# Interaction Study of Oxygen and Iron-Sulfur Clusters Based on the Density Functional Theory

Authors: Jiancun Gao; Hongbin Sui; Siyuan Wu; Renyou Zhang; Mengxin Zhang; Bolun Cui; Huilin Chu
Journal: International Journal of Chemical Engineering
 (2022)

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## Abstract

For the petrochemical industry, the spontaneous burning of iron sulfide compounds has been a major issue. In this study, XRD characterization of samples of iron sulfide compounds with spontaneous combustion tendency revealed that amorphous FeS was the primary constituent of the samples. A molecular simulation was used to build an amorphous FeS cluster model, and the density functional theory was used to examine the adsorption and reactivity characteristics of Fe4S4 clusters with O2. Different adsorption structures are generated by considering different adsorption sites and the electronic characteristics of each adsorption structure are evaluated. The results show that O2 prefers to adsorb around Fe atoms and has repulsion with S atoms, and the adsorption energy is maximum when two O atoms are co-adsorbed around Fe atoms, which is 198.13 kJ/mol. After adsorption charge, oxygen is in the superoxide state. The calculation of the reaction path divides the reaction process into different stages and considers different reaction routes. A thorough evaluation of the energy barriers and reaction energies of the two exothermic reactions leads to the conclusion that reaction path 1 is the optimal reaction path, and the reaction can release a total of 582.76 kJ/mol of heat. According to calculations, dimeric sulfur S2 must absorb a large part amount of energy in order to conduct the oxidation process. However, because S2 is present in the Fe4S4 reaction system, it may start the oxidation reaction by absorbing heat from the system and releasing 470.94 kJ/mol of heat. As a result, we conclude that this spontaneous exothermic reaction is a major cause of iron sulfide compounds spontaneous combustion. The thermal oxidation of the dimeric sulfur S2 generated in the reaction system releases heat that aggregates with the heat from the Fe4S4 cluster’s oxidation reaction system, eventually causing spontaneous combustion as a result of the heat’s continual buildup. In this study, we explore the reason for the extremely easy oxidation and spontaneous burning of iron sulfide compounds from a microscopic perspective to provide a theoretical foundation for the prevention and control of iron sulfide compound spontaneous combustion in the petrochemical sector.


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## Body

## 1. Introduction

Due to their distinctive chemical characteristics, transition metal sulfide clusters have drawn considerable interest in a number of disciplines, including materials science, geophysics, catalysis, and biology. There have been efforts to investigate these characteristic features from a microscopic perspective. In recent years, quantum chemical computation techniques based on the density functional theory have given an efficient means of investigating these transition metal complexes. This approach has been widely used in the investigation of transition metal complex adsorption and reaction processes. For example, studies on the interaction of water and the surface of CuAl2O4 [1], adsorption of Fe, Co, Ni, and other metals on the surface of CuAl2O4 [2], the electronic structure and magnetic aspects of monolayer MoS2 doped with 3d transition metal atoms and metal oxide clusters [3], and the mechanism of the acetylene hydrogenation reaction catalyzed by FeO, Fe2O3, Fe3O4 clusters [4], etc. The approach gives information on substances at the molecular level.Currently, iron-sulfur clusters are frequently used as models in theoretical investigations of sulfur-iron complexes. These iron-sulfur clusters have alternating iron-sulfur bonding, and planar rhombic [2Fe-2S] assembly generates bigger size iron-sulfur clusters [5, 6]. Knowing how to correctly describe the magnetic and structural characteristics of iron-sulfur clusters is one of the challenges faced by theoretical workers. Photoelectron spectroscopy (PES) studies of (FeS)m indicate that these iron-sulfur clusters may have multiple spin states. The iron-sulfur system is usually described by DFT, CASSCF, and CASPT2 methods in theoretical calculations [7–9]. However, the properties calculated by different generalized methods deviate from the experimental values. For example, parameters such as vertical ionization potential (VIP) and adiabatic electron affinity energy (AEA) differ greatly from experimental values. Amitouche et al. [10], Li et al. [11], and Yin et al. [12] tested the structure of the iron-sulfur system using a variety of generalized functions in combination with basis groups. Among them, the B3LYP generalized function and the PBE generalized function agree well with the experimental values, and these two generalized functions are consistent in describing the spin states of the iron-sulfur clusters, but both methods underestimate the experimental values of the interatomic distances in terms of structural properties. For the vibrational frequencies, the calculated results of B3LYP differ from the experimental values by 20%, while the PBE functional only differs from the experimental values by 6%. In addition, the two methods are consistent in the description of the adiabatic electron affinity energy (AEA) and the vertical ionization potential (VDE). Tazibt et al. [13] investigated the structure and magnetic properties of pure Fe clusters, on the basis of which the effect of doping with sulfur elements on the pure Fe cluster system was examined. The results show that the doping of sulfur with Fe enhances the binding energy of the atoms but has no significant effect on the magnetic properties of the system, implying that the magnetic properties of the iron-sulfur clusters are mainly dominated by the Fe atoms.Because the outermost d orbital of Fe atom in the iron-sulfur cluster contains unpaired single electrons, the iron-sulfur cluster has good reactivity [14, 15]. Iron-sulfur clusters were found to be very sensitive to oxygen (O2), carbon monoxide (CO), and nitric oxide (NO) in the study. When iron-sulfur clusters are in contact with gases such as O2, NO, and CO, CO and NO reduce the spin polarization and change the magnetic coupling of the clusters, and the reduction of spin polarization is reflected in the transition metal cluster atoms, especially the Fe atoms in contact with C or N. The effect of O2 chemisorption on the spin-polarized electronic structure is also quite significant, with oxygen tending to strongly decrease the spin polarization of Fe atoms and weaken Fe-Fe interactions, inducing antiparallel coupling. Heim et al. [16] performed kinetic measurements of the interaction of iron-sulfur clusters with N2 in an ion trap. The results show that iron-sulfur clusters can adsorb N2, and in addition, they present the first experimentally obtained binding energy of N2 with iron-sulfur clusters. Sandra M. Lang et al. [17] proposed that the reaction of iron-sulfur clusters with oxygen follows an oxygen-sulfur exchange mechanism, but this mechanism can only occur in a proton-free environment, while the oxidation reaction performance of iron-sulfur clusters will be better when water is present in the reaction environment [18].Active sulfur corrosion of equipment surfaces during crude oil refining and storage in the petrochemical sector frequently creates iron sulfide compounds that are prone to spontaneous combustion when exposed to oxygen or air. These iron sulfide compounds exhibit distinct electrical properties as well as exceptionally strong oxidation properties. Mackinawite [19], Cubic FeS [20–22], and pyrite had previously been recognized as the primary iron sulfide compounds. These iron sulfide compounds have amorphous structures [23] and are often loose and porous. For a long time, most investigations on this subject were conducted using experimental approaches, which cannot give insights into the microscopic mechanisms of iron sulfide compounds’ oxidation. This study uses the density functional theory to investigate the interactions between oxygen and iron-sulfur clusters, including oxygen adsorption, charge distribution, and reaction pathways. This offers a molecular-level understanding of the process underlying iron sulfide compound spontaneous combustion.


