  → SFn−1−  + F, SFn−  → SFn−1 + F−, and SFn−  → SFn−1 + F + e will occur, and the reactions that occur at various temperature ranges as the temperature rises vary. When the second electron hits the SFn−, the SFn−  + e → SFn−1−  + F reaction will occur. The △G of this reaction slowly decreases with an increase in temperature. This study in clearer terms explains the decomposition process and mechanism of SFn at different temperatures.


Introduction
high voltage switch equipment has a number of advantages. These include small size, high safety, and long maintenance period. With the improvement of power system voltage level, SF 6 high voltage switch equipment use has drastically grown. SF 6 is a colorless, tasteless, non-toxic, non-flammable stable gas. Because of its good electron affinity, thermodynamic stability, and good dielectric property, it is commonly used as insulating medium and arc extinguishing medium for gas-insulated equipment [1]. However, when partial discharge or arc discharge occurs in the equipment, SF 6 gas will decompose on reacting with heat and electricity and form neutral low-flourine flourosulfur species, such as SF 5 , SF 4 , SF 3 , SF 2 , SF, and anions SF 6 − , SF 5 − , SF 4 − , SF 3 − , etc. [2,3]. Most of the low-fluorine sulfides (99.9%) will react with F atoms to regenerate SF 6 in a very short period of time. But, a small part will react with a trace amount of water and oxygen inside the equipment in a series of complex chemical reactions and finally produce SOF 4 , SOF 2 , SO 2 F 2 , HF, SO 2 , CF 4, CO 2 , CS 2 , and other by-products [4]. As much as these products reduce the purity of SF 6 gas and affect its insulation and arc extinguishing performance, they also corrode the metal parts and solid insulating materials in the equipment, lowering the durability of the equipment. On the other hand, the components and contents of some characteristic products can be utilized in evaluating the deterioration of the metal and solid insulating materials in the equipment and to identify the discharge defects in the equipment.
Many scholars have done a lot of research on the decomposition products of SF 6 under discharge conditions. Local overheating is an important cause of the decomposition of SF 6 molecule. Wilkins found through experimental research that at a temperature of 1500 K, the main decomposition product of SF 6 gas is SF 4 [5]. Frie used the counter ion concentration calculation method to roughly estimate the number of equilibrium particles in SF 6 plasma at various temperatures [6]. It was found that when the temperature of SF 6 gas was higher than 1500 K, its concentration was significantly lower, and the SF 4 concentration and F atoms would rise rapidly. At temperatures higher than 4000 K, most of the SF 6 molecules would be completely decomposed, but the decomposition mechanism has not been further studied. Under arc discharge, electron collision is another key factor affecting the decomposition of SF 6 molecules. Ziegler theoretically studied the decomposition process of anion low-fluoride sulfide and found that further decomposition of SF 5 − , SF 4 − , SF 3 − , SF 2 − , SF − , and other anions would lead to a formation of a lower level of neutral low-fluoride sulfide molecule and an F − anion, but he did not take a keen note on the process in which electrons participate in the reaction [7]. Fifen found that the thermodynamic data of electrons would vary greatly with temperature change, and he corrected the thermodynamic data of 0-10,000 K through algorithm iteration [8]. Wang et al. studied the particle compositions of an SF 6 arc using a two-temperature chemical kinetics model. The chemical reaction system consists of 18 particles, and 63 chemical reactions are taken into consideration. But, they did not consider the effect of temperature change on the reaction and did not include reactions involving SF 2 − andSF 3 − . The chemical reaction equation was incomplete [9]. Yang et al. studied the composition of SF 6 arc plasma using the local thermodynamic equilibrium hypothesis (LET). In pure SF 6 plasma, 12 particles such as SF 6 , SF 5 , SF 4 , SF 3 , SF 2 , SF, S, and F were considered. The study found that SF 6 molecules began to decompose at about 1000 K and basically disappeared at 2700 K. First, SF 5 , SF 4 , and F atoms are formed. With the increase of arc temperature, SF 3 , SF 2 , and SF begin to form. When the arc temperature is greater than 3000 K, the low-fluorine sulfide is decomposed into S and F atoms [10]. Pelc studied the generation of negative ions from SF 6 gas by means of hot surface ionization. He found eight ion species: SF 5 − , F − , SF 6 − , SF 4 − , SF 3 − , SF 2 − , SF − , and F 2 − , with ion current intensities ratios of 1000:200:100:10:5:0.5:0.5:0.05. He also found the optimal temperatures at which the maximum of ion current intensity is observed were estimated in 1830-2000 ± 10 °C range [11]. Shi et al. established a mathematical model of non-equilibrium dual-temperature plasma in the temperature range of 300-41,300 K. They considered 20 kinds of ions. The study found that the appearance time of electrons was strongly correlated with temperature, and they all appeared at the temperature of 7000 K, but had little relationship with pressure [12].
