Theoretical Study on Adsorption Behavior of SF6 Decomposition Components on Mg-MOF-74

SF6 gas is an arc extinguishing medium that is widely used in gas insulated switchgear (GIS). When insulation failure occurs in GIS, it leads to the decomposition of SF6 in partial discharge (PD) and other environments. The detection of the main decomposition components of SF6 is an effective method to diagnose the type and degree of discharge fault. In this paper, Mg-MOF-74 is proposed as a gas sensing nanomaterial for detecting the main decomposition components of SF6. The adsorption of SF6, CF4, CS2, H2S, SO2, SO2F2 and SOF2 on Mg-MOF-74 was calculated by Gaussian16 simulation software based on density functional theory. The analysis includes parameters of the adsorption process such as binding energy, charge transfer, and adsorption distance, as well as the change in bond length, bond angle, density of states, and frontier orbital of the gas molecules. The results show that Mg-MOF-74 has different degrees of adsorption for seven gases, and chemical adsorption will lead to changes in the conductivity of the system; therefore, it can be used as a gas sensing material for the preparation of SF6 decomposition component gas sensors.


Introduction
Sulfur hexafluoride gas is an arc extinguishing medium widely used in gas insulated switch gear (GIS). However, insulation defects inside GIS can lead to partial discharge (PD) and other faults. SF 6 decomposes into extremely unstable low-fluorine sulfides (SF n , n = 1~5) in an overheated environment with long-term failure [1][2][3][4][5]. Although SF n can collide with F atoms in the environment to recover to SF 6 molecules, in the presence of micro-amounts of O 2 and H 2 O, SF n further reacts to form SO 2 , SOF 2 , SO 2 F 2 , H 2 S and other major products [6][7][8]; if the fault occurs on the basin insulator, SF n can react with electrode materials, insulation materials, etc., to generate characteristic gases CF 4 , CS 2 , etc. [9,10]; therefore, the types of the above decomposition products are closely related to the fault types. Detecting the main decomposition components of SF 6 in GIS equipment by the gas sensor method is an effective method to diagnose discharge faults and types [11][12][13][14], and guarantees the safe operation of electrical insulation equipment.

Calculation Parameter Setting and Model Construction
The modeling involved in this paper is completed in GaussView, and the structural optimization and single point calculation are completed in Gaussian 16 software. In the application of Gaussian series quantum chemistry simulation software, Sciortino, G. et al. found that the PBE0 functional and the def2-tzvp basis set have extremely high accuracy in the calculation of Ni(II) complexes [58]. PBE0 functional together with def-tzvp is the best-performing method, and is excellent in the study of platinum-catalyzed chemical reaction mechanism based on DFT principle [59].
Therefore, when dealing with the exchange correlation term of electrons, we also use the PBE0 hybrid functional with higher calculation accuracy than LDA, GGA and meta-GGA. Because the sensitivity of geometric structure optimization to the basis set is much lower than that of single point energy calculation, and the time consumption of these tasks is much higher than that of single point calculation, the def2-svp (2-zeta) basis set with appropriate accuracy is selected for structural optimization, and the def2-tzvp (3-zeta) basis set with higher accuracy is used in single point energy calculation; the GD3BJ algorithm is used to correct the Van der Waals effect, and sets the charge to 0 and the spin multiplicity to 1.
By reading the crystallographic information (.cif) file, each periodic structural unit of Mg-MOF-74 contains 638 atoms, 704 chemical bonds and 18 polyhedra. Due to the application of high-precision functional, the computational power cannot meet the optimization of the overall periodic structure and the single point calculation of adsorption. It can be seen from Figure 2 that the smallest repeating unit in Mg-MOF-74 is a cluster containing four Mg atoms, three benzene rings, three hydroxyl groups, three carboxyl groups and one coordinated water (inside the white dotted box). Therefore, this paper uses this cluster (without bound water) as the adsorption substrate to simulate the adsorption characteristics of seven gas molecules on this segment, and then infers the macroscopic adsorption characteristics of the material on gases.