## 2. Computational Methods and Models

### 2.1. Computational Methods

In this work, we use the Dmol3 [24] module in Materials Studio software based on the density functional theory. We use the Perdew–Burke–Ernzerhof (PBE) [25] exchange-correlation generalization in the generalized gradient approximation (GGA) [26]. We choose the double numerical extended basis group (DNP) for all-electron calculations. The accuracy of the structural optimization parameters is fine, the energy convergence is 1.0 e − 5 Ha, the maximum force convergence is 0.002 Ha/Å, the maximum displacement convergence is 0.005 Å, and the self-consistent field (SCF) accuracy is set to 1.0 ∗ 10−6 ev. Because the iron sulfide compound system contains transition metal Fe, the 3d orbitals contain unpaired single electrons. Therefore, the ground state configuration of the system is in the high spin state. In previous studies, it was pointed out that the most stable configuration of the ground state of the Fe4S4 structure is the nine-fold state. Therefore, the calculations are performed in the nine-fold state in this work. It should be noted that the ground state stable structure of the oxygen molecule is the triplet state. The structures of O2 molecules and Fe4S4 clusters were optimized, respectively, and frequency calculations were performed on all optimized configurations. The vibration frequency results were all positive values, indicating that the optimized structure is a stable configuration on the potential energy surface. We use the LST/QST method to search and optimize the transition state and calculate the frequency of the transition state to ensure that there is a unique virtual frequency in the transition state. The adsorption energy is defined as follows:(1)Eads=EO2/FeS−EO2−EFeS,where Eads is the adsorption energy, EO2/FeS is the total energy of the model after adsorption, EO2 is the total energy of the oxygen molecule, and EFeS is the total energy of the iron sulfide cluster. According to the definition, the negative value of the adsorption energy indicates the exothermic process, and the larger the value, the stronger the adsorption of O2 and Fe4S4 clusters.


### 2.2. Computational Models

In this work, XRD characterization of iron sulfide samples with spontaneous combustion tendency was carried out and is shown in red in Figure1. It can be seen from the diffraction peaks in the figure that the crystallinity of the sample is poor, and the type of peak is a typical amorphous structure diffraction peak. Compared with the standard FeS diffraction pattern, the sample is amorphous FeS.Figure 1
Comparison of the experimental X-ray diffraction pattern of active iron sulfide compounds sample with simulated X-ray diffraction pattern of FeS crystal model.The FeS crystal structure was found in the inorganic crystal database, as illustrated in Figure2(a). The FeS crystal structure's XRD diffraction pattern was acquired by scanning the FeS crystal structure using the Reflex software, as demonstrated by the diffraction peaks highlighted in black in Figure 1.Figure 2
(a) FeS crystal model. (b) Fe4S4 cluster model. (c) O2 structure model. (Purple represents Fe atoms, yellow represents S atoms, and red represents O atoms). M represents spin multiplicity; bond length unit: Å.Comparisons were made between the experimental and simulated X-ray diffraction patterns. The X-ray diffraction peaks in the experiment appear at 16.7°, 30°, 38.8°, and 49.9°. The simulated X-ray diffraction peaks appear at corresponding angles of 17.6, 30.1, 39, and 50.45°. In other words, the discrepancy between the simulated and experimental diffraction peaks is kept to a maximum of 1°. Based on the FeS crystal model, the Fe4S4 cluster model was created. The cluster structure was then optimized and the result is shown in Figure 2(b). The optimized cluster structure was compared with previous research data [10] to confirm the reasonableness of the calculation method and structure used in this work, and the results of the comparison are provided in the supporting information. M denotes the spin multiplet degree. The bond length of the triplet state of the ground state oxygen molecule is 1.23 Å (as shown in Figure 2(c)).


## 2.1. Computational Methods

In this work, we use the Dmol3 [24] module in Materials Studio software based on the density functional theory. We use the Perdew–Burke–Ernzerhof (PBE) [25] exchange-correlation generalization in the generalized gradient approximation (GGA) [26]. We choose the double numerical extended basis group (DNP) for all-electron calculations. The accuracy of the structural optimization parameters is fine, the energy convergence is 1.0 e − 5 Ha, the maximum force convergence is 0.002 Ha/Å, the maximum displacement convergence is 0.005 Å, and the self-consistent field (SCF) accuracy is set to 1.0 ∗ 10−6 ev. Because the iron sulfide compound system contains transition metal Fe, the 3d orbitals contain unpaired single electrons. Therefore, the ground state configuration of the system is in the high spin state. In previous studies, it was pointed out that the most stable configuration of the ground state of the Fe4S4 structure is the nine-fold state. Therefore, the calculations are performed in the nine-fold state in this work. It should be noted that the ground state stable structure of the oxygen molecule is the triplet state. The structures of O2 molecules and Fe4S4 clusters were optimized, respectively, and frequency calculations were performed on all optimized configurations. The vibration frequency results were all positive values, indicating that the optimized structure is a stable configuration on the potential energy surface. We use the LST/QST method to search and optimize the transition state and calculate the frequency of the transition state to ensure that there is a unique virtual frequency in the transition state. The adsorption energy is defined as follows:(1)Eads=EO2/FeS−EO2−EFeS,where Eads is the adsorption energy, EO2/FeS is the total energy of the model after adsorption, EO2 is the total energy of the oxygen molecule, and EFeS is the total energy of the iron sulfide cluster. According to the definition, the negative value of the adsorption energy indicates the exothermic process, and the larger the value, the stronger the adsorption of O2 and Fe4S4 clusters.