Early research mainly focused on the qualitative analysis of the types of SF 6 gas decomposition products. The thermal decomposition mechanism and electron impact decomposition mechanism of SF n at different temperatures has not been systematically studied. During the installation and operation of SF 6 high voltage switchgear, electrode surface burrs, free conducting particles, and suspension potential may exist in the equipment, leading to partial discharge or overheating in the equipment, making the gas temperature near the fault center higher compared to the ambient temperature. Under the parameters of arc and spark discharge, the decomposition of SF 6 mostly results from electron impact or high temperature. Under partial discharge and corona discharge, SF 6 dissociation is a result of electron collisions in the discharge area due to low temperature. Therefore, this paper thoroughly investigates the thermal decomposition and electron collision decomposition of SF 6 in the temperature range of 298-10,000 K by means of high-level quantum chemistry calculations with density functional theory (DFT). The structural optimizations and thermal correction to Gibbs free energy of all chemical configurations involved in the decomposition system are carried out with the DFT-B3LYP method. Detailed single-point energy is then investigated with a more sophisticated CCSD(T) method. The KisTheIP program was used to calculate the Gibbs free energy of all species at different temperatures, and finally, the reaction mechanisms of SF 6 thermal decomposition and electron collision dissociation in different temperature ranges were obtained. In addition, this article also has certain reference significance for establishing a complete arc plasma model.

Calculation method
In this paper, the quantum chemistry method is used to find out the reaction mechanism of SF n (n = 1-6) under overheating and electron impact conditions under discharge conditions. Table 1 lists all the reaction equations in this paper. It is divided into two types of processes: overheating decomposition and electron impact decomposition. Taking the decomposition of SF 6 as an example, R1 is the process of covalent bond homolysis resulting from overheating, R2 and R3 are the process of covalent bond heterolysis, R4 and R8 are electron capture process while R5, R6, and R7 are decomposition processes resulting from R4.
All the calculations of quantum chemistry in this study are completed in Gaussian 09 [13]. Gaussian 09 is currently the most popular and powerful quantum chemical calculation software. The core problem of quantum chemistry is to solve the Schrodinger equation of molecular system: where Ĥ tot is the Hamiltonian; Ψ tot (R;r) is the wave function of the particle; and E tot is the energy of the particle. Strictly solving the Schrodinger equation for molecular systems requires considering electrons and nuclei together in a quantum mechanical way, which is extremely complicated. Various approximations are always used in practical solution, and the method used in this paper is Born-Oppenheimer (BO) approximation: where Ĥ ele (R) is the electron Hamiltonian operator; Ψ ele (R) (r) is the electron wave function; and E ele (R) is the electron energy. The BO approximation takes into account that the mass of the nucleus is much larger than that of the electron, so the quantum effect is much smaller than that of the electron. Therefore, the position of the nucleus is regarded as a fixed parameter when solving the electron wave function. At extremely high temperatures, because molecules are decomposed into atoms and electrons, the nucleus only moves in translation without rotation and vibration, so BO approximation is available.
In this paper, the structure of all reactants and products was optimized at the B3LYP/6-311 + + G(d, P) level [14,15]. The structures of the reactants and products, which satisfy the minimum energy principle, were obtained. Since S is the element of the third period and F is the element of the second period, the atomic mass is small, so the influence of the relativistic effect is not so great, which will not cause large errors. Therefore, relativistic effects are not considered in this paper. Use optimized structures to calculate thermodynamic data. The Gibbs free energy at any temperature is expressed as: where G corr (T) is the thermal correction to Gibbs free energy and ε ele is the single-point energy.