Calculation Parameter Setting and Model Construction
The modeling involved in this paper is completed in GaussView, and the structural optimization and single point calculation are completed in Gaussian 16 software. In the application of Gaussian series quantum chemistry simulation software, Sciortino, G. et al. found that the PBE0 functional and the def2-tzvp basis set have extremely high accuracy in the calculation of Ni(II) complexes [58]. PBE0 functional together with def-tzvp is the best-performing method, and is excellent in the study of platinum-catalyzed chemical reaction mechanism based on DFT principle [59].
Therefore, when dealing with the exchange correlation term of electrons, we also use the PBE0 hybrid functional with higher calculation accuracy than LDA, GGA and meta-GGA. Because the sensitivity of geometric structure optimization to the basis set is much lower than that of single point energy calculation, and the time consumption of these tasks is much higher than that of single point calculation, the def2-svp (2-zeta) basis set with appropriate accuracy is selected for structural optimization, and the def2-tzvp (3-zeta) basis set with higher accuracy is used in single point energy calculation; the GD3BJ algorithm is used to correct the Van der Waals effect, and sets the charge to 0 and the spin multiplicity to 1.
By reading the crystallographic information (.cif) file, each periodic structural unit of Mg-MOF-74 contains 638 atoms, 704 chemical bonds and 18 polyhedra. Due to the application of high-precision functional, the computational power cannot meet the optimization of the overall periodic structure and the single point calculation of adsorption. It can be seen from Figure 2 that the smallest repeating unit in Mg-MOF-74 is a cluster containing four Mg atoms, three benzene rings, three hydroxyl groups, three carboxyl groups and one coordinated water (inside the white dotted box). Therefore, this paper uses this cluster (without bound water) as the adsorption substrate to simulate the adsorption characteristics of seven gas molecules on this segment, and then infers the macroscopic adsorption characteristics of the material on gases.

Calculation Parameter Setting and Model Construction
The modeling involved in this paper is completed in GaussView, and the structural optimization and single point calculation are completed in Gaussian 16 software. In the application of Gaussian series quantum chemistry simulation software, Sciortino, G. et al. found that the PBE0 functional and the def2-tzvp basis set have extremely high accuracy in the calculation of Ni(II) complexes [58]. PBE0 functional together with def-tzvp is the best-performing method, and is excellent in the study of platinum-catalyzed chemical reaction mechanism based on DFT principle [59].
Therefore, when dealing with the exchange correlation term of electrons, we also use the PBE0 hybrid functional with higher calculation accuracy than LDA, GGA and meta-GGA. Because the sensitivity of geometric structure optimization to the basis set is much lower than that of single point energy calculation, and the time consumption of these tasks is much higher than that of single point calculation, the def2-svp (2-zeta) basis set with appropriate accuracy is selected for structural optimization, and the def2-tzvp (3-zeta) basis set with higher accuracy is used in single point energy calculation; the GD3BJ algorithm is used to correct the Van der Waals effect, and sets the charge to 0 and the spin multiplicity to 1.
By reading the crystallographic information (.cif) file, each periodic structural unit of Mg-MOF-74 contains 638 atoms, 704 chemical bonds and 18 polyhedra. Due to the application of high-precision functional, the computational power cannot meet the optimization of the overall periodic structure and the single point calculation of adsorption. It can be seen from Figure 2 that the smallest repeating unit in Mg-MOF-74 is a cluster containing four Mg atoms, three benzene rings, three hydroxyl groups, three carboxyl groups and one coordinated water (inside the white dotted box). Therefore, this paper uses this cluster (without bound water) as the adsorption substrate to simulate the adsorption characteristics of seven gas molecules on this segment, and then infers the macroscopic adsorption characteristics of the material on gases.  The optimized Mg-MOF-74 cluster and gas molecular model are shown in Figure 3. In order to represent the total energy change of gas molecules adsorbed on Mg-MOF-74, the binding energy during adsorption is defined as:  The optimized Mg-MOF-74 cluster and gas molecular model are shown in Figure 3. In order to represent the total energy change of gas molecules adsorbed on Mg-MOF-74, the binding energy during adsorption is defined as: In Equation (1): EMOF-gas is the total energy of the system after Mg-MOF-74 adsorbs gas molecules, EMOF is the total energy of Mg-MOF-74 clusters before adsorption, and Egas is the total energy of gas molecules before adsorption. The basis set superposition error (BSSE) is corrected using the counterpoise method proposed by Boys and Bernardi [60], and EBSSE is the correction value.
The charge transfer amount is the number of charge transfer obtained by analyzing the charge population through the Hirshfeld charge model.
In Equation (2): ΔQ is the charge transfer amount of the system, Q1 is the charge of gas molecules after adsorption, and Q2 is the charge of gas molecules before adsorption.
The adsorption distance is defined as the distance between the gas molecule and the adsorption site of Mg-MOF-74. The Van der Waals radius is 1/2 of the distance between two adjacent nuclei when atoms interact with each other through Van der Waals force. The covalent radius is 1/2 of the nucleus spacing when the atoms of the same element form diatomic molecules.
The change of charge density is analyzed by the distribution of the yellow region (atom has electron loss property) and the blue region (atom has electron gain property) in the differential charge density diagram.
In this paper, the discrete orbital occupation diagram is broadened by Gaussian function to obtain the density of states (DOS) curve, and the chemical adsorption of Mg-MOF-74 on gas is further analyzed by the total density of states, gas density of states and local density of states.