## 2.2. Computational Models

In this work, XRD characterization of iron sulfide samples with spontaneous combustion tendency was carried out and is shown in red in Figure1. It can be seen from the diffraction peaks in the figure that the crystallinity of the sample is poor, and the type of peak is a typical amorphous structure diffraction peak. Compared with the standard FeS diffraction pattern, the sample is amorphous FeS.Figure 1
Comparison of the experimental X-ray diffraction pattern of active iron sulfide compounds sample with simulated X-ray diffraction pattern of FeS crystal model.The FeS crystal structure was found in the inorganic crystal database, as illustrated in Figure2(a). The FeS crystal structure's XRD diffraction pattern was acquired by scanning the FeS crystal structure using the Reflex software, as demonstrated by the diffraction peaks highlighted in black in Figure 1.Figure 2
(a) FeS crystal model. (b) Fe4S4 cluster model. (c) O2 structure model. (Purple represents Fe atoms, yellow represents S atoms, and red represents O atoms). M represents spin multiplicity; bond length unit: Å.Comparisons were made between the experimental and simulated X-ray diffraction patterns. The X-ray diffraction peaks in the experiment appear at 16.7°, 30°, 38.8°, and 49.9°. The simulated X-ray diffraction peaks appear at corresponding angles of 17.6, 30.1, 39, and 50.45°. In other words, the discrepancy between the simulated and experimental diffraction peaks is kept to a maximum of 1°. Based on the FeS crystal model, the Fe4S4 cluster model was created. The cluster structure was then optimized and the result is shown in Figure 2(b). The optimized cluster structure was compared with previous research data [10] to confirm the reasonableness of the calculation method and structure used in this work, and the results of the comparison are provided in the supporting information. M denotes the spin multiplet degree. The bond length of the triplet state of the ground state oxygen molecule is 1.23 Å (as shown in Figure 2(c)).


## 3. Results and Discussion

### 3.1. Adsorption of O2 on Fe4S4 Clusters

On Fe and S sites, respectively, we took into account O2 adsorbed. Each adsorption location is subdivided into three adsorption modes: O2 adsorbed at one end, O2 adsorbed at both ends, and O2 adsorbed at the Fe-S bond bridge location. To obtain stable adsorption structures, structural optimization and frequency calculations were done for each adsorption model (as shown in Figures 3 and 4). The information in Figure 5 includes the adsorption schematic and the adsorption energy for each adsorption struture.Figure 3
Adsorption structures of O2 on Fe sites on Fe4S4 clusters and the charge density of each adsorption structure. The bond lengths in the figure are in Å, 1 Å = 1 ∗ 10−10 m; the blue part of the charge density diagram indicates no charge aggregation, and the red part indicates charge aggregation.Figure 4
Adsorption structures of O2 on S sites on Fe4S4 clusters and the charge density of each adsorption structure. The bond lengths in the figure are in Å, 1 Å = 1 ∗ 10−10 m; the blue part of the charge density diagram indicates no charge aggregation, and the red part indicates charge aggregation.From Figure3(a), it can be seen that when two oxygen atoms are co-adsorbed on Fe atoms, the two Fe-O bonds formed have lengths of 2.08 Å and 2.09 Å, respectively, and the O-O bond grows from 1.23 Å to 1.34 Å in the ground state. It can be seen from the charge density diagram that a large number of charges are distributed around the Fe-O bond after O2 adsorption, which indicates that O2 forms chemisorption with Fe4S4. From the Mulliken charge population analysis (Table 1), a total of 0.35 e electrons were obtained by O2 after adsorption and the adsorption energy of this adsorption mode is −198.13 kJ/mol. In Figure 3(b), O2 was adsorbed on Fe atoms with one end and the O-O bond grew from the ground state of 1.23 Å to 1.30 Å The charge density diagram showed that a large number of charges were distributed around the Fe-O bond, indicating that this adsorption mode also belongs to chemisorption. It is calculated that O2 adsorption gains a total of 0.28 e electrons and the adsorption energy is −43.11 kJ/mol. In Figure 3(c), when O2 is adsorbed at the bridge site, the O-O bond length differs very little from the ground state bond length, and the distances between the two oxygen atoms and the Fe and S atoms are 3.67 Å and 3. 73 Å, respectively. It can be seen from the charge density diagram that there is no charge distribution between the O2 and Fe4S4 clusters and the Mulliken charges of the two O atoms are −0.06 and −0.08, respectively, indicating that this O2 did not involve in chemisorption with the Fe4S4 cluster. The calculated adsorption energy is 10.94 kJ/mol and this adsorption mode does not form a stable adsorption structure.Table 1
Mulliken atomic population values of O atoms before and after adsorption.
FigureBefore adsorptionAfter adsorptionO1O2O1O2A00−0.18−0.17B00−0.17−0.11C00−0.06−0.08d00−0.05−0.06e00−0.06−0.05f00−0.17−0.10When O2 is adsorbed at the S position, as shown in Figures 4(d)–4(f), O2 shows strong repulsion with Fe4S4 in one-end adsorption and two-end adsorption. The charge density diagram shows that there is no charge distribution between O2 and Fe4S4 clusters, and the O-O bond length is not much different from the ground state bond length. Mulliken’s atomic population also show no large charge transfer after O2 adsorption. This indicates that O2 will not adsorb at the S site. The adsorption energies of these two adsorption structures are 11.47 kJ/mol and 27.38 kJ/mol, respectively. The adsorption energy is positive, indicating that no chemical adsorption will be formed. In Figure 4(f), we examine O2 adsorption at the Fe-S bridge site; however, the calculations show that there is a repulsion between the O atom and the S atom and the other O atom forms a Fe-O bond with the Fe atom; this adsorption is similar to the O2 adsorption structure at one end of the Fe site with an O-O bond length of 1.30 Å and adsorption energy of −36.72 kJ/mol.The abovementioned analysis shows that O2, when adsorbed in the molecular state, tends to adsorb around Fe atoms on the Fe4S4 cluster and not around S atoms. The energy of 198.13 kJ/mol is released when two O atoms are co-adsorbed on Fe atoms, which provides the energy basis for the subsequent reaction process.Figure 5
Adsorption energy of O2 on Fe4S4 clusters. (ad represents adsorption).


### 3.2. Reaction Path Calculation

The reaction path of Fe4S4 with O2 was computed in this study, with the first two reaction stages occurring on the nine-fold state potential energy surface, and the last reaction stage occurring on the three-fold state potential energy surface. The initial stage of the reaction is the formation of the stage products Fe2S2O2 and dimeric sulfur (S2) from Fe4S4 and O2. As the reaction proceeds, new O atoms continue to react with these products to form FeO and dimeric sulfur (S2). It should be noted that dimeric sulfur (S2) is formed at different stages of the reaction and is eventually oxidized to SO2. The reaction potential energy profiles are given in Figures 6–8, where the initial adsorption structure is denoted by R, TS represents the transition state, and IM represents the intermediate. The initial reactant energy is used as the zero point to compute the energy difference of each intermediate, transition state, and product with regard to the reactants. Table 2 shows the unique imaginary frequencies of the reaction path’s transition states.Figure 6
The stage 1 reaction path of Fe4S4 clusters with O2 on the nine-fold state potential energy surface.Figure 7
The stage 2 reaction path of Fe4S4 clusters with O2 on the nine-fold state potential energy surface.Figure 8
The stage 3 reaction path of S2 with O2 on the triplet state potential energy surface.Table 2
Imaginary frequency of transition state in the reaction between O2 and Fe4S4 clusters.
SpeciesFrequency/cm−1TS1−483.77TS2−241.04TS3−62.04TS4−46.10TS5−91.56TS6−14.76TS7−56.66TS8−41.79TS9−264.29TS10−119.14TS11−404.57TS12−126.30TS13−9.41TS14−638.53TS15−744.97——