In the above formula, the magnitude and calculation error of G corr (T) are much lower than ε ele . Accurate G corr (T) can be obtained at the B3LYP/6-311 + + G(d, P) level [14,15], while the calculation of ε ele using the high-level CCSD(T)/ aug-cc-pVTZ [16] can greatly improve the accuracy of total energy [17]. Xu et al. studied the reaction process of SF 6 with PTFE and the reaction mechanism of SF 6 − and H 2 O under discharge conditions using the B3LYG/6-311G** level. They calculated the harmonic vibration frequency and reaction rate and calculated the single-point energy of the reaction using CCSD(T) method [18,19]. Fu et al. used the same method to calculate the decomposition mechanism of SF 6 in trace water and trace oxygen [20]. Their studies have produced good results. Therefore, the quantum chemistry methods are SF − + e → S − + F − feasible in the investigation of gas decomposition mechanism and thus adopted in this paper. To ensure accuracy in the calculated outcome, the frequency vibration factor is considered. When using the B3LYP/6-311 + + G(d, p) level, the frequency vibration factor is 0.967 [21]. Because of some limitations of Gaussian 09 in obtaining thermodynamic data, this paper used the KisTheIP to obtain thermodynamic data of all structures at 298-10,000 K [22]. For the record, KisTheIP cannot get the thermodynamic data of electrons. The thermodynamic data of electrons used in this paper uses the thermodynamic data mentioned in Fifen's article as shown in Table 2 [11]. The Gibbs free energy of gas-phase electrons changes with temperature as shown in Fig. 1; the curve is fitted by cubic spline interpolation. After obtaining the thermodynamic data of all the structures, △G of all the reactions in this paper was got by the following formula: where G p is the product and G R is the reactant. For example, at 298 K, for the reaction SF 6 → SF 5 + F in Table 5, the G of SF 6 is − 996.1496484Hartree, the G of SF 5 is − 896.3641003Hartree, the G of F is − 99.64262951Hartree, the △G of this reaction is: Calculate the △G of all reactions in the temperature range of 298-10,000 K and get the curve in Figs. 3, 4, 5, 6, 7, 8, 9, 10.

Structural optimizations and energies
The optimized structure of reactants and products in reactions R1-R48 is displayed in Fig. 2. In this paper, structural optimization was performed at the B3LYP/6-311 + + G(d,p) level of theory. The optimized structure of all reactants and products was compared with the experimental geometric data in the NIST database and the outcomes of other theoretical calculations (B3LYP/6-31 g (d)) [18]. The structural parameters of all reactants and products coincide with the literature of Tom Ziegler and Cheung [2,23]. The key structural parameters are shown in Fig. 2. In comparison to the experimental data, the bond angle error of all structures was < 0.1 Å, and the bond length error of all structures was < 2.6°. The error mainly results from the difference in theoretical level. The energies of all species were compared with the data from CCCBDB and previous papers, as shown in Table 3. The bond dissociation energies of all species were compared with the experimental data and the data in the previous papers, as shown in Table 4, and good agreement was obtained. The unit of energy in Table 3 is Hartree. The unit of bond dissociation energy in Table 4 is ev. Table 5 shows the △G of all reactions at 298 K, 5000 K, and 10,000 K. From the data in Table 5, we can roughly see   Table 5.

Thermal decomposition of SF n (n = 1 ~ 6) under overheating conditions
The decomposition of SF 6 is the process of S-F bond breaking in its molecular structure to form free radicals. The thermal decomposition process of SF 6 may be directly decomposed into SF 5 and F atoms, or heterocracking of covalent bonds may lead to the formation of SF 5 + , F − , or SF 5 − , F + . Figure 3 shows the change of △G of R1, R2, and R3 at the temperature of 298-10,000 K. Figure 3 shows that the △G of R1-R3 decreases linearly with the increase of temperature. The △G of R1 at 298 K is 375.2 kJ/mol. When the temperature reaches about 2450 K, △G falls below 0 kJ/ mol, and the reaction can proceed spontaneously. When the temperature reaches 10,000 K, △G drops to -1274 kJ/mol. The △G of R2 at 298 K is 1004.3 kJ/mol; when the temperature reaches about 7400 K, the △G of reaction can drop  below 0 kJ/mol; when the temperature reaches 10,000 K, the △G of reaction is -353 kJ/mol. The △G of R3 at 298 K is 1913.5 kJ/mol, when the temperature reaches 10,000 K, △G is 70 kJ/mol, and it does not drop below 0 kJ/mol. Therefore, for the thermal decomposition process of SF 6 , R1 is most likely to occur within the temperature range of 298-10,000 K.