Results
The adsorption calculation in this paper makes the SF6, CF4, CS2, H2S, SO2, SO2F2 and-SOF2 gas molecules vertically close to the unsaturated sites on the Mg-MOF-74 material; In Equation (1): E MOF-gas is the total energy of the system after Mg-MOF-74 adsorbs gas molecules, E MOF is the total energy of Mg-MOF-74 clusters before adsorption, and E gas is the total energy of gas molecules before adsorption. The basis set superposition error (BSSE) is corrected using the counterpoise method proposed by Boys and Bernardi [60], and E BSSE is the correction value.
The charge transfer amount is the number of charge transfer obtained by analyzing the charge population through the Hirshfeld charge model.
In Equation (2): ∆Q is the charge transfer amount of the system, Q 1 is the charge of gas molecules after adsorption, and Q 2 is the charge of gas molecules before adsorption.
The adsorption distance is defined as the distance between the gas molecule and the adsorption site of Mg-MOF-74. The Van der Waals radius is 1/2 of the distance between two adjacent nuclei when atoms interact with each other through Van der Waals force. The covalent radius is 1/2 of the nucleus spacing when the atoms of the same element form diatomic molecules.
The change of charge density is analyzed by the distribution of the yellow region (atom has electron loss property) and the blue region (atom has electron gain property) in the differential charge density diagram.
In this paper, the discrete orbital occupation diagram is broadened by Gaussian function to obtain the density of states (DOS) curve, and the chemical adsorption of Mg-MOF-74 on gas is further analyzed by the total density of states, gas density of states and local density of states.

Results
The adsorption calculation in this paper makes the SF 6 , CF 4 , CS 2 , H 2 S, SO 2 , SO 2 F 2 andSOF 2 gas molecules vertically close to the unsaturated sites on the Mg-MOF-74 material; after reaching the most stable state, by extracting the adsorption parameters (binding energy, charge transfer amount, adsorption distance), the change of bond length and bond angle of gas analysis after adsorption is measured, and the adsorption capacity of Mg-MOF-74 to seven gases is comprehensively judged by analyzing the change of orbital occupancy.
It can be seen that the F atoms in CF 4 and SF 6 interact with the Mg atoms in the adsorbed substrate, Figure 4a after reaching the most stable state, by extracting the adsorption parameters (binding energy, charge transfer amount, adsorption distance), the change of bond length and bond angle of gas analysis after adsorption is measured, and the adsorption capacity of Mg-MOF-74 to seven gases is comprehensively judged by analyzing the change of orbital occupancy.
It can be seen that the F atoms in CF4 and SF6 interact with the Mg atoms in the adsorbed substrate, Figure 4a

Parameters of adsorption behavior:
The adsorption energies, charge transfer and adsorption distance in the adsorption process of seven gas molecules SF6, CF4, CS2, H2S, SO2, SO2F2 and SOF2 on Mg-MOF-74 are listed in Table 1.

2.
Parameters of adsorption behavior: The adsorption energies, charge transfer and adsorption distance in the adsorption process of seven gas molecules SF 6 , CF 4 , CS 2 , H 2 S, SO 2 , SO 2 F 2 and SOF 2 on Mg-MOF-74 are listed in Table 1. Combined with Formula (1), the adsorption energy of Mg-MOF-74 material to each gas molecule is less than 0, indicating that the adsorption process system reaches a lower energy stable state after heat-releasing; the relationship among the adsorption capacity of the material to each gas is: H 2 S > SO 2 > SOF 2 > SO 2 F 2 > CS 2 > SF 6 > CF 4 .
According to Formula (2) in this paper, the gas molecules lose electrons during the adsorption process, and the substrate material Mg-MOF-74 obtains electrons.
The adsorption distance among each gas molecule and the substrate is less than the sum of Van der Waals radius and larger than the sum of covalent radius (shown in Supplemental material Table S1). Therefore, according to the adsorption distance, it can be inferred that the strength of the chemical bond formed by the adsorption of seven gases by Mg atoms on Mg-MOF-74 material belongs to weaker chemical action.

