Adsorption and Gas-Sensing Properties of Agn (n = 1–4) Cluster Doped GeSe for CH4 and CO Gases in Oil-Immersed Transformer

The adsorption mechanism of CO and CH4 on GeSe, modified with the most stable 1–4 Ag-atom clusters, is studied with the help of density functional theory. Adsorption distance, adsorption energy, total density of states (TDOS), projected density of states (PDOS), and molecular orbital theory were all used to analyze the results. CO was found to chemisorb exothermically on GeSe, independent of Ag cluster size, with Ag4-GeSe representing the optimum choice for CO gas sensors. CH4, in contrast, was found to chemisorb on Ag-GeSe and Ag2-GeSe and to physisorb on Ag3-GeSe and Ag4-GeSe. Here, Ag GeSe was found to be the optimum choice for CH4 gas sensors. Overall, our calculations suggest that GeSe modified by Ag clusters of different sizes could be used to advantage to detect CO and CH4 gas in ambient air.


Introduction
The oil-immersed transformer has been widely used in the modern power system due to its low cost and high power conversion efficiency [1]. Transformer insulation oil is mainly alkanes, cycloalkanes, saturated hydrocarbons, aromatic unsaturated hydrocarbons, and their compounds [2][3][4]. However, during a long service period, a transformer may inevitably suffer from local overheating and partial discharge faults [5,6]. These faults threaten the safety of the entire electrical system because the huge heat and strong distorted electrical field released by the faults may lead to the rupture of the C-C bond and C-H bond of the insulating oil medium, resulting in the generation of activated hydrogen and unstable hydrocarbon free radicals [7][8][9]. With the existence of impurities (H 2 O and O 2 ) in the transformer, various decomposition products are dissolved in oil products, such as H 2 , CH 4 , CO, CO 2 , C 2 H 2 , and C 2 H 6 [10][11][12]. Decomposition product detection is an effective method for online monitoring of transformer faults [13,14]. Since CO and CH 4 are two typical gases in transformer faults, the condition of a transformer can be predicted by analyzing the concentrations of these two gases [15][16][17]. Due to the low cost and portability of gas sensors, it has been widely used in various fields, including electric power online monitoring [18,19]. Therefore, the gas sensor-based detection of CO and CH 4 could be a potentially effective means to realize fault detection in transformers [20].
In recent years, GeSe has been widely used in gas-sensing materials because it has a large specific surface area and abundant hole structure [21,22]. More resistant to oxidation and more stable at high temperatures than carbon nanotubes, GeSe is therefore more suitable for gas detection than carbon nanotubes [23,24]. As a result, it is one of the most widely used materials in high temperature and high pressure environments [25]. Gui et al. studied the adsorption behavior of CO, CH 4 , C 2 H 2 , C 2 H 4 on metal oxide (CuO, NiO, Ag 2 O)-doped GeSe surfaces; Guo et al. investigated the adsorption characteristics of C 2 H 2 , CH 4 , H 2 on SnO 2 -GeSe (SnO 2 doped onto GeSe surfaces) [26,27]. However, the ability of intrinsic GeSe to adsorb gases is limited, such as CH 4 , C 2 H 2 , H 2 , etc., [12,28].