The thermal decomposition process of SF 5 may directly decompose SF 4 and F atoms, or the covalent bond may heterocrack to produce SF 4 + , F − , or SF 4 − , F + . The SF 5 thermal decomposition △G changes with temperature as Fig. 4 shows. It can be seen from Fig. 4 that △G of R9-R11 also decreases linearly with the temperature rise. During the thermal decomposition of SF 5 , the △G of R9 at 298 K is 134 kJ/ mol; when the temperature reaches about 1270 K, △G falls below 0 kJ/mol, and the reaction can proceed spontaneously. When the temperature reaches 10,000 K, the △G decreases to − 1143.9 kJ/mol. The △G of R10 at 298 K is 936.2 kJ/ mol; when the temperature reaches about 7400 K, △G drops below 0 kJ/mol, and the reaction can be spontaneous. When the temperature reaches 10,000 K, △G drops to − 333.3 kJ/ mol. The △G of R11 at 298 K is 1884.6 kJ/mol; when the temperature reaches 10,000 K, △G decreases to 281.8 kJ/ mol. Therefore, for the thermal decomposition process of SF 5 , R9 will most probably occur within the temperature range of 298-10,000 K.
From the above analysis, it can be seen that △G of SF n displayed similar thermal decomposition rules within the temperature range of 298-10,000 K, and there was a decrease in energy required for the reaction as the temperature increased. Moreover, the energy required for the homolytic reaction is far less than the other two heterolytic reactions, so the homolytic reaction is most probable to take place. This is because SF n and F are both highly electronegative molecules. It is very hard for each molecule to lose an electron and need to absorb a lot of energy. In addition, the same is the heterolytic dissociation, the reactions R2 and R10 can proceed spontaneously as the temperature increases, but the reactions R3 and R11 still cannot proceed spontaneously at very high temperatures. This is because the electronegativity of F is greater than that of SF n (n = 1-5), so the stability of SF n + in the product is better than F + . The reaction process curve and mechanism of other reactants SF m (m = 1-4) are similar to that of SF 5 and SF 6 . Please refer to the supplementary materials for details.

The electron impact decomposition process of SF n (n = 1-6)
SF n in gas insulation equipment will be decomposed by energy because of electron impact in addition to simple thermal decomposition. Figure 5 shows the change of △G of R4-R8 reaction at 298-10,000 K. From Fig. 5, we realize that △G of R4-R8 showed a decreasing trend with the increase of temperature. SF 6 is a highly electronegative gas. When the energy of electrons in space is low, SF 6 can be combined with electrons in space to form a metastable molecular group (SF 6 )*. In a short while, this molecular group can further generate anion SF 6 − . That is, R4: SF 6 + e → SF 6 − . When the temperature is 298 K, △G is 126.1 kJ/mol; when the temperature rises to 5000 K, △G is − 246.5 kJ/mol; when the temperature reaches 10,000 K, △G is − 255.5 kJ/mol. With the temperature rise, the △G of this reaction was less than zero, so it could proceed spontaneously.
When electrons continue to hit SF 6 − , R8: SF 6 − + e → SF 5 − + F − occurs. When the temperature is 298 K, △G is 209 kJ/mol; when the temperature rises to 5000 K, △G is − 403.6 kJ/mol; when the temperature When the energy of electrons hitting SF 6 is high, SF 6 + e → SF 6 − reaction will occur first, and then, SF 6 − will be decomposed because of the huge energy of electrons, and three reactions of R5-R7 may occur: SF 6 − → SF 5 − + F, SF 6 − → SF 5 + F − , SF 6 − → SF 5 + F + e. At a temperature of 298 K, the △G of R5 is 105.2 kJ/mol; with a rise to about 1200 K, it decreases to 0 kJ/mol; when the temperature reaches 10,000 K, the △G is − 933.3 kJ/mol. The △G of R6 at 298 K is 105.2 kJ/mol; when the temperature increases to about 2600 K, it drops to 0 kJ/mol; when the temperature reaches 10,000 K, △G is − 545.4 kJ/mol. The △G of R7 at 298 K is 501.3 kJ/mol; when the temperature rises to about 3800 K, it drops to 0 kJ/mol, and when the temperature reaches 10,000 K, the △G is − 1018.5 kJ/mol. Since the curve of reactions R5-R7 has an intersection point in the temperature range of 298-10,000 K, the reaction that takes place with temperature rise varies. At 298-8700 K, R5 has the lowest △G, so it is most likely to occur. The reaction produces SF 5 − and F. The △G of R7 is the lowest at 8700-10,000 K, and the probability of R7 is greater in this temperature range. Figure 6 shows the change of ΔG of the R12-R16 reaction at a temperature of 298-10,000 K. It can be seen from Fig. 6 that the △G of R13-R16 shows a downward trend with temperature rise, but the △G of R12 increases with increasing temperature. When the electron energy in the space is low, the R12 reaction will occur: SF 5 + e → SF 5 − .