3.
Differential charge density: Combined with Formula (1), the adsorption energy of Mg-MOF-74 material to ea gas molecule is less than 0, indicating that the adsorption process system reaches a low energy stable state after heat-releasing; the relationship among the adsorption capacity the material to each gas is: H2S > SO2 > SOF2 > SO2F2 > CS2 > SF6 > CF4.
According to Formula (2) in this paper, the gas molecules lose electrons during t adsorption process, and the substrate material Mg-MOF-74 obtains electrons.
The adsorption distance among each gas molecule and the substrate is less than t sum of Van der Waals radius and larger than the sum of covalent radius (shown in Su plemental material Table S1). Therefore, according to the adsorption distance, it can inferred that the strength of the chemical bond formed by the adsorption of seven gas by Mg atoms on Mg-MOF-74 material belongs to weaker chemical action.
3. Differential charge density: Figure 5a-g shows the charge density difference in the adsorption process. The y low regions show the electron losing property and the blue regions show the electr gaining property. The charge distribution near the F atom of SF6 and CF4 is relatively uniform, and t charge distribution inside the molecule does not change significantly. The charge dist bution near the C atom in CS2 is uniform, and the Mg atom bonded to the S atom in CS wrapped by the yellow regions. The charge distribution near the H atom in H2S is unifor and the Mg atom bonded to the S atom in H2S is surrounded by the yellow regions. T Mg atom bonded to the O atom in SO2 is wrapped by the yellow regions. The charge d tribution near the S atom and F atom in SO2F2 is uniform, and the Mg atom bonded to t O atom in SO2F2 is wrapped by the yellow regions. The charge distribution near the S a F atoms in SOF2 is uniform, and the Mg atom bonded to the O atom in SOF2 is wrapp by the yellow regions. The above results show that the Mg atoms on the Mg-MOF-74 m terial exhibit electron-gaining properties during the adsorption process, while the g molecules exhibit electron-losing properties. The charge distribution near the F atom of SF 6 and CF 4 is relatively uniform, and the charge distribution inside the molecule does not change significantly. The charge distribution near the C atom in CS 2 is uniform, and the Mg atom bonded to the S atom in CS 2 is wrapped by the yellow regions. The charge distribution near the H atom in H 2 S is uniform, and the Mg atom bonded to the S atom in H 2 S is surrounded by the yellow regions. The Mg atom bonded to the O atom in SO 2 is wrapped by the yellow regions. The charge distribution near the S atom and F atom in SO 2 F 2 is uniform, and the Mg atom bonded to the O atom in SO 2 F 2 is wrapped by the yellow regions. The charge distribution near the S and F atoms in SOF 2 is uniform, and the Mg atom bonded to the O atom in SOF 2 is wrapped by the yellow regions. The above results show that the Mg atoms on the Mg-MOF-74 material exhibit electron-gaining properties during the adsorption process, while the gas molecules exhibit electron-losing properties.

The Change of Bond Length and Bond Angle of Gas Molecules after Adsorption
The bond length changes of SF 6 , CF 4 , CS 2 , H 2 S, SO 2 , SO 2 F 2 and SOF 2 molecules before and after adsorption and the bond angle changes are shown in Supplementary Materials Tables S1-S8.
The bond length of SF 6 , CF 4 , CS 2 , H 2 S, SO 2 , SO 2 F 2 and SOF 2 gas molecules changes slightly due to adsorption; the obvious changes in the bond angle (atomic number shown in Figure 2b The changes of bond length and bond angle before and after adsorption of the above seven gas molecules, together with the adsorption energy, adsorption distance, charge transfer amount and differential charge density diagram, strongly prove that there are certain interactions among gas molecules and the adsorption substrate.

The Orbital Occupation Changes of Each System before and after Gas Adsorption
The orbital occupation calculation results of Gaussian 16 software are imported into Multiwfn software to obtain discrete orbital occupation information under different energies, as indicated by the blue arrow in Figure 6a.
The changes of bond length and bond angle before and after adsorption of the above seven gas molecules, together with the adsorption energy, adsorption distance, charge transfer amount and differential charge density diagram, strongly prove that there are certain interactions among gas molecules and the adsorption substrate.

The Orbital Occupation Changes of Each System before and after Gas Adsorption
The orbital occupation calculation results of Gaussian 16 software are imported into Multiwfn software to obtain discrete orbital occupation information under different energies, as indicated by the blue arrow in Figure 6a. The Gaussian function is used for broadening, and the half-peak width is set to 0.01 eV to obtain a continuous density of states diagram (as indicated by the green arrow in Figure 6b, which can clearly and intuitively analyze the orbital occupation change. According to the extra-nuclear electron arrangement of Mg atoms, there are no filled electrons in the 3p orbital of Mg atoms, and Mg atoms form Mg 2+ by losing two electrons in the 3s orbital. Therefore, the bonding interaction during adsorption is analyzed by the overlap of the 3s and 3p orbital curves of Mg atoms on Mg-MOF-74 material with the outer orbital curves of SF6, CF4, CS2, H2S, SO2, SO2F2 and SOF2 gas molecules. The Gaussian function is used for broadening, and the half-peak width is set to 0.01 eV to obtain a continuous density of states diagram (as indicated by the green arrow in Figure 6b, which can clearly and intuitively analyze the orbital occupation change. According to the extra-nuclear electron arrangement of Mg atoms, there are no filled electrons in the 3p orbital of Mg atoms, and Mg atoms form Mg 2+ by losing two electrons in the 3s orbital. Therefore, the bonding interaction during adsorption is analyzed by the overlap of the 3s and 3p orbital curves of Mg atoms on Mg-MOF-74 material with the outer orbital curves of SF 6 , CF 4 , CS 2 , H 2 S, SO 2 , SO 2 F 2 and SOF 2 gas molecules.