Computational Details and Methods
All calculations were performed based on the density functional theory (DFT) [33,38]. A generalized gradient approximation (GGA) was used to calculate the electron exchange and correlation energy [39,40]. The Perdew-Burke-Ernzerhof (PBE) function was used to calculate the interaction effect between electrons [41]. The DFT-based semi-core pseudopotential (DSPP) and double numerical plus polarization (DNP) were selected [42]. The self-consistent field convergence precision was set to 1 × 10 −6 Ha. The energy convergence accuracy, maximum stress, and max displacement were set as 1 × 10 −5 Ha, 2 × 10 −3 Ha/Å, and 5 × 10 −3 Ha, respectively [43,44]. Since Ag n -GeSe is not magnetic, the spin polarization is limited during structural optimization [45]. A k-point grid of 5 × 5 × 1 was selected for the Brillouin zone integration to obtain accurate energies and structures [46]. In the solvent model, the dielectric constant was set to 2.2 to simulate the insulating oil model. To avoid layer-to-layer interactions, we constructed a 4 × 4 × 1 single nanotube supercell containing 32 Se atoms and 32 Ge atoms for DFT calculations. The distance between layers was greater than 25 Å.
As defined in Equation (1), the adsorption energy represents the energy change in the adsorption process and can be analyzed to find the most stable structure of gas adsorption. If the adsorption energy is negative, it means that the reaction is exothermic and occurs spontaneously. Charge transfer (Q T ) was obtained by Mulliken population analysis. As defined in Equation (2), Q ads and Q iso , respectively, represent the net carried charges of the gas molecule after and before adsorption. A positive Q T shows that electrons transfer from the gas molecule to the Ag n -GeSe monolayer. The energy gap between the highest occupied orbit (HOMO) and the lowest unoccupied orbit (LUMO) is defined in Equation (3). The total density of states (TDOS) and projected density of states (PDOS) were analyzed in detail to analyze the mechanism of the adsorption process.

Geometry Optimization
In order to study the gas adsorption characteristics of GeSe, the top view and side view of GeSe were obtained through modeling, as shown in Figure 1. The structures of CO and CH 4 molecules were obtained as shown in Figure 1c,d. The bond lengths between Ge and Se were 2.543 Å (longitudinal) and 2.612 Å (transverse). The reason why the transverse distance is larger than the longitudinal distance is that Ge bonds with two transverse Se atoms, while the longitudinal one bonds with only one Se atom, making the longitudinal Se atom more stable and the longitudinal bond length shorter. The CO molecule is a linear structure with a bond length of only 1.142 Å. The CH 4 molecule is a regular tetrahedral structure, and it is a stable gas molecule in air. The bond length of each C-H bond is 1.096 Å, and the bond angle is 109.480 • .