When the temperature is 298 K, the △G is − 396.1 kJ/ mol; when the temperature is increased to 5000 K, the △G is − 222.5 kJ/mol; when the temperature reaches 10,000 K, the △G is 85.2 kJ/mol, showing an upward trend with increased temperature. When electrons continue to hit SF 5 − , R16 will occur: SF 5 − + e → SF 4 − + F − . When the temperature of R16 is 298 K, △G is 32.2 kJ/mol; when the temperature is increased to 5000 K, △G is − 340.7 kJ/mol; when the temperature reaches 10,000 K, △G is − 589.2 kJ/mol. At 298 K, the △G of this reaction is very low and it is likely to take place. With an increase in temperature, the reaction can proceed spontaneously.
When the energy of electrons hitting SF 5 is high, SF 5 + e → SF 5 − reaction will occur first, and then, SF 5 − will be decomposed as a result of the huge energy of electrons, and three reactions R13-R15 may occur: SF 5 − → SF 4 − + F, SF 5 − → SF 4 + F − , SF 5 − → SF 4 + F + e. When the temperature is 298 K, the △G of R13 is 346.4 kJ/mol; when the temperature rises to about 2600 K, it drops to 0 kJ/mol; and when the temperature reaches 10,000 K, the △G is − 1062.2 kJ/mol. The △G of R14 at 298 K is 215.9 kJ/ mol; when the temperature rises to about 2300 K, it drops to 0 kJ/mol, and when the temperature reaches 10,000 K, the △G is − 756 kJ/mol. The △G of R15 at 298 K is 530.1 kJ/ mol; when the temperature rises to about 3500 K, it drops to 0 kJ/mol, and when the temperature reaches 10,000 K, the △G is − 1229.1 kJ/mol. In the temperature range of 298-3250 K, the △G of R14 is the lowest, so there is a Table 4 Comparison of bond dissociation energies between this paper and experiment, Zigger's paper [7], and Cheung's paper [23]    high likelihood of occurrence. The reaction produces SF 4 and F − . At 3250-6700 K, the △G of R13 is the lowest, and the probability of occurrence of R13 is higher in this temperature range. When the temperature continues to rise to 6700-10,000 K, the probability of R15 is greatest. Figure 7 shows the change of ΔG of the R20-R24 reaction at a temperature of 298-10,000 K. It can be seen from Fig. 7 that the △G of R21-R24 displays a downward trend with increasing temperature, but the △G of R20 rises with increasing temperature. When the electron energy in the space is low, the R20 reaction will occur: SF 4 + e → SF 4 − . When the temperature is 298 K, the △G is − 183.7 kJ/ mol; when the temperature is increased to 5000 K, the △G is -73 kJ/mol; when the temperature reaches 10,000 K, the △G is 166.8 kJ/mol, showing an upward trend with increased temperature.