1.
The orbital occupation of Mg-MOF-74 after adsorbing SF 6 gas is shown in Figure 7a-c.
By observing Figure 7a, it can be found that after adsorbing SF 6 gas, a new orbital occupation appears near the position of −1.95 eV, and the other energy positions do not change significantly. Compared with the total orbital occupation, it can be seen that the orbital occupation changes near the energy of −1.95 eV, 0.44 eV and 1.65 eV after adsorption of SF 6 are contributed by SF 6 , as shown in Figure 7b. By analyzing the 3s, 3p orbitals of the adsorbed substrate Mg atom and the 2p orbital occupation of the SF 6 gas molecule F atom, it can be clearly found that the 2p orbital of the F atom and the 3s orbital occupation broadening curve of the Mg atom overlap near the energy −1.95 eV position (as shown in Figure 7c), which indicates that the Mg-MOF-74 material has bonding adsorption effect on the SF 6 gas.

The Change of Bond Length and Bond Angle of Gas Molecules after Adsorption
The bond length changes of SF6, CF4, CS2, H2S, SO2, SO2F2 and SOF2 molecules before and after adsorption are shown in Table 4, and the bond angle changes are shown in Supplementary Materials Table S1-14.
The bond length of SF6, CF4, CS2, H2S, SO2, SO2F2 and SOF2 gas molecules changes slightly due to adsorption; the obvious changes in the bond angle (atomic number shown in Figure 2b The changes of bond length and bond angle before and after adsorption of the above seven gas molecules, together with the adsorption energy, adsorption distance, charge transfer amount and differential charge density diagram, strongly prove that there are certain interactions among gas molecules and the adsorption substrate.

The Orbital Occupation Changes of Each System before and after Gas Adsorption
The orbital occupation calculation results of Gaussian 16 software are imported into Multiwfn software to obtain discrete orbital occupation information under different energies, as indicated by the blue arrow in Figure 6a. The Gaussian function is used for broadening, and the half-peak width is set to 0.01 eV to obtain a continuous density of states diagram (as indicated by the green arrow in Figure 6b, which can clearly and intuitively analyze the orbital occupation change. According to the extra-nuclear electron arrangement of Mg atoms, there are no filled electrons in the 3p orbital of Mg atoms, and Mg atoms form Mg 2+ by losing two electrons in the 3s orbital. Therefore, the bonding interaction during adsorption is analyzed by the overlap of the 3s and 3p orbital curves of Mg atoms on Mg-MOF-74 material with the outer orbital curves of SF6, CF4, CS2, H2S, SO2, SO2F2 and SOF2 gas molecules. Figure 7ac.  The orbital occupation of Mg-MOF-74 after adsorbing CF 4 gas is shown in Figure 8a-c.

The orbital occupation of Mg-MOF-74 after adsorbing SF6 gas is shown in
orbital occupation changes near the energy of −1.95 eV, 0.44 eV and 1.65 eV after adsorption of SF6 are contributed by SF6, as shown in Figure 7b. By analyzing the 3s, 3p orbitals of the adsorbed substrate Mg atom and the 2p orbital occupation of the SF6 gas molecule F atom, it can be clearly found that the 2p orbital of the F atom and the 3s orbital occupation broadening curve of the Mg atom overlap near the energy −1.95 eV position (as shown in Figure 7c), which indicates that the Mg-MOF-74 material has bonding adsorption effect on the SF6 gas. Figure 8 ac.

The orbital occupation of Mg-MOF-74 after adsorbing CF4 gas is shown in
(a) (b) (c) By observing Figure 8a, it can be found that there is no new orbital occupation after adsorption of CF4 gas. Compared with the total orbital occupation, it can be seen that the orbital occupation changes near the energy of 0.42 eV, 1.16 eV and 2.21 eV after CF4 adsorption are contributed by CF4, as shown in Figure 8b.
By analyzing the 3s and 3p orbitals of the Mg atom of the adsorption substrate and the 2p orbital occupation of the F atom of the CF4 gas molecule, it can be clearly found that the 2p orbital of the F atom does not overlap with the 3s and 3p orbital occupation broadening curves of the Mg atom (as shown in Figure 8c), which indicates that the Mg-MOF-74 material barely has bonding adsorption effect on the CF4 gas.  By observing Figure 8a, it can be found that there is no new orbital occupation after adsorption of CF 4 gas. Compared with the total orbital occupation, it can be seen that the orbital occupation changes near the energy of 0.42 eV, 1.16 eV and 2.21 eV after CF 4 adsorption are contributed by CF 4 , as shown in Figure 8b.
By analyzing the 3s and 3p orbitals of the Mg atom of the adsorption substrate and the 2p orbital occupation of the F atom of the CF 4 gas molecule, it can be clearly found that the 2p orbital of the F atom does not overlap with the 3s and 3p orbital occupation broadening curves of the Mg atom (as shown in Figure 8c), which indicates that the Mg-MOF-74 material barely has bonding adsorption effect on the CF 4 gas.