Geometry Optimization
In order to study the gas adsorption characteristics of GeSe, the top view and side view of GeSe were obtained through modeling, as shown in Figure 1. The structures of CO and CH4 molecules were obtained as shown in Figure 1c,d. The bond lengths between Ge and Se were 2.543 Å (longitudinal) and 2.612 Å (transverse). The reason why the transverse distance is larger than the longitudinal distance is that Ge bonds with two transverse Se atoms, while the longitudinal one bonds with only one Se atom, making the longitudinal Se atom more stable and the longitudinal bond length shorter. The CO molecule is a linear structure with a bond length of only 1.142 Å. The CH4 molecule is a regular tetrahedral structure, and it is a stable gas molecule in air. The bond length of each C-H bond is 1.096 Å, and the bond angle is 109.480°.   Figure 2 shows the most stable structure of Agn-GeSe obtained by doping one to four Ag atoms. The doping distance is 2.499 Å, 2.539 Å, 2.680 Å, and 2.702 Å for 1-4 Ag atoms modified GeSe. Based on the Mulliken population, the four types of Ag cluster act as electron acceptors obtaining 0.048 e, 0.184 e, 0.206 e, and 0.288 e electron from GeSe, respectively. The redistribution of electric charge leads to the change of conductivity of the system. As shown in Figure 3, TDOS and PDOS were analyzed to further analyze the doping mechanism of Ag atom doping on GeSe. The peak values of the TDOS of the four Ag cluster-doped GeSe bases shift to the left obviously, which makes the Fermi level continuous. Figure 3(a2-d2) shows the PDOS of GeSe doped with four types Agn-GeSe. The analysis of PDOS showed that the peak value above the Fermi level shifted to the left due to the hybridization of Ag-4d, Se-4p, and Ge-4p orbits, thus improving the conductivity of the system. It can be seen from Figure 3(a1,a2) that the hybridization of Ag-4d and Se-4p orbits in one Ag atom doping system from −4.0 eV to −6.0 eV resulted in a significant increase in TDOS at −5.0 eV. It can be seen from Figure 3(b1,b2) that the Ag-4d and Se-4p orbits of double Ag atoms doping system hybridized at −1.0 eV~−2.0 eV, resulting in a significant increase in TDOS at −1.5 eV. Figure 3(c1,c2) shows that the Ag-4d and Se-4p orbits hybridized at −3.0 eV~−4.0 eV in the triple Ag atoms doping system, resulting in a significant increase in TDOS at −4.0 eV. It can be seen from Figure 3(d1,d2) that the hybridization of Ag-4d and Ge-4p orbits of the quadruple Ag atoms doping  Figure 2 shows the most stable structure of Ag n -GeSe obtained by doping one to four Ag atoms. The doping distance is 2.499 Å, 2.539 Å, 2.680 Å, and 2.702 Å for 1-4 Ag atoms modified GeSe. Based on the Mulliken population, the four types of Ag cluster act as electron acceptors obtaining 0.048 e, 0.184 e, 0.206 e, and 0.288 e electron from GeSe, respectively. The redistribution of electric charge leads to the change of conductivity of the system. As shown in Figure 3, TDOS and PDOS were analyzed to further analyze the doping mechanism of Ag atom doping on GeSe. The peak values of the TDOS of the four Ag cluster-doped GeSe bases shift to the left obviously, which makes the Fermi level continuous. Figure 3(a2-d2) shows the PDOS of GeSe doped with four types Ag n -GeSe. The analysis of PDOS showed that the peak value above the Fermi level shifted to the left due to the hybridization of Ag-4d, Se-4p, and Ge-4p orbits, thus improving the conductivity of the system. It can be seen from Figure 3(a1,a2) that the hybridization of Ag-4d and Se-4p orbits in one Ag atom doping system from −4.0 eV to −6.0 eV resulted in a significant increase in TDOS at −5.0 eV. It can be seen from Figure 3(b1,b2) that the Ag-4d and Se-4p orbits of double Ag atoms doping system hybridized at −1.0 eV~−2.0 eV, resulting in a significant increase in TDOS at −1.5 eV. Figure 3(c1,c2) shows that the Ag-4d and Se-4p orbits hybridized at −3.0 eV~−4.0 eV in the triple Ag atoms doping system, resulting in a significant increase in TDOS at −4.0 eV. It can be seen from Figure 3(d1,d2) that the hybridization of Ag-4d and Ge-4p orbits of the quadruple Ag atoms doping system at −4.0 eV~−5.0 eV resulted in a significant increase in TDOS at −4.5 eV. In general, a strong orbital hybridization results in a stable Ag n -GeSe structure, indicating that Ag cluster-doping on the GeSe surface is stable enough for further gas adsorption. Nanomaterials 2022, 12, x FOR PEER REVIEW 4 of 11 system at −4.0 eV~−5.0 eV resulted in a significant increase in TDOS at −4.5 eV. In general, a strong orbital hybridization results in a stable Agn-GeSe structure, indicating that Ag cluster-doping on the GeSe surface is stable enough for further gas adsorption.

Analysis of CO Gas Adsorption on Agn-GeSe Surface
To study the adsorption behavior of gas molecules on Agn-GeSe, gas molecules were made to approach Ag atoms from different directions and angles. The adsorption position with the largest adsorption energy was taken as the most stable adsorption structure, and then the density of states, band structure, and molecular orbit of the adsorption structures was analyzed. Figure 4 shows the most stable CO adsorption structure. The adsorption distances of CO on the four Agn-GeSe systems were 2.080, 2.157, 2.194, and 2.086 Å respectively, and the C-O bond was not damaged in the adsorption process. It can be seen that the adsorption ability of our Agn-GeSe systems to CO was relatively moderate, which was conducive to the subsequent desorption process, resulting in high sensitivity and system at −4.0 eV~−5.0 eV resulted in a significant increase in TDOS at −4.5 eV. In general, a strong orbital hybridization results in a stable Agn-GeSe structure, indicating that Ag cluster-doping on the GeSe surface is stable enough for further gas adsorption.