When electrons continue to hit SF 4 − , R24 will occur: SF 4 − + e → SF 3 − + F − . When the temperature of R24 is 298 K, △G is − 110.9 kJ/mol; when the temperature is increased to 5000 K, △G is − 284.4 kJ/mol; when the temperature reaches 10,000 K, △G is − 319.3 kJ/mol. The △G of this reaction is less than zero, so it can carry on spontaneously. When the energy of electrons hitting SF 4 is high, the SF 4 + e → SF 4 − reaction will take place first, and then, SF 4 − will be decomposed due to the huge energy of the electrons, and three reactions R21-R23 may occur: When the temperature of R21 is 298 K, △G is 203.3 kJ/mol; with a rise to about 2200 K, it drops to 0 kJ/mol; when the temperature reaches 10,000 K, △G is − 792.3 kJ/mol. The △G of R22 at 298 K is 242.1 kJ/mol; when the temperature rises to about 2700 K, it drops to 0 kJ/mol, and when the temperature reaches 10,000 K, the △G is − 687.4 kJ/mol. The △G of R23 at 298 K is 556.3 kJ/mol; with the temperature rise to about 3700 K, it drops to 0 kJ/mol, and when the temperature reaches 10,000 K, the △G is − 1160.4 kJ/mol. In the temperature range of 298-5800 K, the ΔG of R21 is the lowest, so it has the highest likelihood to take place. The reaction produces SF 3 − and F. The ΔG of R23 is the lowest at 5800-10,000 K, and the probability of occurrence of R23 is the highest in this temperature range. Figure 8 shows the change of the ΔG of the R28-R32 reaction at a temperature of 298-10,000 K. It can be seen from Fig. 8 that the △G of R29-R32 shows a downward trend with temperature rise, but the △G of R28 increases with increasing temperature. When the electron energy in the space is low, the R28 reaction will occur: SF 3 + e → SF 3 − . When the temperature is 298 K, △G is − 353 kJ/mol; when the temperature rises to 5000 K, △G is − 63.6 kJ/mol; when the temperature reaches 10,000 K, △G is 368.1 kJ/mol, showing an upward trend as the temperature rises. When electrons continue to hit SF 3 − , R32 will occur: SF 3 − + e → SF 2 − + F − . When the temperature of R32 is 298 K, △G is − 111.9 kJ/mol; on increasing it to 5000 K, △G is − 28.8 kJ/mol; when the temperature reaches 10,000 K, △G is − 4.5 kJ/mol. The △G of this reaction is less than zero, so it can proceed spontaneously.
When the energy of electrons hitting SF 3 is high, the SF 3 + e → SF 3 − reaction will occur first, and then, SF 3 − will decompose as a result of the huge energy of the electrons, and three reactions R29-R31 may occur: SF 3 − → SF 2 − + F, SF 3 − → SF 2 + F − , SF 3 − → SF 2 + F + e. The △G of R29 at 298 K is 426.1 kJ/mol; when the temperature rises to about 4600 K, it drops to 0 kJ/mol, and with the temperatures at 10,000 K, the △G is − 477.6 kJ/mol. The △G of R30 at 298 K is 183.3 kJ/mol; when the temperature rises to about 2000 K, it drops to 0 kJ/mol, and when the temperature reaches 10,000 K, the △G is − 791.4 kJ/mol. The △G of R31 at 298 K is 497.5 kJ/mol; when the temperature rises to about 3300 K, it drops to 0 kJ/mol, and when the temperature reaches 10,000 K, the △G is − 1264.5 kJ/mol. In the temperature range of 298-5000 K, R30 has the lowest △G, so it has the highest occurrence likelihood. The reaction produces SF 2 and F − . The G of R31 is the lowest at 5000-10,000 K, and the probability of occurrence of R31 is the highest in this temperature range. Figure 9 shows the change of ΔG of the R36-R40 reaction at a temperature of 298-10,000 K. It can be seen from Fig. 9 that the △G of R37-R40 shows a downward trend with increasing temperature, but the △G of R36 increases with increasing temperature. With a low electron energy in the space, the R36 reaction will occur: SF 2 + e → SF 2 − . When the temperature is 298 K, the △G is − 71.4 kJ/mol; when the temperature is increased to 5000 K, the △G is 272.6 kJ/mol; when the temperature reaches 10,000 K, the △G is 786.9 kJ/mol, showing an upward trend with the increase of temperature.
When electrons continue to hit SF 2 − , R40 will occur: SF 2 − + e → SF − + F − . When the temperature of R40 is 298 K, △G is − 143.9 kJ/mol; when the temperature is increased to 5000 K, △G is -389 kJ/mol; and when the temperature reaches 10,000 K, △G is − 549.8 kJ/mol. The △G of this reaction is less than zero, so it can proceed spontaneously.
