Pd-GaSe and Pd 3 -GaSe Monolayers: Two Promising Candidates for Detecting Dissolved Gases in Transformer Oil

: In this paper, the adsorption behaviors of three gases (H 2 , CO, and C 2 H 2 ) decomposed by the transformer oil on Pd-GaSe and Pd 3 -GaSe monolayers were calculated by density functional theory. Compared with Pd single-atom doping, Pd 3 cluster doping changed the original structure and charge distribution to a greater extent, and more obviously improved the conductivity. According to the analysis of adsorption energy, charge transfer and deformation charge density, the results show that the two doped structures have better adsorption performance for the three gas molecules (H 2 , CO, and C 2 H 2 ) than the intrinsic GaSe monolayer. Compared with Pd-GaSe, Pd 3 -GaSe showed stronger adsorption property for the three gases. Analysis of frontier molecular orbitals and recovery characteristics shows that Pd 3 -GaSe can be used as an ideal gas sensitive material for H 2 detection because of its good desorption properties and obvious conductivity changes. Pd-GaSe can be used as a disposable resistive sensor for CO. Pd 3 -GaSe is a kind of sensing material suitable for disposable resistance sensors for CO and C 2 H 2 . These two doped structures have great application potential in gas adsorption and detection, and provide indications for further study on gas sensor detection by means of metal-doped GaSe monolayer.


Introduction
The stability and reliability of power systems play a vital role in the prosperity of any country and the happiness of its people. Therefore, performance requirements for power network equipment are subject to gradual improvement. Power transformers are a crucial and expensive power network equipment necessary for voltage conversion [1][2][3][4]. Among them, oil-immersed transformers account for about 90%. Over the long-term operation of the equipment, insulation oil is decomposed into H 2 , CO, C 2 H 2 , and other gases due to insulation overheating, low energy spark, arc, partial discharge, and other faults [5]. Dissolved gas analysis (DGA) is commonly used to diagnose transformer faults because it provides great information about thermal anomalies and electricity [6]. Therefore, early detection of equipment faults helps reduce the losses caused by these faults.
Recently, with the successful research and development of graphene materials, twodimensional (2D) materials have been broadly studied and successfully applied in many areas such as energy storage and transformation, electronics, and sensing materials due to their unique molecular structure and physicochemical properties [7][8][9][10][11][12]. In addition, many two-dimensional materials are used for gas sensor detection of dissolved gas in transformer oil in the field of dissolved gas analysis (DGA). By detecting the type and proportion of dissolved gas in transformer oil, we can assess the operation of electrical equipment, analyze the fault type, and then determine the corresponding maintenance method to reduce the loss, which is a significant topic in electric power research in recent times [13][14][15][16]. For instance, Qian et al. found that an Au-doped MoS 2 monolayer can remarkably improve the adsorption performance for C 2 H 6 and C 2 H 4 gases [17]. At present, the requirement of characteristic gas detection is gradually increasing, and various gas sensors are in the research stage. Two-dimensional materials such as metal oxides, transition metal dihalogens (TMDs), metal nitrides, and carbides have attracted extensive attention in the academic world [18][19][20]. It is a promising research direction for the study and design of a gas sensor with better performance to detect the characteristic gases.