### 3.3. Reaction Path Analysis

#### 3.3.1. Stage 1: Fe4S4 Reacts with O2 to Form Fe4S2O2 and S2

When the Fe4S4 cluster comes in contact with O2, O2 preferentially adsorbs on the Fe atom of the Fe4S4 cluster to form the composite reactant R1. As shown in Figure 6, the reactions are discussed in two pathways depending on the different intermediates. The formation of the complex reactant R is an exothermic reaction. It was calculated that the process released 198.13 kJ/mol of energy. The reactant R forms the stable intermediate IM1 through the transition state TS1, during which the O-O bond breaks and the O atom attacks the flanking S atom to form an S-O bond, a process that requires overcoming an energy barrier of 49.9 kJ/mol. Intermediate IM1 overcomes the energy barrier of 64.56 kJ/mol to form intermediate IM2, and another O atom in O2 attacks the S atom below to form an S-O bond. The energy barrier of 10.28 kJ/mol formed by the transition state TS3 needs to be overcome from the intermediate IM2 to the formation stage product P1. Two S atoms in this process form dimeric sulfur S2, and the remaining part is the incompletely reacted Fe4S2O2.In reaction path 2, reactantR passes through the transition state TS4 to form intermediate IM3, a process that requires an energy barrier of 43.89 kJ/mol to be overcome. This process breaks the O-O bond, one of the O atoms is bonded to a Fe atom on one side. Intermediate IM3 passes through the transition state TS5 to form intermediate IM4, which requires an energy barrier of 18.31 kJ/mol to be overcome. This process involves the formation of a Fe-O bond by another O atom with the Fe atom below. Thereafter, two S atoms in intermediate IM4 form S2, a step that requires a large energy barrier to be experienced to proceed, which is calculated to be 166.85 kJ/mol for the formation of transition state TS6.In stage 1, the two reaction routes proceed through distinct intermediates and transition states to yield products P1 and P2. Both P1 and P2 are Fe4S2O2 and dimeric sulfur S2. The difference is that Fe4S2O2 in P1 is a blocky structure, while Fe4S2O2 in P2 is a planar structure. From the stage 1 reaction as a whole, the reaction of Fe4S4 with O2 to form Fe4S2O2 and S2 is similar to the substitution of sulfur atoms in Fe4S4 by oxygen atoms, which is consistent with the iron-sulfur cluster oxidation mechanism proposed by Sandra M. Lang et al. [17]. Fe4S2O2 and S2 will continue to react upon exposure to new O2, which we discuss in the reaction of stage 2.


#### 3.3.2. Stage 2: Fe4S2O2 Reacts with O2 to Form 4FeO and S2

When the reaction product Fe4S2O2 in stage 1 continues to react with O2, O2 also preferentially adsorbs around the Fe atom. This stage of the reaction takes into account the different intermediates and transition states, and we divide it into two reaction paths for discussion. Path 1 and path 2 correspond to the two paths in stage 1. O2 adsorption on the Fe4S2O2 cluster releases 200.06 kJ/mol of energy to form intermediate IM5, and after the transition state TS7 to form intermediate IM6, the O-O bond breaks in this step and one of the O atoms attacks the S atom to form an S-O bond, a process that requires overcoming an energy barrier of 44.17 kJ/mol. Intermediate IM6 overcomes the energy barrier of 18.67 kJ/mol passing through the transition state TS8 to form intermediate IM7. The S atom is replaced out of its original ligand environment during this process. Subsequently, another O atom attacks the S atom to form an S-O bond, as shown in IM8 in Figure 7. This step requires overcoming an energy barrier of 74.41 kJ/mol. IM8 passes through the transition state TS10 to form product P3. This process overcomes the energy barrier of 18.75 kJ/mol and the S atom is completely replaced out of the original ligand environment to form dimeric sulfur S2 and FeO.In path 2, O2 adsorbed on Fe atoms releases 179.25 kJ/mol of energy to form intermediate IM9. IM9 overcomes the energy barrier of 40.39 kJ/mol and passes through the transition state TS11 to form intermediate IM10. After the O-O bond is broken, the O atom attacks the S atom to break the Fe-S bond. Subsequently, the O atom will continue to attack the sulfur atom leading to the complete reaction of the S atom and the formation of intermediate IM11. This process can proceed by overcoming an energy barrier of 80.5 kJ/mol. The intermediate IM11 overcomes an energy barrier of 63.83 kJ/mol to form the product P4. The two products of this stage, P3 and P4, are both FeO and dimeric sulfur (S2).When seen as a whole, the stage reaction is effectively a continuous reaction process, with stage 2 occurring after stage 1. FeO and S2 are eventually produced in both phases of the reaction. Because FeO is unstable, it will progressively oxidize in the environment to generate Fe2O3, a process that is thought to occur naturally and is not further explored in this research.