When the energy of electrons hitting SF 2 is high, the SF 2 + e → SF 2 − reaction will occur first, and then, SF 2 − will be decomposed because of the huge electrons' energy, and three reactions R37-R39 may occur: SF 2 − → SF − + F, SF 2 − → SF + F − , SF 2 − → SF + F + e. The △G of R37 at 298 K is 170.3 kJ/mol; when the temperature rises to about 1750 K, it drops to 0 kJ/mol, and when the temperature reaches 10,000 K, the △G is − 1072.8 kJ/mol. The △G of R38 at 298 K is 60.7 kJ/mol; when the temperature rises to about 850 K, it is reduced to 0 kJ/mol, and when the temperature reaches 10,000 K, the △G is − 1098.5 kJ/mol. The △G of R39 at 298 K is 374.9 kJ/mol; when the temperature rises to about 2500 K, it reduces to 0 kJ/mol, and when the temperature reaches 10,000 K, the △G is − 1571.6 kJ/mol. The temperature is in the range of 298-4900 K, and R38 has the lowest △G, so it has the highest occurrence likelihood. The reaction produces SF and F − . The △G of R39 is the lowest at 4900-10,000 K, and the probability of occurrence of R39 is the highest in this temperature range. Figure 10 shows the change of △G in the R44-R48 reaction at a temperature of 298-10,000 K. It can be seen from Fig. 10 that the △G of R45-R48 shows a downward trend when the temperature is increased, but the △G of R44 increases with increasing temperature. When the electron energy in the space is low, the R44 reaction will occur: SF + e → SF − . When the temperature is 298 K, △G is − 204.6 kJ/mol; when the temperature rises to 5000 K, △G is 100.2 kJ/mol; when the temperature reaches 10,000 K, △G is 548.8 kJ/mol, showing an upward trend with increasing temperature.
When electrons continue to hit SF − , R48 will occur: SF − + e → S − + F − . When the temperature of R48 is 298 K, △G is 9.9 kJ/mol; when the temperature is increased to 5000 K, △G is − 140.2 kJ/mol; with the temperatures at 10,000 K, △G is − 200.6 kJ/mol. At 298 K, the ΔG of the reaction is relatively low. As the temperature increases, the ΔG decreases to below 0, which was easy to occur.
When the energy of the electrons hitting the SF is high, the SF + e → SF − reaction will occur first, and then, the SF − will decompose because of the huge energy of the electrons, and three reactions R37-R39 may occur: SF − → S − + F, SF − → S + F − , SF − → S + F + e. The △G of R45 at 298 K is 324.1 kJ/mol; when the temperature rises to about 3600 K, it is minimized to 0 kJ/mol, and when the temperature reaches 10,000 K, the △G is − 673.6 kJ/ mol. The △G of R46 at 298 K is 193.2 kJ/mol; when the temperature rises to about 2300 K, it goes down to 0 kJ/ mol, and when the temperature reaches 10,000 K, the △G is − 781.3 kJ/mol. The △G of R47 at 298 K is 507.4 kJ/mol; when the temperature rises to about 3500 K, it drops to 0 kJ/ mol, and when the temperature reaches 10,000 K, the △G is − 1254.4 kJ/mol. In the temperature range of 298-4900 K, R46 has the lowest ΔG, so it is most probable to take place. The reaction produces S and F − . The △G of R47 is the lowest at 4900-10,000 K, and the probability of occurrence of R47 is the highest in this temperature range.
We have noticed the △G of R4(SF 6 + e → SF 6 − ) gradually decreases with the increase of temperature, but the △G of SF n + e → SF n − (n < 6) increases with increasing temperature. The △G of a chemical reaction is defined as Among them, △H is the enthalpy change, T is the temperature, and △S is the entropy change. Through the previous calculations, we obtained the △H and △S of all reaction processes at the same time, and the entropy of electrons was obtained in Fifen's article. Figures 11-13 are obtained by calculating other thermodynamic data of these six reactions.
From Fig. 11, it can be found that the ΔH of these six reactions decreases with the increase of temperature, and the rate of decrease is almost the same, and they are all less than zero.
From Fig. 12, it can be found that the entropy changes of these six reactions all decrease with the increase of temperature. The difference is that the entropy change of R4 is always greater than 0 in the temperature range of 298-10,000 K, while the entropy change of SF n + e → SF n − (n < 6) is less than 0 with increasing temperature.

ΔG = ΔH − ΔTS
It can also be seen from Fig. 13 that the rate of decrease of △T·S product of R4 is much lower than that of the other five reactions, and the decrease rate of the △T·S is lower than that of ΔH. It can be seen from the definition of free energy that the △G of R4 increases with increasing temperature. In the other five reactions, the △T·S decrease rate is greater than the decrease rate of ΔH, that is, the increase rate of -△T·S is greater than the decrease rate of ΔH. Therefore, the △G of SF n + e → SF n − (n < 6) increases with increasing temperature.