GaSe is a kind of metal-chalcogen compound with a layered hexagonal structure, belonging to a layered III-VI semiconductor and has been studied since last century. Hu et al. prepared two-dimensional nanosheets of ultrathin GaSe by using mechanical cleavage and solvent exfoliation method [21]. Due to its good ON/OFF ratio, electron differential mobility, low energy of formation and second-order nonlinearity, GaSe has shown wide application prospects in the fields of transistors, water splitting photocatalysts, and nonlinear optics [22][23][24]. Zhou et al. studied the adsorption performance of monolayer GaSe on several small molecule gases such as H 2 , O 2 , NO 2 , and H 2 O, and found that monolayer GaSe has a wide application prospect as O 2 and NO 2 sensors [25]. Increasing research has found that the doping of transition metal (TM) can improve the charge transfer rate between gas and material, thus greatly improving the sensitivity of gas molecules [26][27][28]. Jiang et al. found that V-GaSe monolayer had higher conductivity and better gas adsorption performance than an intrinsic GaSe monolayer, and could better adsorb SF 6 decomposition products [29]. Among TM atoms, Pd atom, as a doped atom, has significantly enhanced the adsorption performance of the substrate to characteristic gases in many materials doping studies. Cui et al. found that Pd-doped HfSe 2 has good adsorption performance for NO 2 and SO 2 molecules [30][31][32]. At present, there is little research on Pd atom-doped GaSe gas sensitive materials. In this paper, Pd atom-doped GaSe materials for several gases were studied.
To the present time, only few studies have investigated the influence of cluster doping on gas adsorption performance. For example, Gao et al. studied the effect of Ni n (n = 1, 2, 3, and 4) doped graphene on NO adsorption, and found that the more Ni atoms, the more obvious the effect of Ni on NO adsorption [33]. Cui et al. have studied the structure and electronic characteristics of Rh n (n = 1-4) cluster doped MoS 2 monolayer, and found that Rh 3 -MoS 2 has the best stability and the best electronic behavior [34]. For the above reasons, the Pd 3 cluster doping method is adopted in this paper. Therefore, this paper studies the adsorption behavior of Pd monatomic doped GaSe molecules and Pd 3 cluster-doped GaSe molecules on dissolved gases in transformer oil, and compares the adsorption performance of the two materials.

Computation Methods
In this study, all microscopic calculations based on density functional theory (DFT) were performed in Dmol 3 module of Materials Studio (MS). For dealing with the electron exchange correlation function and correlation energy, we use the Perdew-Burke-Ernzerhof (PBE) function to calculate the generalized gradient approximation (GGA) [35,36]. We used the Tkatchenko and Schefflfler (TS) method to correct the weak van der Waals forces between the gas molecules and the monolayer material [37]. The DFT-D method was used to calculate the weak interaction between adsorbed atom and substrate to obtain a more accurate result. The DFT semi-core pseudopotential (DSPP) method was used to deal with core electron relativity effects [38]. The double numerical plus polarization (DNP) method was selected for the linear combination of atomic orbitals [39,40]. GaSe supermonomer was constructed for atomic doping and gas adsorption, and was designed to be 14.972 Å × 14.972 Å × 24.7757 Å. To avoid interactions between adjacent cells, the vacuum region of a GaSe supercell was set to 20 Å vertically [41]. A 4 × 4 × 1 Monkhorst-Pack of k-point was used to analyze the Brillouin zones for geometric optimization and electronic structure calculation [42]. Electron spin is unrestricted [29,43,44]. The value of convergence criteria for the energy, maximum force and displacement were severally set as 1 × 10 −5 Ha, 2 × 10 −3 Ha/Å, and 5 × 10 −3 Å. By calculating binding energy (E b ), the most stable doping structure can be determined. When n is equal to 1 or 3, the binding energy formula of Pd n doping GaSe is defined as: [45] where, E Pdn−GaSe and E GaSe are the total energy of Pd n -doped GaSe and the total energy of GaSe molecular layer respectively. E Pd is the energy of a single Pd atom, when n is equal to 3, 3 E Pd represents the energies of the three isolated Pd atoms [46]. When the gas molecules approach the sensor surface in different ways, the adsorption energy (E ad ) is used to characterize the adsorption performance of the material to a single gas molecule [47]. E ad = E Pd n −GaSe/gas − E Pd n −GaSe + E gas (2) In the above formula, E Pdn−GaSe/gas represents the total energy of the gas adsorption system, E gas represents the total energy of the gas molecule [48]. A larger absolute value of E ad means that the system is more stable [49]. If the absolute value of E ad is less than 0.6 eV, it indicates that the adsorption process is physical adsorption, while when the absolute value of E ad is greater than 0.8 eV, it indicates that chemical adsorption exists in the process [50][51][52].