#### 3.3.3. Stage 3: S2 Reacts with 2O2 to Form 2SO2

Because SO2 is released during the oxidation of Fe4S4, the subsequent reaction of dimeric sulfur S2 is further investigated in this paper. The oxidation of S2 is treated as the third stage of the reaction in this work, but it does not occur exactly after the first two stages in time because S2 is generated in both of the first two processes. The oxidation of S2 takes place on the triplet potential energy surface. S2 interacts with O2 to form SO2, and the initial step of the reaction requires 275.59 kJ/mol energy absorption. As a result, under ambient circumstances, S2 does not oxidize. However, the initial two stages of the oxidation reaction system of iron sulfide compounds emit a significant amount of heat, raising the temperature of the entire reaction system and providing a reaction foundation for the oxidation of S2. When S2 has absorbed sufficient heat, the reaction can proceed by only overcoming a small energy barrier. At this stage, the S-S bond breaks and the S atom attacks O2 to form the SO2 molecule. To form SO2, the intermediate IM13 merely has to overcome a potential barrier of 19.9 kJ/mol.The reaction between Fe4S4 and O2 is exothermic at every stage, which is advantageous thermodynamically. The heat of reaction for each stage is displayed in Table 3. On adsorption in the first stage of the reaction, the two reactants in path 1 generated 198.13 kJ/mol of heat, which laid the groundwork for the subsequent reaction. The reaction between reactant R and stage product P1 is exothermic. The maximal energy barrier encountered throughout this process is 64.56 kJ/mol, and the heat emitted at the start of the reaction is enough to keep the reaction going. The heat released from reaction path 1 is calculated to be 294.78 kJ/mol. In contrast, the maximum energy barrier to be overcome in reaction path 2 is 166.85 kJ/mol required to pass through TS6, and the release of 369.99 kJ/mol from the start of the reaction to the formation of intermediate IM5 is sufficient to support the reaction. Therefore, reaction path 1 is more likely to occur than reaction path 2 in comparison.Table 3
Heat of reaction for each phase of the reaction.
ProcessReaction pathHeat of reaction/kJ·mol−1Stage1Path1Fe4S4+O2⟶P1−294.78Path2Fe4S4+O2⟶P2−222.82Stage2Path1Fe4S2O2⟶P3−287.98Path2Fe4S2O2⟶P4−278.83Stage3S2+2O2⟶2SO2−470.94Overall, the stage’s two chemical paths are both exothermic, with path 1 releasing 287.98 kJ/mol of heat and path 2 releasing 278.83 kJ/mol of heat. The largest energy barrier to cross in reaction path 1 is 74.41 kJ/mol. The largest energy barrier that must be overcome in reaction path 2 is 80.49 kJ/mol. Reaction path 1 facilitates the reaction’s progression more than reaction path 2. In the oxidation of Fe4S4 clusters, reaction path 1 is the optimum reaction channel. However, whether reaction path 1 or reaction path 2, the reaction products are FeO and S2, and the entire reaction process is exothermic.There may be no SO2 release at the start of the reaction because the S2 yield and heat released by the reaction system are insufficient to sustain the oxidation of dimeric sulfur S2. Dimer sulfur S2 is gradually oxidized as the reaction progresses, and as the reaction system continues to build up heat, it will encourage the oxidation of dimer sulfur S2 and release a significant quantity of heat, which raises the reaction system’s temperature once more. Table 3 shows that the heat of the S2 oxidation reaction in stage 3 is 470.94 kJ/mol. Therefore, the oxidative exothermic process of S2 has a nonnegligible effect on the spontaneous combustion of iron sulfide compounds.


## 3.1. Adsorption of O2 on Fe4S4 Clusters

On Fe and S sites, respectively, we took into account O2 adsorbed. Each adsorption location is subdivided into three adsorption modes: O2 adsorbed at one end, O2 adsorbed at both ends, and O2 adsorbed at the Fe-S bond bridge location. To obtain stable adsorption structures, structural optimization and frequency calculations were done for each adsorption model (as shown in Figures 3 and 4). The information in Figure 5 includes the adsorption schematic and the adsorption energy for each adsorption struture.Figure 3
Adsorption structures of O2 on Fe sites on Fe4S4 clusters and the charge density of each adsorption structure. The bond lengths in the figure are in Å, 1 Å = 1 ∗ 10−10 m; the blue part of the charge density diagram indicates no charge aggregation, and the red part indicates charge aggregation.Figure 4
Adsorption structures of O2 on S sites on Fe4S4 clusters and the charge density of each adsorption structure. The bond lengths in the figure are in Å, 1 Å = 1 ∗ 10−10 m; the blue part of the charge density diagram indicates no charge aggregation, and the red part indicates charge aggregation.From Figure3(a), it can be seen that when two oxygen atoms are co-adsorbed on Fe atoms, the two Fe-O bonds formed have lengths of 2.08 Å and 2.09 Å, respectively, and the O-O bond grows from 1.23 Å to 1.34 Å in the ground state. It can be seen from the charge density diagram that a large number of charges are distributed around the Fe-O bond after O2 adsorption, which indicates that O2 forms chemisorption with Fe4S4. From the Mulliken charge population analysis (Table 1), a total of 0.35 e electrons were obtained by O2 after adsorption and the adsorption energy of this adsorption mode is −198.13 kJ/mol. In Figure 3(b), O2 was adsorbed on Fe atoms with one end and the O-O bond grew from the ground state of 1.23 Å to 1.30 Å The charge density diagram showed that a large number of charges were distributed around the Fe-O bond, indicating that this adsorption mode also belongs to chemisorption. It is calculated that O2 adsorption gains a total of 0.28 e electrons and the adsorption energy is −43.11 kJ/mol. In Figure 3(c), when O2 is adsorbed at the bridge site, the O-O bond length differs very little from the ground state bond length, and the distances between the two oxygen atoms and the Fe and S atoms are 3.67 Å and 3. 73 Å, respectively. It can be seen from the charge density diagram that there is no charge distribution between the O2 and Fe4S4 clusters and the Mulliken charges of the two O atoms are −0.06 and −0.08, respectively, indicating that this O2 did not involve in chemisorption with the Fe4S4 cluster. The calculated adsorption energy is 10.94 kJ/mol and this adsorption mode does not form a stable adsorption structure.Table 1
Mulliken atomic population values of O atoms before and after adsorption.
FigureBefore adsorptionAfter adsorptionO1O2O1O2A00−0.18−0.17B00−0.17−0.11C00−0.06−0.08d00−0.05−0.06e00−0.06−0.05f00−0.17−0.10When O2 is adsorbed at the S position, as shown in Figures 4(d)–4(f), O2 shows strong repulsion with Fe4S4 in one-end adsorption and two-end adsorption. The charge density diagram shows that there is no charge distribution between O2 and Fe4S4 clusters, and the O-O bond length is not much different from the ground state bond length. Mulliken’s atomic population also show no large charge transfer after O2 adsorption. This indicates that O2 will not adsorb at the S site. The adsorption energies of these two adsorption structures are 11.47 kJ/mol and 27.38 kJ/mol, respectively. The adsorption energy is positive, indicating that no chemical adsorption will be formed. In Figure 4(f), we examine O2 adsorption at the Fe-S bridge site; however, the calculations show that there is a repulsion between the O atom and the S atom and the other O atom forms a Fe-O bond with the Fe atom; this adsorption is similar to the O2 adsorption structure at one end of the Fe site with an O-O bond length of 1.30 Å and adsorption energy of −36.72 kJ/mol.The abovementioned analysis shows that O2, when adsorbed in the molecular state, tends to adsorb around Fe atoms on the Fe4S4 cluster and not around S atoms. The energy of 198.13 kJ/mol is released when two O atoms are co-adsorbed on Fe atoms, which provides the energy basis for the subsequent reaction process.Figure 5
Adsorption energy of O2 on Fe4S4 clusters. (ad represents adsorption).