In the process of SF n − decomposition, the heterolysis reaction of SF n − occurs when the temperature is low, which is a process in which SF n-1 competes with the F atom for electrons. As the temperature rises, there are three twostep paths to go from SF n − to [SF n-1 + F + e], as shown in For the SF n − + e → SF n-1 − + F − reaction, the energy required is lowest at lower temperatures. Because this reaction requires more electrons to collide with SF n , it is most likely to occur when there are a large number of electrons in space after the discharge occurs inside the SF 6 switchgear, for example, continuous partial discharge conditions inside the equipment.

Conclusion
This paper uses quantum chemistry theory to study the reaction mechanism of SF n thermal decomposition and electrical decomposition at 298-10,000 K, including a total of 17 particles and 48 chemical reactions. The Gibbs free energy data of electrons are acquired by cubic spline difference fitting, and the electrons are taken into account in the reaction equation. Structural optimizations and thermal correction to Gibbs free energy for the reactants and products were performed at the B3LYP/6-311 + + G(d,p) level of theory. The single-point energies of all species were obtained at the CCSD(T)/aug-cc-PVTZ level. The frequency vibration factor (0.967) is taken into consideration. The main conclusions drawn are: (1) In the temperature range of 298-10,000 K, the △G of SF n thermal decomposition and homocracking reaction starts to decrease from 200 kJ/mol, while the △G of the other two heterocracking reactions starts to decrease from 1000 kJ/mol and 2000 kJ/mol respectively. Both show a downward trend with an almost similar slope, and a homolytic reaction is more likely to occur. (2) In the temperature range of 298-10,000 K, the SF n electron impact decomposition process can be divided into three possibilities based on the size of the electron energy. When the electron energy is low, SF n + e → SF n − occurs, and the △G of SF 5 , SF 4 , SF 3 , SF 2 , and SF decomposition reaction increases with the rise in temperature, while the △G of SF 6 decomposition decreases with increasing temperature.
(3) When the electron energy is high, the electrons hitting SF n will not generate SF n − but directly decompose SF n − : In the temperature range of 298-8700 k, △G of R5 is the lowest, so it has the highest probable occurrence. SF 6 − decomposition produces SF 5 − and F. In the temperature range of 8700-10,000 K, △G of R7 is the lowest, and R7 has a greater probability of occurrence in this temperature range. (4) In the temperature range of 298-3250 K, the △G of R14 is the lowest, so it will most likely occur. SF 5 − decomposes to produce SF4 and F − . In the temperature range of 3250-6700 K, the △G of R13 is the lowest, and the probability of occurrence of R13 is greater in this temperature range. SF 5 − decomposes to produce SF 4 − and F. When the temperature continues to rise to 6700-10,000 K, the probability of occurrence of R15 is greatest. (5) In the temperature range of 298-5800 K, the ΔG of R21 is the lowest, so it has the highest occurrence likelihood. SF 4 − decomposes to produce SF 3 − and F. In the temperature range of 5800-10,000 K, the △G of R23 is the lowest, and the probability of occurrence of R23 is the highest in this temperature range. (6) In the temperature range of 298-5000 K, R30 has the lowest △G, so it is most probable to occur. SF 3 − decomposition produces SF 2 and F − . In the temperature range of 5000-10,000 K, the △G of R31 is the lowest, and the probability of occurrence of R31 is the highest in this temperature range. (7) In the temperature range of 298-4900 K, R38 has the lowest △G, so it is most likely to occur. SF 2 − generates SF and F − . In the temperature range of 4900-10,000 K, the △G of R39 is the lowest, and the probability of occurrence of R39 is the highest in this temperature range. (8) In the temperature range of 298-4900 K, R46 has the lowest ΔG; thus, it has the highest occurrence likeli- Fig. 13 △T·S of SF n + e → SF n − varies with temperature hood. The decomposition of SF − produces S and F − . In the temperature range of 4900-10,000 K, the △G of R47 is the lowest, and the probability of occurrence of R47 is the highest in this temperature range. (9) When the second electron hits SF n − , the SF n − + e → SF n−1 − + F − occurs. And, the ΔG of the reaction gradually decreases with the increase of temperature. The ΔG of this series of reactions is lower and more likely to occur.
This work provides a reference for studying the byproducts of the reaction of SF 6 with micro water or micro oxygen.
Author contribution There were equal contributions of the authors to the completion of this work.

Availability of data and material
The data that support the findings of this study are available within the article.
Code availability The author's organization owns the copyright of the software program used in the article, and there is no custom code in this article.

Competing interests
The authors declare no competing interests.