We use Muliken charge analysis to calculate the charge transfer between the gases and the Pd n -GaSe, represented by Q T .
Q after means the charge of the gas molecules after the system absorbs the gases, and Q before represents the charge of the gas molecules before the system absorbs the gases. When Q T is a positive value, it means that in the adsorption process, the gas loses electrons, and electrons with a value corresponding to |Q T | are transferred from the gas molecules to the adsorption material. On the contrary, when Q T is negative, gas acts as an electron acceptor, accepting electrons transferred from the crystal surface [53].

Structures of Characteristic Gases, Pd-GaSe, and Pd 3 -GaSe Monolayers
Figures 1 and 2 show the optimized dissolved gas molecular structures in transformer oil and the optimized GaSe monolayer, respectively. The H 2 molecule and C 2 H 2 molecule have a symmetrical structure. The length of H-H bond in H 2 is 0.749 Å and the length of C-O bond in CO is 1.142 Å. The C-C and C-H bonds in C 2 H 2 molecule are 1.211 Å and 1.071 Å in length, separately. The optimized data of gas molecular structures are the same as the experimental results of previous research [54,55]. Figure 2 shows the top and side views of the intrinsic GaSe, where the Ga-Se bond length is 2.472 Å. GaSe belongs to two-dimensional network structure.  Firstly, Pd single-doped GaSe was studied. There were three possible doping positions considered, namely TH (hexagonal ring center of GaSe), TGa (top of Ga atom), TSe (top of Se atom), and TB (bridge site between two Se atoms) [30]. The configurations of the four doping sites were optimized, and the binding energies of the four models were calculated as −2.214 eV, −2.316 eV, −1.901 eV and −2.170 eV, respectively. The more negative Eb is, the better the stability is, it corresponds to the most ideal doping site. Therefore, TGa was selected as the doping site for subsequent research. Figure 3 shows its structure. The TDOS and PDOS diagrams of Pd-doped system are given in Figure 4. One can see that the TDOS of the Pd-GaSe system moves to the lower energy level as a whole, and the intercept at Fermi level decreases. Therefore, this shows that doping of Pd reduces the energy band of GaSe. The decrease of energy band indicates that the transition of electrons becomes easier, so the conductivity of the system is enhanced [56]. It can be seen from PDOS in Figure 4b that Pd-4d orbital overlaps with Se-4p orbital near −2.7 eV, indicating that a chemical bond between Pd and Se is formed, thus changing the charge distribution of the system. The results show that Pd and Se interact with each other.   Firstly, Pd single-doped GaSe was studied. There were three possible doping positions considered, namely T H (hexagonal ring center of GaSe), T Ga (top of Ga atom), T Se (top of Se atom), and T B (bridge site between two Se atoms) [30]. The configurations of the four doping sites were optimized, and the binding energies of the four models were calculated as −2.214 eV, −2.316 eV, −1.901 eV and −2.170 eV, respectively. The more negative E b is, the better the stability is, it corresponds to the most ideal doping site. Therefore, T Ga was selected as the doping site for subsequent research. Figure 3 shows its structure. The TDOS and PDOS diagrams of Pd-doped system are given in Figure 4. One can see that the TDOS of the Pd-GaSe system moves to the lower energy level as a whole, and the intercept at Fermi level decreases. Therefore, this shows that doping of Pd reduces the energy band of GaSe. The decrease of energy band indicates that the transition of electrons becomes easier, so the conductivity of the system is enhanced [56]. It can be seen from PDOS in Figure 4b that Pd-4d orbital overlaps with Se-4p orbital near −2.7 eV, indicating that a chemical bond between Pd and Se is formed, thus changing the charge distribution of the system. The results show that Pd and Se interact with each other. Firstly, Pd single-doped GaSe was studied. There were three possible doping