## 3.2. Reaction Path Calculation

The reaction path of Fe4S4 with O2 was computed in this study, with the first two reaction stages occurring on the nine-fold state potential energy surface, and the last reaction stage occurring on the three-fold state potential energy surface. The initial stage of the reaction is the formation of the stage products Fe2S2O2 and dimeric sulfur (S2) from Fe4S4 and O2. As the reaction proceeds, new O atoms continue to react with these products to form FeO and dimeric sulfur (S2). It should be noted that dimeric sulfur (S2) is formed at different stages of the reaction and is eventually oxidized to SO2. The reaction potential energy profiles are given in Figures 6–8, where the initial adsorption structure is denoted by R, TS represents the transition state, and IM represents the intermediate. The initial reactant energy is used as the zero point to compute the energy difference of each intermediate, transition state, and product with regard to the reactants. Table 2 shows the unique imaginary frequencies of the reaction path’s transition states.Figure 6
The stage 1 reaction path of Fe4S4 clusters with O2 on the nine-fold state potential energy surface.Figure 7
The stage 2 reaction path of Fe4S4 clusters with O2 on the nine-fold state potential energy surface.Figure 8
The stage 3 reaction path of S2 with O2 on the triplet state potential energy surface.Table 2
Imaginary frequency of transition state in the reaction between O2 and Fe4S4 clusters.
SpeciesFrequency/cm−1TS1−483.77TS2−241.04TS3−62.04TS4−46.10TS5−91.56TS6−14.76TS7−56.66TS8−41.79TS9−264.29TS10−119.14TS11−404.57TS12−126.30TS13−9.41TS14−638.53TS15−744.97——


## 3.3. Reaction Path Analysis

### 3.3.1. Stage 1: Fe4S4 Reacts with O2 to Form Fe4S2O2 and S2

When the Fe4S4 cluster comes in contact with O2, O2 preferentially adsorbs on the Fe atom of the Fe4S4 cluster to form the composite reactant R1. As shown in Figure 6, the reactions are discussed in two pathways depending on the different intermediates. The formation of the complex reactant R is an exothermic reaction. It was calculated that the process released 198.13 kJ/mol of energy. The reactant R forms the stable intermediate IM1 through the transition state TS1, during which the O-O bond breaks and the O atom attacks the flanking S atom to form an S-O bond, a process that requires overcoming an energy barrier of 49.9 kJ/mol. Intermediate IM1 overcomes the energy barrier of 64.56 kJ/mol to form intermediate IM2, and another O atom in O2 attacks the S atom below to form an S-O bond. The energy barrier of 10.28 kJ/mol formed by the transition state TS3 needs to be overcome from the intermediate IM2 to the formation stage product P1. Two S atoms in this process form dimeric sulfur S2, and the remaining part is the incompletely reacted Fe4S2O2.In reaction path 2, reactantR passes through the transition state TS4 to form intermediate IM3, a process that requires an energy barrier of 43.89 kJ/mol to be overcome. This process breaks the O-O bond, one of the O atoms is bonded to a Fe atom on one side. Intermediate IM3 passes through the transition state TS5 to form intermediate IM4, which requires an energy barrier of 18.31 kJ/mol to be overcome. This process involves the formation of a Fe-O bond by another O atom with the Fe atom below. Thereafter, two S atoms in intermediate IM4 form S2, a step that requires a large energy barrier to be experienced to proceed, which is calculated to be 166.85 kJ/mol for the formation of transition state TS6.In stage 1, the two reaction routes proceed through distinct intermediates and transition states to yield products P1 and P2. Both P1 and P2 are Fe4S2O2 and dimeric sulfur S2. The difference is that Fe4S2O2 in P1 is a blocky structure, while Fe4S2O2 in P2 is a planar structure. From the stage 1 reaction as a whole, the reaction of Fe4S4 with O2 to form Fe4S2O2 and S2 is similar to the substitution of sulfur atoms in Fe4S4 by oxygen atoms, which is consistent with the iron-sulfur cluster oxidation mechanism proposed by Sandra M. Lang et al. [17]. Fe4S2O2 and S2 will continue to react upon exposure to new O2, which we discuss in the reaction of stage 2.


### 3.3.2. Stage 2: Fe4S2O2 Reacts with O2 to Form 4FeO and S2

When the reaction product Fe4S2O2 in stage 1 continues to react with O2, O2 also preferentially adsorbs around the Fe atom. This stage of the reaction takes into account the different intermediates and transition states, and we divide it into two reaction paths for discussion. Path 1 and path 2 correspond to the two paths in stage 1. O2 adsorption on the Fe4S2O2 cluster releases 200.06 kJ/mol of energy to form intermediate IM5, and after the transition state TS7 to form intermediate IM6, the O-O bond breaks in this step and one of the O atoms attacks the S atom to form an S-O bond, a process that requires overcoming an energy barrier of 44.17 kJ/mol. Intermediate IM6 overcomes the energy barrier of 18.67 kJ/mol passing through the transition state TS8 to form intermediate IM7. The S atom is replaced out of its original ligand environment during this process. Subsequently, another O atom attacks the S atom to form an S-O bond, as shown in IM8 in Figure 7. This step requires overcoming an energy barrier of 74.41 kJ/mol. IM8 passes through the transition state TS10 to form product P3. This process overcomes the energy barrier of 18.75 kJ/mol and the S atom is completely replaced out of the original ligand environment to form dimeric sulfur S2 and FeO.In path 2, O2 adsorbed on Fe atoms releases 179.25 kJ/mol of energy to form intermediate IM9. IM9 overcomes the energy barrier of 40.39 kJ/mol and passes through the transition state TS11 to form intermediate IM10. After the O-O bond is broken, the O atom attacks the S atom to break the Fe-S bond. Subsequently, the O atom will continue to attack the sulfur atom leading to the complete reaction of the S atom and the formation of intermediate IM11. This process can proceed by overcoming an energy barrier of 80.5 kJ/mol. The intermediate IM11 overcomes an energy barrier of 63.83 kJ/mol to form the product P4. The two products of this stage, P3 and P4, are both FeO and dimeric sulfur (S2).When seen as a whole, the stage reaction is effectively a continuous reaction process, with stage 2 occurring after stage 1. FeO and S2 are eventually produced in both phases of the reaction. Because FeO is unstable, it will progressively oxidize in the environment to generate Fe2O3, a process that is thought to occur naturally and is not further explored in this research.