Analysis of CO Gas Adsorption on Agn-GeSe Surface
To study the adsorption behavior of gas molecules on Agn-GeSe, gas molecules were made to approach Ag atoms from different directions and angles. The adsorption position with the largest adsorption energy was taken as the most stable adsorption structure, and then the density of states, band structure, and molecular orbit of the adsorption structures was analyzed. Figure 4 shows the most stable CO adsorption structure. The adsorption distances of CO on the four Agn-GeSe systems were 2.080, 2.157, 2.194, and 2.086 Å respectively, and the C-O bond was not damaged in the adsorption process. It can be seen that the adsorption ability of our Agn-GeSe systems to CO was relatively moderate, which was conducive to the subsequent desorption process, resulting in high sensitivity and

Analysis of CO Gas Adsorption on Ag n -GeSe Surface
To study the adsorption behavior of gas molecules on Ag n -GeSe, gas molecules were made to approach Ag atoms from different directions and angles. The adsorption position with the largest adsorption energy was taken as the most stable adsorption structure, and then the density of states, band structure, and molecular orbit of the adsorption structures was analyzed. Figure 4 shows the most stable CO adsorption structure. The adsorption distances of CO on the four Ag n -GeSe systems were 2.080, 2.157, 2.194, and 2.086 Å respectively, and the C-O bond was not damaged in the adsorption process. It can be seen that the adsorption ability of our Ag n -GeSe systems to CO was relatively moderate, which was conducive to the subsequent desorption process, resulting in high sensitivity and reusability of the gassensing material. The C atom tends to adsorb on the Ag atom in the CO adsorption process.    Figure 5 shows the DOS analysis of Ag n -GeSe before and after CO adsorption. It can be seen from Figure 5(a1-d1) that the peak value of TDOS shifted significantly to the left after gas adsorption, making it continuous at the Fermi level. It can be seen from Figure 5(a1,a2) that Ag-GeSe had a new peak value due to the hybridization of Ag-4d, C-2p, and O-2p from −11.0 to −12.0 eV in the CO adsorption process. In Figure 5(b1,b2), it can be seen that Ag 2 -GeSe had a new peak value due to the hybridization of Ag-4d, C-2p, and O-2p from −10.0 to −11.0 eV during CO adsorption. The peak of Ag 3 -GeSe and Ag 4 -GeSe was roughly the same as that of Ag 2 -GeSe.