positions considered, namely TH (hexagonal ring center of GaSe), TGa (top of Ga atom), TSe (top of Se atom), and TB (bridge site between two Se atoms) [30]. The configurations of the four doping sites were optimized, and the binding energies of the four models were calculated as −2.214 eV, −2.316 eV, −1.901 eV and −2.170 eV, respectively. The more negative Eb is, the better the stability is, it corresponds to the most ideal doping site. Therefore, TGa was selected as the doping site for subsequent research. Figure 3 shows its structure. The TDOS and PDOS diagrams of Pd-doped system are given in Figure 4. One can see that the TDOS of the Pd-GaSe system moves to the lower energy level as a whole, and the intercept at Fermi level decreases. Therefore, this shows that doping of Pd reduces the energy band of GaSe. The decrease of energy band indicates that the transition of electrons becomes easier, so the conductivity of the system is enhanced [56]. It can be seen from PDOS in Figure 4b that Pd-4d orbital overlaps with Se-4p orbital near −2.7 eV, indicating that a chemical bond between Pd and Se is formed, thus changing the charge distribution of the system. The results show that Pd and Se interact with each other.   Firstly, Pd single-doped GaSe was studied. There were three possible doping positions considered, namely TH (hexagonal ring center of GaSe), TGa (top of Ga atom), TSe (top of Se atom), and TB (bridge site between two Se atoms) [30]. The configurations of the four doping sites were optimized, and the binding energies of the four models were calculated as −2.214 eV, −2.316 eV, −1.901 eV and −2.170 eV, respectively. The more negative Eb is, the better the stability is, it corresponds to the most ideal doping site. Therefore, TGa was selected as the doping site for subsequent research. Figure 3 shows its structure. The TDOS and PDOS diagrams of Pd-doped system are given in Figure 4. One can see that the TDOS of the Pd-GaSe system moves to the lower energy level as a whole, and the intercept at Fermi level decreases. Therefore, this shows that doping of Pd reduces the energy band of GaSe. The decrease of energy band indicates that the transition of electrons becomes easier, so the conductivity of the system is enhanced [56]. It can be seen from PDOS in Figure 4b that Pd-4d orbital overlaps with Se-4p orbital near −2.7 eV, indicating that a chemical bond between Pd and Se is formed, thus changing the charge distribution of the system. The results show that Pd and Se interact with each other.   Secondly, the Pd 3 -GaSe system was analyzed. Three common doping sites were considered in this paper, [19] and two relatively stable models were obtained by optimizing the established model without serious distortion, as illustrated in the Figure 5. The optimized binding energies of the two structures are −6.616 eV and −6.627 eV severally. Similarly, a larger absolute value of binding energy means that the structure is more stable. Therefore, the model B is selected for subsequent research. Bonds are formed between Pd and Se atoms, and the three Pd atoms form an approximate equilateral triangle with 2.932 Å, 2.910 Å and 2.842 Å in bond length separately. Figure 6a shows the TDOS image before and after doping Pd 3 cluster. After doping, the system curve moves to the direction of low energy level, indicating that the Pd 3 cluster doping reduces the band gap of GaSe. TDOS appeared a new peak near −0.6 eV, which may be caused by the hybridization of Pd and Se orbits. It can be perceived from the PDOS image in Figure 5b that Pd-4d orbital and Se-4p orbital are hybridized at the −0.6 eV, proving that Pd can form a stable chemical bond with Se and verifying the previous idea. Compared with the TDOS of Pd-GaSe system, the TDOS of Pd 3 -GaSe system has a larger moving distance. Therefore, it is considered that the conductivity of GaSe system doped with Pd 3 cluster is improved more significantly than that of GaSe system doped with Pd. To sum up, it is speculated that Pd 3 -GaSe system may have better gas adsorption.