3.
The orbital occupation of Mg-MOF-74 after adsorbing CS 2 gas is shown in Figure 9a-c.
It can be seen from Figure 9a that after adsorbing CS 2 gas, a new orbital occupation appears near the position of −2.03 eV, and the other energy positions do not change significantly. Compared with the total orbital occupancy, it can be seen that the orbital occupancy changes near the energy of −2.03 eV, 0.84 eV and 3.69 eV after adsorption of CS 2 are contributed by CS 2 , as shown in Figure 9b. By analyzing the 3s and 3p orbitals of the Mg atom of the adsorption substrate and the 3p orbital occupation of the S atom of the CS 2 gas molecule, it can be clearly found that the 3p orbital of the S atom and the 3p orbital occupation broadening curve of the Mg atom overlap near the energy −2.03 eV position (as shown in Figure 9c), which indicates that the Mg-MOF-74 material has bonding adsorption effect on the CS 2 gas. By observing Figure 7a, it can be found that after adsorbing SF6 gas, a new orbital occupation appears near the position of −1.95 eV, and the other energy positions do not change significantly. Compared with the total orbital occupation, it can be seen that the orbital occupation changes near the energy of −1.95 eV, 0.44 eV and 1.65 eV after adsorption of SF6 are contributed by SF6, as shown in Figure 7b. By analyzing the 3s, 3p orbitals of the adsorbed substrate Mg atom and the 2p orbital occupation of the SF6 gas molecule F atom, it can be clearly found that the 2p orbital of the F atom and the 3s orbital occupation broadening curve of the Mg atom overlap near the energy −1.95 eV position (as shown in Figure 7c), which indicates that the Mg-MOF-74 material has bonding adsorption effect on the SF6 gas. Figure 8  By observing Figure 8a, it can be found that there is no new orbital occupation after adsorption of CF4 gas. Compared with the total orbital occupation, it can be seen that the orbital occupation changes near the energy of 0.42 eV, 1.16 eV and 2.21 eV after CF4 adsorption are contributed by CF4, as shown in Figure 8b  occupation broadening curve of the Mg atom overlap near the energy −2.03 eV position (as shown in Figure 9c), which indicates that the Mg-MOF-74 material has bonding adsorption effect on the CS2 gas.

The orbital occupation of Mg-MOF-74 after adsorbing CF4 gas is shown in
4. The orbital occupation of Mg-MOF-74 after adsorbing H2S gas is shown in Figure  10a-c.
It can be found from Figure 10a that there is no new orbital occupation after adsorption of H2S gas. Compared with the total orbital occupation, it can be seen that the orbital occupation changes of the system near the energy of 0.35 eV, −6.95 eV and −7.47 eV after adsorption of H2S are contributed by H2S, as shown in Figure 10b. By analyzing the 3s and 3p orbitals of the Mg atom of the adsorption substrate and the 3p orbital occupation of the S atom of the H2S gas molecule, it can be clearly found that the 3p orbital of the S atom and the 3s orbital occupation broadening curve of the Mg atom overlap near the energy of 0.35 eV (as shown in Figure 10c), which indicates that the Mg-MOF-74 material has bonding adsorption effect on the H2S gas. Figure  11a-c. It can be found from Figure 10a that there is no new orbital occupation after adsorption of H 2 S gas. Compared with the total orbital occupation, it can be seen that the orbital occupation changes of the system near the energy of 0.35 eV, −6.95 eV and −7.47 eV after adsorption of H 2 S are contributed by H 2 S, as shown in Figure 10b.

The orbital occupation of Mg-MOF-74 after adsorbing SO2 gas is shown in
By analyzing the 3s and 3p orbitals of the Mg atom of the adsorption substrate and the 3p orbital occupation of the S atom of the H 2 S gas molecule, it can be clearly found that the 3p orbital of the S atom and the 3s orbital occupation broadening curve of the Mg atom overlap near the energy of 0.35 eV (as shown in Figure 10c), which indicates that the Mg-MOF-74 material has bonding adsorption effect on the H 2 S gas.

5.
The orbital occupation of Mg-MOF-74 after adsorbing SO 2 gas is shown in Figure 11a-c.
It can be seen from Figure 11a that after the adsorption of SO 2 gas, a new orbital occupation occurs near −3.56 eV, and the remaining energy positions do not change significantly. Compared with the total orbital occupation, it can be seen that the change of orbital occupation near the energy of −3.56 eV, −10.35 eV and 1.38 eV after SO 2 adsorption is contributed by SO 2 , as shown in Figure 11b. By analyzing the 3s and 3p orbitals of the Mg atom of the adsorption substrate and the 2p orbital occupation of the O atom of the SO 2 gas molecule, it can be clearly found that the 2p orbital of the O atom and the 3p orbital occupation broadening curve of the Mg atom overlap near the energy −3.56 eV position (as shown in Figure 11c), which indicates that the Mg-MOF-74 material has bonding adsorption effect on the SO 2 gas. It can be seen from Figure 11a that after the adsorption of SO2 gas, a new orbital occupation occurs near −3.56 eV, and the remaining energy positions do not change significantly. Compared with the total orbital occupation, it can be seen that the change of orbital occupation near the energy of −3.56 eV, −10.35 eV and 1.38 eV after SO2 adsorption is con-