Configuration
The adsorption parameters of CO on the four doping structures are shown in Table  1, including adsorption distance, adsorption energy, and charge transfer. The adsorption energies of the four adsorption structures were −0.177, −0.166, −0.171, −0.193 eV. The charge transfer of the four adsorption structures during the adsorption process was 0.134, 0.105, −0.014, −0.165 e. The negative charge transfer indicates that the electron transfers from CO gas to Agn-GeSe, while the positive charge transfer indicates the transfer of electrons from Agn-GeSe to CO gas. From the moderate adsorption distance, large adsorption energy, and charge transfer, Ag4-GeSe is more suitable for CO gas adsorption.     Figure 6 shows the most stable CH4 adsorption structure. The adsorption distances of CH4 on 1-4 Ag atom-doped GeSe were 2.778, 2.957, 4.164, and 3.328 Å, respectively. The structure of CH4 did not change during the adsorption process. Compared with CO adsorption, the adsorption distance of CH4 was much larger. The adsorption distances of Ag3-GeSe and Ag4-GeSe to CH4 reached 4.164 and 3.328 Å, respectively. With such a large adsorption distance, it can be inferred that Ag3-GeSe and Ag4-GeSe show physical The adsorption parameters of CO on the four doping structures are shown in Table 1 −0.014, −0.165 e. The negative charge transfer indicates that the electron transfers from CO gas to Ag n -GeSe, while the positive charge transfer indicates the transfer of electrons from Ag n -GeSe to CO gas. From the moderate adsorption distance, large adsorption energy, and charge transfer, Ag 4 -GeSe is more suitable for CO gas adsorption. Table 1. Adsorption parameters of CO gas molecules on Ag n -GeSe.  Figure 6 shows the most stable CH 4 adsorption structure. The adsorption distances of CH 4 on 1-4 Ag atom-doped GeSe were 2.778, 2.957, 4.164, and 3.328 Å, respectively. The structure of CH 4 did not change during the adsorption process. Compared with CO adsorption, the adsorption distance of CH 4 was much larger. The adsorption distances of Ag 3 -GeSe and Ag 4 -GeSe to CH 4 reached 4.164 and 3.328 Å, respectively. With such a large adsorption distance, it can be inferred that Ag 3 -GeSe and Ag 4 -GeSe show physical adsorption to CH 4 . Since the C atom is surrounded by four H atoms in the CH 4 molecular structure, the H atom approaches the substrate in the adsorption process. In the four adsorption processes, C-H bonds elongate due to the effect of H-Ag bonding.  Figure 6 shows the most stable CH4 adsorption structure. The adsorption distances of CH4 on 1-4 Ag atom-doped GeSe were 2.778, 2.957, 4.164, and 3.328 Å, respectively. The structure of CH4 did not change during the adsorption process. Compared with CO adsorption, the adsorption distance of CH4 was much larger. The adsorption distances of Ag3-GeSe and Ag4-GeSe to CH4 reached 4.164 and 3.328 Å, respectively. With such a large adsorption distance, it can be inferred that Ag3-GeSe and Ag4-GeSe show physical adsorption to CH4. Since the C atom is surrounded by four H atoms in the CH4 molecular structure, the H atom approaches the substrate in the adsorption process. In the four adsorption processes, C-H bonds elongate due to the effect of H-Ag bonding.  Figure 7 shows the density of states before and after CH4 adsorption on Agn-GeSe. After CH4 adsorption, the TDOS of the system moved significantly to the left, and the filling of electrons at the Fermi level increased, increasing the probability of electrons crossing the gap from the valence band to the conduction band. Therefore, the conductivity increased after CH4 adsorption. The TDOS of the four adsorption structures increased at −7.0, −6.0, −6.5 and −5.0 eV, respectively. This is mainly due to the strong hybridization of Ag-4d, H-1s, and C-2p orbits. It can be seen from Figure 7(a2,b2), that there was a strong chemical bond between CH4 and Ag. However, the narrow orbital spike in Figure 7 (c2,d2) indicated that there was no chemical bond between CH4 and Ag atoms, but only physical adsorption. The invariance of Ag3-GeSe and Ag4-GeSe at the Fermi level, and the minimal peak changes at other places also confirmed that the reaction was physical adsorption.

Analysis of CH4 Gas Adsorption on Agn-GeSe Surface
The adsorption parameters of CH4 on Agn-GeSe are listed in Table 2, including adsorption distance, adsorption energy, and charge transfer. The adsorption energies of the four structures were −0.158, −0.159, −0.122 and −0.018 eV, respectively. The charge  Figure 7 shows the density of states before and after CH 4 adsorption on Ag n -GeSe. After CH 4 adsorption, the TDOS of the system moved significantly to the left, and the filling of electrons at the Fermi level increased, increasing the probability of electrons crossing the gap from the valence band to the conduction band. Therefore, the conductivity increased after CH 4 adsorption. The TDOS of the four adsorption structures increased at −7.0, −6.0, −6.5 and −5.0 eV, respectively. This is mainly due to the strong hybridization of Ag-4d, H-1s, and C-2p orbits. It can be seen from Figure 7(a2,b2), that there was a strong chemical bond between CH 4 and Ag. However, the narrow orbital spike in Figure 7 (c2,d2) indicated that there was no chemical bond between CH 4 and Ag atoms, but only physical adsorption. The invariance of Ag 3 -GeSe and Ag 4 -GeSe at the Fermi level, and the minimal peak changes at other places also confirmed that the reaction was physical adsorption.