Secondly, the Pd3-GaSe system was analyzed. Three common doping sites were considered in this paper, [19] and two relatively stable models were obtained by optimizing the established model without serious distortion, as illustrated in the Figure 5. The optimized binding energies of the two structures are −6.616 eV and −6.627 eV severally. Similarly, a larger absolute value of binding energy means that the structure is more stable. Therefore, the model B is selected for subsequent research. Bonds are formed between Pd and Se atoms, and the three Pd atoms form an approximate equilateral triangle with 2.932 Å, 2.910 Å and 2.842 Å in bond length separately. Figure 6a shows the TDOS image before and after doping Pd3 cluster. After doping, the system curve moves to the direction of low energy level, indicating that the Pd3 cluster doping reduces the band gap of GaSe. TDOS appeared a new peak near −0.6 eV, which may be caused by the hybridization of Pd and Se orbits. It can be perceived from the PDOS image in Figure 5b that Pd-4d orbital and Se-4p orbital are hybridized at the −0.6 eV, proving that Pd can form a stable chemical bond with Se and verifying the previous idea. Compared with the TDOS of Pd-GaSe system, the TDOS of Pd3-GaSe system has a larger moving distance. Therefore, it is considered that the conductivity of GaSe system doped with Pd3 cluster is improved more significantly than that of GaSe system doped with Pd. To sum up, it is speculated that Pd3-GaSe system may have better gas adsorption.
We consider all the adsorption sites for each gas, and build models to make gas molecules approach the adsorption materials in different ways. After geometric optimization, the adsorption energy of each adsorption model is calculated by Formula (2), and the models with the largest absolute value of adsorption energy are selected as the models for subsequent research.   Secondly, the Pd3-GaSe system was analyzed. Three common doping sites were considered in this paper, [19] and two relatively stable models were obtained by optimizing the established model without serious distortion, as illustrated in the Figure 5. The optimized binding energies of the two structures are −6.616 eV and −6.627 eV severally. Similarly, a larger absolute value of binding energy means that the structure is more stable. Therefore, the model B is selected for subsequent research. Bonds are formed between Pd and Se atoms, and the three Pd atoms form an approximate equilateral triangle with 2.932 Å, 2.910 Å and 2.842 Å in bond length separately. Figure 6a shows the TDOS image before and after doping Pd3 cluster. After doping, the system curve moves to the direction of low energy level, indicating that the Pd3 cluster doping reduces the band gap of GaSe. TDOS appeared a new peak near −0.6 eV, which may be caused by the hybridization of Pd and Se orbits. It can be perceived from the PDOS image in Figure 5b that Pd-4d orbital and Se-4p orbital are hybridized at the −0.6 eV, proving that Pd can form a stable chemical bond with Se and verifying the previous idea. Compared with the TDOS of Pd-GaSe system, the TDOS of Pd3-GaSe system has a larger moving distance. Therefore, it is considered that the conductivity of GaSe system doped with Pd3 cluster is improved more significantly than that of GaSe system doped with Pd. To sum up, it is speculated that Pd3-GaSe system may have better gas adsorption.
We consider all the adsorption sites for each gas, and build models to make gas molecules approach the adsorption materials in different ways. After geometric optimization, the adsorption energy of each adsorption model is calculated by Formula (2), and the models with the largest absolute value of adsorption energy are selected as the models for subsequent research.   We consider all the adsorption sites for each gas, and build models to make gas molecules approach the adsorption materials in different ways. After geometric optimization, the adsorption energy of each adsorption model is calculated by Formula (2), and the models with the largest absolute value of adsorption energy are selected as the models for subsequent research.