### 3.3.3. Stage 3: S2 Reacts with 2O2 to Form 2SO2

Because SO2 is released during the oxidation of Fe4S4, the subsequent reaction of dimeric sulfur S2 is further investigated in this paper. The oxidation of S2 is treated as the third stage of the reaction in this work, but it does not occur exactly after the first two stages in time because S2 is generated in both of the first two processes. The oxidation of S2 takes place on the triplet potential energy surface. S2 interacts with O2 to form SO2, and the initial step of the reaction requires 275.59 kJ/mol energy absorption. As a result, under ambient circumstances, S2 does not oxidize. However, the initial two stages of the oxidation reaction system of iron sulfide compounds emit a significant amount of heat, raising the temperature of the entire reaction system and providing a reaction foundation for the oxidation of S2. When S2 has absorbed sufficient heat, the reaction can proceed by only overcoming a small energy barrier. At this stage, the S-S bond breaks and the S atom attacks O2 to form the SO2 molecule. To form SO2, the intermediate IM13 merely has to overcome a potential barrier of 19.9 kJ/mol.The reaction between Fe4S4 and O2 is exothermic at every stage, which is advantageous thermodynamically. The heat of reaction for each stage is displayed in Table 3. On adsorption in the first stage of the reaction, the two reactants in path 1 generated 198.13 kJ/mol of heat, which laid the groundwork for the subsequent reaction. The reaction between reactant R and stage product P1 is exothermic. The maximal energy barrier encountered throughout this process is 64.56 kJ/mol, and the heat emitted at the start of the reaction is enough to keep the reaction going. The heat released from reaction path 1 is calculated to be 294.78 kJ/mol. In contrast, the maximum energy barrier to be overcome in reaction path 2 is 166.85 kJ/mol required to pass through TS6, and the release of 369.99 kJ/mol from the start of the reaction to the formation of intermediate IM5 is sufficient to support the reaction. Therefore, reaction path 1 is more likely to occur than reaction path 2 in comparison.Table 3
Heat of reaction for each phase of the reaction.
ProcessReaction pathHeat of reaction/kJ·mol−1Stage1Path1Fe4S4+O2⟶P1−294.78Path2Fe4S4+O2⟶P2−222.82Stage2Path1Fe4S2O2⟶P3−287.98Path2Fe4S2O2⟶P4−278.83Stage3S2+2O2⟶2SO2−470.94Overall, the stage’s two chemical paths are both exothermic, with path 1 releasing 287.98 kJ/mol of heat and path 2 releasing 278.83 kJ/mol of heat. The largest energy barrier to cross in reaction path 1 is 74.41 kJ/mol. The largest energy barrier that must be overcome in reaction path 2 is 80.49 kJ/mol. Reaction path 1 facilitates the reaction’s progression more than reaction path 2. In the oxidation of Fe4S4 clusters, reaction path 1 is the optimum reaction channel. However, whether reaction path 1 or reaction path 2, the reaction products are FeO and S2, and the entire reaction process is exothermic.There may be no SO2 release at the start of the reaction because the S2 yield and heat released by the reaction system are insufficient to sustain the oxidation of dimeric sulfur S2. Dimer sulfur S2 is gradually oxidized as the reaction progresses, and as the reaction system continues to build up heat, it will encourage the oxidation of dimer sulfur S2 and release a significant quantity of heat, which raises the reaction system’s temperature once more. Table 3 shows that the heat of the S2 oxidation reaction in stage 3 is 470.94 kJ/mol. Therefore, the oxidative exothermic process of S2 has a nonnegligible effect on the spontaneous combustion of iron sulfide compounds.


## 3.3.1. Stage 1: Fe4S4 Reacts with O2 to Form Fe4S2O2 and S2

When the Fe4S4 cluster comes in contact with O2, O2 preferentially adsorbs on the Fe atom of the Fe4S4 cluster to form the composite reactant R1. As shown in Figure 6, the reactions are discussed in two pathways depending on the different intermediates. The formation of the complex reactant R is an exothermic reaction. It was calculated that the process released 198.13 kJ/mol of energy. The reactant R forms the stable intermediate IM1 through the transition state TS1, during which the O-O bond breaks and the O atom attacks the flanking S atom to form an S-O bond, a process that requires overcoming an energy barrier of 49.9 kJ/mol. Intermediate IM1 overcomes the energy barrier of 64.56 kJ/mol to form intermediate IM2, and another O atom in O2 attacks the S atom below to form an S-O bond. The energy barrier of 10.28 kJ/mol formed by the transition state TS3 needs to be overcome from the intermediate IM2 to the formation stage product P1. Two S atoms in this process form dimeric sulfur S2, and the remaining part is the incompletely reacted Fe4S2O2.In reaction path 2, reactantR passes through the transition state TS4 to form intermediate IM3, a process that requires an energy barrier of 43.89 kJ/mol to be overcome. This process breaks the O-O bond, one of the O atoms is bonded to a Fe atom on one side. Intermediate IM3 passes through the transition state TS5 to form intermediate IM4, which requires an energy barrier of 18.31 kJ/mol to be overcome. This process involves the formation of a Fe-O bond by another O atom with the Fe atom below. Thereafter, two S atoms in intermediate IM4 form S2, a step that requires a large energy barrier to be experienced to proceed, which is calculated to be 166.85 kJ/mol for the formation of transition state TS6.In stage 1, the two reaction routes proceed through distinct intermediates and transition states to yield products P1 and P2. Both P1 and P2 are Fe4S2O2 and dimeric sulfur S2. The difference is that Fe4S2O2 in P1 is a blocky structure, while Fe4S2O2 in P2 is a planar structure. From the stage 1 reaction as a whole, the reaction of Fe4S4 with O2 to form Fe4S2O2 and S2 is similar to the substitution of sulfur atoms in Fe4S4 by oxygen atoms, which is consistent with the iron-sulfur cluster oxidation mechanism proposed by Sandra M. Lang et al. [17]. Fe4S2O2 and S2 will continue to react upon exposure to new O2, which we discuss in the reaction of stage 2.


## 3.3.2. Stage 2: Fe4S2O2 Reacts with O2 to Form 4FeO and S2

When the reaction product Fe4S2O2 in stage 1 continues to react with O2, O2 also preferentially adsorbs around the Fe atom. This stage of the reaction takes into account the different intermediates and transition states, and we divide it into two reaction paths for discussion. Path 1 and path 2 correspond to the two paths in stage 1. O2 adsorption on the Fe4S2O2 cluster releases 200.06 kJ/mol of energy to form intermediate IM5, and after the transition state TS7 to form intermediate IM6, the O-O bond breaks in this step and one of the O atoms attacks the S atom to form an S-O bond, a process that requires overcoming an energy barrier of 44.17 kJ/mol. Intermediate IM6 overcomes the energy barrier of 18.67 kJ/mol passing through the transition state TS8 to form intermediate IM7. The S atom is replaced out of its original ligand environment during this process. Subsequently, another O atom attacks the S atom to form an S-O bond, as shown in IM8 in Figure 7. This step requires overcoming an energy barrier of 74.41 kJ/mol. IM8 passes through the transition state TS10 to form product P3. This process overcomes the energy barrier of 18.75 kJ/mol and the S atom is completely replaced out of the original ligand environment to form dimeric sulfur S2 and FeO.In path 2, O2 adsorbed on Fe atoms releases 179.25 kJ/mol of energy to form intermediate IM9. IM9 overcomes the energy barrier of 40.39 kJ/mol and passes through the transition state TS11 to form intermediate IM10. After the O-O bond is broken, the O atom attacks the S atom to break the Fe-S bond. Subsequently, the O atom will continue to attack the sulfur atom leading to the complete reaction of the S atom and the formation of intermediate IM11. This process can proceed by overcoming an energy barrier of 80.5 kJ/mol. The intermediate IM11 overcomes an energy barrier of 63.83 kJ/mol to form the product P4. The two products of this stage, P3 and P4, are both FeO and dimeric sulfur (S2).When seen as a whole, the stage reaction is effectively a continuous reaction process, with stage 2 occurring after stage 1. FeO and S2 are eventually produced in both phases of the reaction. Because FeO is unstable, it will progressively oxidize in the environment to generate Fe2O3, a process that is thought to occur naturally and is not further explored in this research.