6.
The orbital occupation of Mg-MOF-74 after adsorbing SO 2 F 2 gas is shown in Figure 12a-c.
occupation near the energy of −3.56 eV, −10.35 eV and 1.38 eV after SO2 adsorption is contributed by SO2, as shown in Figure 11b. By analyzing the 3s and 3p orbitals of the Mg atom of the adsorption substrate and the 2p orbital occupation of the O atom of the SO2 gas molecule, it can be clearly found that the 2p orbital of the O atom and the 3p orbital occupation broadening curve of the Mg atom overlap near the energy -3.56 eV position (as shown in Figure 11c), which indicates that the Mg-MOF-74 material has bonding adsorption effect on the SO2 gas.
6. The orbital occupation of Mg-MOF-74 after adsorbing SO2F2 gas is shown in Figure  12a-c.
(a) (b) (c) By observing Figure 11a, it can be found that there is no new orbital occupation after adsorption of SO2F2 gas. Compared with the total orbital occupation, it can be seen that the change of orbital occupation near the energy of −1.02 eV, −0.1 eV and 0.89 eV after adsorption of SO2F2 is contributed by SO2F2, as shown in Figure 12b.
By analyzing the 3s and 3p orbitals of the Mg atom of the adsorption substrate and the 2p orbital occupation of the O atom of the SO2F2 gas molecule, it can be clearly found that the 2p orbital of the O atom and the 3p orbital occupation broadening curve of the Mg atom overlap near the energy -1.02 eV position (as shown in Figure 12c), which indicates that the Mg-MOF-74 material has bonding adsorption effect on the SO2F2 gas.  By observing Figure 11a, it can be found that there is no new orbital occupation after adsorption of SO 2 F 2 gas. Compared with the total orbital occupation, it can be seen that the change of orbital occupation near the energy of −1.02 eV, −0.1 eV and 0.89 eV after adsorption of SO 2 F 2 is contributed by SO 2 F 2 , as shown in Figure 12b.
By analyzing the 3s and 3p orbitals of the Mg atom of the adsorption substrate and the 2p orbital occupation of the O atom of the SO 2 F 2 gas molecule, it can be clearly found that the 2p orbital of the O atom and the 3p orbital occupation broadening curve of the Mg atom overlap near the energy −1.02 eV position (as shown in Figure 12c), which indicates that the Mg-MOF-74 material has bonding adsorption effect on the SO 2 F 2 gas.

7.
The orbital occupation of Mg-MOF-74 after adsorbing SOF 2 gas is shown in Figure 13a-c.
It can be found from Figure 13a that after the adsorption of SOF 2 gas, a new orbital occupation appears near −2.07 eV after adsorption, and the other energy positions do not change significantly. Compared with the total orbital occupation, it can be seen that the orbital occupation changes near the energy of −2.07 eV, −0.93 eV and 0.77 eV after adsorption of SOF 2 are contributed by SOF 2 , as shown in Figure 13b. It can be found from Figure 13a that after the adsorption of SOF2 gas, a new orbital occupation appears near −2.07 eV after adsorption, and the other energy positions do not change significantly. Compared with the total orbital occupation, it can be seen that the orbital occupation changes near the energy of −2.07 eV, −0.93 eV and 0.77 eV after adsorption of SOF2 are contributed by SOF2, as shown in Figure 13b.
By analyzing the 3s and 3p orbitals of the Mg atom of the adsorption substrate and the 2p orbital occupation of the O atom of the SOF2 gas molecule, it can be clearly found that the 2p orbital of the O atom and the 3p orbital occupation broadening curve of the Mg atom overlap near the energy −0.93 eV position (as shown in Figure 13c), which indi- By analyzing the 3s and 3p orbitals of the Mg atom of the adsorption substrate and the 2p orbital occupation of the O atom of the SOF 2 gas molecule, it can be clearly found that the 2p orbital of the O atom and the 3p orbital occupation broadening curve of the Mg atom overlap near the energy −0.93 eV position (as shown in Figure 13c), which indicates that the Mg-MOF-74 material has bonding adsorption effect on the SOF 2 gas.