H 2 Adsorption
The adsorption properties, charge transfer, and E ad of H 2 on Pd-GaSe and Pd 3 -Gase monolayers are shown in Figures 7 and 8, and Table 1. Some data of H 2 adsorption by intrinsic GaSe monolayer are also listed in Table 1. From the data in Table 1, the adsorption energy of H 2 on GaSe monolayer is −0.544 eV, H 2 on Pd-GaSe monolayer is −0.58 eV, and H 2 on Pd 3 -GaSe monolayer is −0.943 eV. It is worth noting that the adsorption distance of GaSe/H 2 system (3.504 Å) is almost twice that of Pd-GaSe/H 2 system (1.820 Å), but the adsorption energy of both systems is close. It can be noted that the Q T of Pd-GaSe/H 2 system (0.108 e) is obviously more than that of GaSe/H 2 system (0.002 e), and the former has stronger charge transfer behavior. The results show that the doping of Pd improves the electronic behavior in the adsorption process, so the adsorption distance of Pd-GaSe/H 2 system is smaller than that of GaSe/H 2 system. However, from the point of view of adsorption energy, the two kinds of adsorption belong to weak physical adsorption, and the doping of Pd does not change the weak adsorption behavior of H 2 . The doping method of Pd 3 cluster significantly enhances the system's adsorption performance for H 2 , which belongs to chemical adsorption. Isolated H 2 has a bond length of 0.749 Å, and both kinds of doping make the H-H bond longer after adsorption. It can also be seen from the adsorption model that Pd 3 -GaSe monolayer is obviously deformed during the adsorption process, and all three Pd atoms have shifted in different degrees. Pd cluster capture H 2 , which indicates that there is a strong interaction between them. Mulliken atomic population analysis of H 2 molecule shows that 0.108 e electrons are transferred to Pd-GaSe monolayer and 0.199 e electrons are transferred to Pd 3 -GaSe monolayer after H 2 adsorption. The results show that the doping method of Pd 3 cluster brings greater charge transfer amount than the doping method of Pd. Figures 7c and 8c show the deformation charge density (DCD) of the two adsorption systems. In the figure, red represents the charge accumulation zone and blue represents the charge depletion zone. In the two systems, there is an obvious blue area around Pd atom, which can be seen as the link of electron transfer between gas and material.
In Figure 7d, TDOS of the Pd-GaSe system shifted slightly to the right after H 2 adsorption, indicating that the electron orbit changed, but TDOS changed little during the adsorption process. The results indicate that H 2 has weak interaction with Pd-GaSe. TDOS shown in Figure 8d shows that after H 2 was adsorbed by Pd 3 -GaSe system, TDOS decreased in the vicinity of −6.2 eV and increased significantly around −8.4 eV. In both systems, the spin-up and spin-down curves are symmetric, which means that the two H 2 adsorption systems are non-magnetic [57]. As shown in Figure 7e, in the Pd-GaSe system, slight hybridization exists between Pd-4d and H-1s orbitals near −7.3 eV and −0.1 eV. As shown in Figure 8e, in the Pd 3 -GaSe system, the peak of H-1s orbital near −8.4 eV not only explains the increase of TDOS at −8.4 eV, but also indicates its hybridization with the Pd-4d orbital. Since the Pd-4d orbital overlaps with the H-1s orbital, it is speculated that a chemical bond may be formed between the two atoms. In conclusion, the doping method Pd n (n is 1 or 3) can improve the H 2 adsorption performance of GaSe monolayer, and the H 2 adsorption performance of the Pd 3 cluster doping method is stronger than that of the Pd doping method. explains the increase of TDOS at −8.4 eV, but also indicates its hybridization with the Pd-4d orbital. Since the Pd-4d orbital overlaps with the H-1s orbital, it is speculated that a chemical bond may be formed between the two atoms. In conclusion, the doping method Pdn (n is 1 or 3) can improve the H2 adsorption performance of GaSe monolayer, and the H2 adsorption performance of the Pd3 cluster doping method is stronger than that of the Pd doping method.