Molecular Orbital Theory Analysis of Gases Adsorption on Agn-GeSe
The behavior of electron distribution in the adsorption process was analyzed by molecular orbital theory. The HOMO and LUMO of the CO and CH4 adsorption systems are shown in Figure 8 and Figure 9, respectively. The energy gap between HOMO and LUMO can be a key indicator to evaluate the conductivity of the target structure. Before gas adsorption on Agn-GeSe, HOMO mainly distributed over Ag, indicating that the Ag atom provided electrons to interact with CO and CH4 gases as an active site. After CO and CH4 adsorption, HOMO changes became more concentrated on Ag, while LUMO became more uniform.
As shown in Table 3, the energy gaps of the four CO adsorption structures were 0.053, 0.037, 0.031 and 0.036 eV, respectively. There was a small HOMO and LUMO distribution of Ag4-GeSe on Ag atoms upon CO adsorption, indicating that the electron distribution of the system was uniform, and the moderate band gap indicated that Ag4-GeSe was more suitable for CO adsorption. The energy gaps of the four CH4 adsorption systems were 0.049, 0.044, 0.046 and 0.025 eV, respectively. After Ag-GeSe adsorbed CH4, the band gap increased significantly, which made the conductivity of the system decrease significantly, so the conductivity change of the target system was more obvious. Therefore, Ag-GeSe is more suitable for the gas-sensing of CH4. The adsorption parameters of CH 4 on Ag n -GeSe are listed in Table 2, including adsorption distance, adsorption energy, and charge transfer. The adsorption energies of the four structures were −0.158, −0.159, −0.122 and −0.018 eV, respectively. The charge transfers were 0.034, 0.013, −0.068, −0.026 e, respectively. The long adsorption distance, small adsorption energy, and small charge transfer confirm that Ag 3 -GeSe and Ag 4 -GeSe are physical adsorptions to CH 4 . Ag-GeSe is more suitable for CH 4 gas adsorption according to the moderate adsorption distance, large adsorption energy, and moderate charge transfer. Table 2. Adsorption parameters of CH 4 gas molecules on Ag n -GeSe.

Molecular Orbital Theory Analysis of Gases Adsorption on Ag n -GeSe
The behavior of electron distribution in the adsorption process was analyzed by molecular orbital theory. The HOMO and LUMO of the CO and CH 4 adsorption systems are shown in Figures 8 and 9, respectively. The energy gap between HOMO and LUMO can be a key indicator to evaluate the conductivity of the target structure. Before gas adsorption on Ag n -GeSe, HOMO mainly distributed over Ag, indicating that the Ag atom provided electrons to interact with CO and CH 4 gases as an active site. After CO and CH 4 adsorption, HOMO changes became more concentrated on Ag, while LUMO became more uniform.
As shown in Table 3, the energy gaps of the four CO adsorption structures were 0.053, 0.037, 0.031 and 0.036 eV, respectively. There was a small HOMO and LUMO distribution of Ag 4 -GeSe on Ag atoms upon CO adsorption, indicating that the electron distribution of the system was uniform, and the moderate band gap indicated that Ag 4 -GeSe was more suitable for CO adsorption. The energy gaps of the four CH 4 adsorption systems were 0.049, 0.044, 0.046 and 0.025 eV, respectively. After Ag-GeSe adsorbed CH 4 , the band gap increased significantly, which made the conductivity of the system decrease significantly, so the conductivity change of the target system was more obvious. Therefore, Ag-GeSe is more suitable for the gas-sensing of CH 4 .

Conclusions
In this work, the adsorption behaviors of 1-4 Ag atom-modified GeSe to CO and CH 4 gases were analyzed based on first principle calculations. The interaction mechanism between Ag n -GeSe and the gas molecules was comprehensively investigated by analyzing adsorption structure, the density of states, and molecular orbital theory. All four Ag n -GeSe structures chemisorb CO gas, but Ag 4 -GeSe is more suitable for CO gas sensors according to proper adsorption distance, large adsorption energy, and proper charge transfer. Ag-GeSe and Ag 2 -GeSe chemisorb, while Ag 3 -GeSe and Ag 4 -GeSe physisorb CH 4 gas. Based on the density of states and molecular orbital theory analysis, it can be concluded that Ag-GeSe is more suitable for the detection of CH 4 gas. Although the adsorption mechanism was slightly different for CO and CH 4 adsorption on different Ag atom-doping systems, the adsorption capacity was very close. In conclusion, Ag cluster-modified GeSe could be a suitable CO and CH 4 gas-sensing material for use in the power system.

Data Availability Statement:
The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest:
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.