## 3.3.3. Stage 3: S2 Reacts with 2O2 to Form 2SO2

Because SO2 is released during the oxidation of Fe4S4, the subsequent reaction of dimeric sulfur S2 is further investigated in this paper. The oxidation of S2 is treated as the third stage of the reaction in this work, but it does not occur exactly after the first two stages in time because S2 is generated in both of the first two processes. The oxidation of S2 takes place on the triplet potential energy surface. S2 interacts with O2 to form SO2, and the initial step of the reaction requires 275.59 kJ/mol energy absorption. As a result, under ambient circumstances, S2 does not oxidize. However, the initial two stages of the oxidation reaction system of iron sulfide compounds emit a significant amount of heat, raising the temperature of the entire reaction system and providing a reaction foundation for the oxidation of S2. When S2 has absorbed sufficient heat, the reaction can proceed by only overcoming a small energy barrier. At this stage, the S-S bond breaks and the S atom attacks O2 to form the SO2 molecule. To form SO2, the intermediate IM13 merely has to overcome a potential barrier of 19.9 kJ/mol.The reaction between Fe4S4 and O2 is exothermic at every stage, which is advantageous thermodynamically. The heat of reaction for each stage is displayed in Table 3. On adsorption in the first stage of the reaction, the two reactants in path 1 generated 198.13 kJ/mol of heat, which laid the groundwork for the subsequent reaction. The reaction between reactant R and stage product P1 is exothermic. The maximal energy barrier encountered throughout this process is 64.56 kJ/mol, and the heat emitted at the start of the reaction is enough to keep the reaction going. The heat released from reaction path 1 is calculated to be 294.78 kJ/mol. In contrast, the maximum energy barrier to be overcome in reaction path 2 is 166.85 kJ/mol required to pass through TS6, and the release of 369.99 kJ/mol from the start of the reaction to the formation of intermediate IM5 is sufficient to support the reaction. Therefore, reaction path 1 is more likely to occur than reaction path 2 in comparison.Table 3
Heat of reaction for each phase of the reaction.
ProcessReaction pathHeat of reaction/kJ·mol−1Stage1Path1Fe4S4+O2⟶P1−294.78Path2Fe4S4+O2⟶P2−222.82Stage2Path1Fe4S2O2⟶P3−287.98Path2Fe4S2O2⟶P4−278.83Stage3S2+2O2⟶2SO2−470.94Overall, the stage’s two chemical paths are both exothermic, with path 1 releasing 287.98 kJ/mol of heat and path 2 releasing 278.83 kJ/mol of heat. The largest energy barrier to cross in reaction path 1 is 74.41 kJ/mol. The largest energy barrier that must be overcome in reaction path 2 is 80.49 kJ/mol. Reaction path 1 facilitates the reaction’s progression more than reaction path 2. In the oxidation of Fe4S4 clusters, reaction path 1 is the optimum reaction channel. However, whether reaction path 1 or reaction path 2, the reaction products are FeO and S2, and the entire reaction process is exothermic.There may be no SO2 release at the start of the reaction because the S2 yield and heat released by the reaction system are insufficient to sustain the oxidation of dimeric sulfur S2. Dimer sulfur S2 is gradually oxidized as the reaction progresses, and as the reaction system continues to build up heat, it will encourage the oxidation of dimer sulfur S2 and release a significant quantity of heat, which raises the reaction system’s temperature once more. Table 3 shows that the heat of the S2 oxidation reaction in stage 3 is 470.94 kJ/mol. Therefore, the oxidative exothermic process of S2 has a nonnegligible effect on the spontaneous combustion of iron sulfide compounds.


## 4. Conclusion

In this work, XRD analysis of iron sulfide compound samples with spontaneous combustion activity was done, structural models of Fe4S4 and O2 were built using molecular simulations, and interactions between Fe4S4 clusters and O2 were computed at the GGA/PBE level, leading to the following primary results:The iron sulfide compound sample’s XRD pattern revealed that it did not have any obvious crystalline diffraction peaks, indicating that it had an amorphous structure. Analysis of the peaks’ peak locations also revealed that the sample was an amorphous FeS.Calculations of the adsorption parameters of O2 and Fe4S4 clusters demonstrate that when adsorbed with Fe4S4, O2 tends to adsorb around Fe atoms and the adsorption energy of O2 is greatest when adsorbed at both ends. When O2 is adsorbed at the Fe-S bridge site, there is no charge transfer between the two and no stable chemisorption is created. It was discovered that there was a repulsion between O and S atoms in the computation of O2 adsorption at S sites, and there was no charge transfer between O2 and Fe4S4 clusters for either end adsorption or both ends adsorption. When O2 is adsorbed at the Fe-S bridge site, the optimized O2 is stabilized around the Fe atom and one of the O atoms is attached to the Fe atom, similar to how O2 is adsorbed at one end of the Fe site. In conclusion, O2 does not stably adsorb close to S atoms.The reaction path analysis of Fe4S4 with O2 is examined by splitting the reaction into 3 stages, the first two of which are effectively the same reaction process. We analyzed the reaction energy barrier and reaction energy for reaction paths 1 and 2 in both stages of the reaction. Reaction path 1 is the ideal reaction path, according to the analysis. The total exergy of reaction path 1 is calculated to be 582.76 kJ/mol. The total energy of reaction path 2 is 501.65 kJ/mol. In this study, the oxidation of dimeric sulfur produced in the first two reaction stages was also analyzed. It was discovered that while the oxidation reaction of dimeric sulfur S2 requires some energy to be absorbed to proceed, a lot of energy is released once the reaction is started. The oxidation reaction of S2 is calculated to release 470.94 kJ/mol of energy.Therefore, we believe that the oxidation reaction of Fe4S4 is a multistage exothermic reaction that can proceed spontaneously, with S2 being continuously generated during the reaction, and the generated S2 absorbs energy in the oxidation reaction system of Fe4S4 to undergo oxidation reactions and release large amounts of heat, accompanied by the release of SO2. This speeds up the oxidation of Fe4S4, which increases the temperature of the reaction system until spontaneous combustion happens.



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*Source: 9812188-2022-09-24.xml*