CO Adsorption
Parameters and structures related to CO adsorption are shown in Figures 9 and 10, and Table 2. From the data in Table 2, after CO adsorption, the adsorption energy of Pd-GaSe and Pd3-GaSe systems are −1.587 eV and −2.427 eV respectively. When the absolute value of adsorption energy is greater than 0.8 eV, chemisorption exists. Therefore, the adsorption of CO by the two doped systems belongs to chemisorption. By comparing with explains the increase of TDOS at −8.4 eV, but also indicates its hybridization with the Pd-4d orbital. Since the Pd-4d orbital overlaps with the H-1s orbital, it is speculated that a chemical bond may be formed between the two atoms. In conclusion, the doping method Pdn (n is 1 or 3) can improve the H2 adsorption performance of GaSe monolayer, and the H2 adsorption performance of the Pd3 cluster doping method is stronger than that of the Pd doping method.

CO Adsorption
Parameters and structures related to CO adsorption are shown in Figures 9 and 10, and Table 2. From the data in Table 2, after CO adsorption, the adsorption energy of Pd-GaSe and Pd3-GaSe systems are −1.587 eV and −2.427 eV respectively. When the absolute value of adsorption energy is greater than 0.8 eV, chemisorption exists. Therefore, the adsorption of CO by the two doped systems belongs to chemisorption. By comparing with

CO Adsorption
Parameters and structures related to CO adsorption are shown in Figures 9 and 10, and Table 2. From the data in Table 2, after CO adsorption, the adsorption energy of Pd-GaSe and Pd 3 -GaSe systems are −1.587 eV and −2.427 eV respectively. When the absolute value of adsorption energy is greater than 0.8 eV, chemisorption exists. Therefore, the adsorption of CO by the two doped systems belongs to chemisorption. By comparing with the adsorption energy for CO of the intrinsic GaSe monolayer (−0.545 eV), indicating that the doping method of Pd n (n is 1 or 3) obviously enhanced the adsorption of CO, and the enhanced adsorption effect may be caused by the formation of chemical bonds between CO and doping groups. In further proof, the length of C-O bond increased from 1.142 Å to 1.158 Å after adsorption on Pd-GaSe monolayer, while the length of C-O bond increased to 1.180 Å after adsorption on Pd 3 -Gase monolayer. The change of bond length indicates that CO has certain activity in the adsorption process. In addition to the C-O bond, some Pd-Se bonds in Pd 3 -GaSe monolayer also increased obviously. Pd cluster capture CO molecules through C. Mulliken population analysis of CO molecule showed that 0.163 e electrons were transferred from CO molecule to Pd-GaSe monolayer after adsorption. After the adsorption of Pd 3 -Gase monolayer, 0.187 e electrons were transferred from CO molecule to Pd 3 -GaSe monolayer. In the DCD diagrams of Figures 9c and 10c, the blue area and the red area represent electron accumulation region and electron depletion region separately. As can be seen from the DCD diagrams of the two doping models, there is an obvious continuous electron region between Pd atom and CO gas molecule, which means that there is a strong chemical interaction between CO and the two adsorption materials.   Figures 11 and 12, and Table 3 show the structures and related parameters of C2H2 adsorption. After the adsorption of C2H2 on the two doped materials, the structure of C2H2 has obvious deformation but still has good symmetry. In the Pd-GaSe/C2H2 system, H-C-C and C-C-H bond angles change to 155.279° and 155.552°, respectively. In the Pd3-GaSe/C2H2 system, H-C-C and C-C-H bond angles decrease to 131.730° and 131.258°. As   Figures 11 and 12, and Table 3 show the structures and related parameters of C2H2 adsorption. After the adsorption of C2H2 on the two doped materials, the structure of C2H2 has obvious deformation but still has good symmetry. In the Pd-GaSe/C2H2 system, H-C-C and C-C-H bond angles change to 155.279° and 155.552°, respectively. In the Pd3-GaSe/C2H2 system, H-C-C and C-C-H bond angles decrease to 131.730° and 131.258°. As    Figure 10d,e show the DOS distribution of the Pd 3 -GaSe system. After adsorption, TDOS