Conductivity Analysis after Adsorption
Pham, H.Q et al. have systematically studied the electronic band structure of a series of reticular metal-organic framework materials based on density functional theory [61]. By calculating the HOMO-LUMO gap under different types, different numbers of substituents and different C Ar -C Ar -C=O dihedral angle models, it is revealed that the band gap energy can be predicted by the HOMO-LUMO gap of MOFs organic ligands. The results show that the electronic band structure of MOFs can be calculated by first-principles calculations of organic linkers instead of complex and time-consuming calculations on periodic systems. In this section, by introducing the frontier molecular orbital theory to calculate the energy gap, the conductivity change of the cluster after adsorbing gas is qualitatively analyzed. It indicates the effect of gas adsorption on the conductivity of Mg-MOF-74 material.
The frontier molecular orbital distribution and energy of Mg-MOF-74 before and after adsorption of seven gases are shown in Figure 14. From the diagram, it can be seen that the highest occupied molecular orbital (HOMO) of the Mg-MOF-74 cluster and the system after adsorbing SF 6 , CF 4 , CS 2 , H 2 S, SO 2 , SO 2 F 2 and SOF 2 are mainly distributed on the surface of the benzene ring, which is also the same as the law in the literature [61]. The lowest unoccupied molecular orbital (LUMO) of SF 6 , CS 2 , SO 2 and SO 2 F 2 systems are mainly distributed on the surface of gas molecules. The LUMO of CF 4 , H 2 S and SO 2 F 2 systems are mainly distributed on the surface of the other benzene ring of the cluster. With the change of frontier orbital distribution, the HOMO and LUMO energies of the seven systems have different degrees of increase and decrease, respectively. For HOMO, the change of SO 2 F 2 system is the most obvious, and for LUMO, the change of SO 2 system is the most obvious.
The energy gap's change demonstrates that when the Mg-MOF-74 cluster only has chemical adsorption for CF 4 , SF 6 , CS 2 , H 2 S, SO 2 , SO 2 F 2 and SOF 2 gases, the conductivity of each system has different degrees of improvement, and the order of promotion is: SO 2 > CS 2 > SOF 2 > SF 6 > SO 2 F 2 > CF 4 > H 2 S. Therefore, in the application, it is possible to analyze the gas composition by comparing the resistance value response difference of the material to seven gases under the same sensor electrode preparation, the same gas flow rate, and the same measurement temperature, and then determine whether SF 6 decomposes or not. The frontier molecular orbital distribution and energy of Mg-MOF-74 before and after adsorption of seven gases are shown in Figure 13. From the diagram, it can be seen that the highest occupied molecular orbital (HOMO) of the Mg-MOF-74 cluster and the system after adsorbing SF6, CF4, CS2, H2S, SO2, SO2F2 and SOF2 are mainly distributed on the surface of the benzene ring, which is also the same as the law in the literature [61]. The lowest unoccupied molecular orbital (LUMO) of SF6, CS2, SO2 and SO2F2 systems are mainly distributed on the surface of gas molecules. The LUMO of CF4, H2S and SO2F2 systems are mainly distributed on the surface of the other benzene ring of the cluster. With the change of frontier orbital distribution, the HOMO and LUMO energies of the seven

Conclusions
In this paper, GaussView software is used to construct the cluster of Mg-MOF-74 material and seven gas molecular models of SF 6 , CF 4 , CS 2 , H 2 S, SO 2 , SO 2 F 2 and SOF 2 . The adsorption properties of Mg-MOF-74 clusters to gases are calculated by Gaussian16 software based on the DFT principle. The main conclusions are as follows: When the adsorption of each gas molecule by Mg-MOF-74 material reaches a stable state, the relationship among the adsorption capacity of each gas is: H 2 S > SO 2 > SOF 2 > SO 2 F 2 > CS 2 > SF 6 > CF 4 .During the adsorption process, the metal atoms in the MOFs gain electrons, the gas molecules lose electrons, and the adsorption process leads to changes in the bond length and bond angle of the gas molecules.
The density of states curve obtained by orbital occupation broadening shows that the adsorption of CF 4 by Mg-MOF-74 belongs to physical adsorption, and the adsorption of the other six gases belongs to chemical adsorption.
The frontier molecular orbital analysis shows that the chemical adsorption of Mg-MOF-74 on gas causes the change of conductivity of the system. Therefore, the response difference of the material to the gas in GIS and pure SF 6 gas can be used to determine whether there is a fault inside the equipment.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/nano13111705/s1, Table S1: The sum of Van der waals radius and covalent radius; Table S2: Changes of bond length and bond angle after SF 6 molecules adsorption; Table S3: Changes of bond length and bond angle after CF 4 molecules adsorption; Table S4: Changes of bond length and bond angle after CS 2 molecules adsorption; Table S5: Changes of bond length and bond angle after H 2 S molecules adsorption; Table S6: Changes of bond length and bond angle after SO 2 molecules adsorption; Table S7: Changes of bond length and bond angle after SO 2 F 2 molecules adsorption; Table S8: Changes of bond length and bond angle after SOF 2 molecules adsorption.