showed a new peak near −9.3 eV and decreased significantly at −0.6 eV. Pd-4d orbital, C-2p orbital, and O-2p orbital have overlapping regions around −0.9 eV and −6.1 eV, C-2p, and O-2p have obvious hybridization around 1.5 eV and −9.3 eV. These hybridization phenomena lead to changes in TDOS of the adsorption system, indicating that the adsorption of gas affects the electron behavior of Pd 3 -GaSe monolayer. The results show that both Pd-GaSe monolayer and Pd 3 -GaSe monolayer have an obvious adsorption effect on CO, and the adsorption performance of CO is significantly improved after doping Pd n (n is 1 or 3). However, higher adsorption energy, higher charge transfer and more obvious gas molecules deformation show that Pd 3 -Gase monolayer has better adsorption performance for CO. Table 3 show the structures and related parameters of C 2 H 2 adsorption. After the adsorption of C 2 H 2 on the two doped materials, the structure of C 2 H 2 has obvious deformation but still has good symmetry. In the Pd-GaSe/C 2 H 2 system, H-C-C and C-C-H bond angles change to 155.279 • and 155.552 • , respectively. In the Pd 3 -GaSe/C 2 H 2 system, H-C-C and C-C-H bond angles decrease to 131.730 • and 131.258 • . As can be seen, in Pd 3 -GaSe/C 2 H 2 system, deformation of the C 2 H 2 molecule is more severe, which may be related to the stronger reaction between adsorbent and C 2 H 2 . The adsorption energy of Pd-GaSe/C 2 H 2 and Pd 3 -GaSe/C 2 H 2 systems are −1.307 eV and −2.757 eV, respectively, both of which belong to chemisorption. Compared with the direct adsorption of intrinsic GaSe monolayer (E ad = −0.7 eV), the adsorption energy of the two doping systems for C 2 H 2 were significantly increased, and the change of adsorption energy of Pd 3 -GaSe/C 2 H 2 system was particularly obvious, which also verified the previous conjecture. Moreover, from the adsorption model, it can be seen that Pd 3 -GaSe has a strong adsorption effect on C 2 H 2 . After adsorption, three Pd atoms shift obviously and capture C 2 H 2 , but the monolayer of Pd-GaSe does not change obviously. In the Pd-GaSe/C 2 H 2 system, Pd atom carries 0.296 e electrons after C 2 H 2 molecule transfers 0.1 e electrons to Pd-GaSe monolayer, indicating that Pd atom obtains electrons from GaSe monolayer. Similarly, Pd acts as an electron acceptor in the Pd 3 -GaSe/C 2 H 2 system, accepting electrons from gas molecules and GaSe monolayer. As can be seen from the DCD diagrams in Figures11c and 12c, the overlap between the red and blue areas between the gas and the material indicates a large amount of electron transfer and strong chemical reaction strength.

Frontier Orbital Theory Analysis
To further elucidate the changes in the conductivity of Pd-GaSe and Pd3-GaSe monolayers caused by gas adsorption, the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) were calculated according to the frontier molecular orbital (FMO) theory. The relationship between band gap and conductivity is shown as follows: where kB and T represent Boltzmann constant and temperature respectively. According to the formula, the narrower the band gap means that it has greater conductivity when the temperature is constant. Thus, the narrower the band gap, the easier the electron transfer.

Frontier Orbital Theory Analysis
To further elucidate the changes in the conductivity of Pd-GaSe and Pd3-GaSe monolayers caused by gas adsorption, the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) were calculated according to the frontier molecular orbital (FMO) theory. The relationship between band gap and conductivity is shown as follows: where kB and T represent Boltzmann constant and temperature respectively. According to the formula, the narrower the band gap means that it has greater conductivity when the temperature is constant. Thus, the narrower the band gap, the easier the electron transfer. DOS distribution of Pd-GaSe/C 2 H 2 system is shown in Figure 11d,e. After adsorption of C 2 H 2 , the TDOS of the system appeared a new peak near −8.8 eV, but there was no obvious change. In addition, the Pd-4d orbital and C-2p orbital overlap at −0.1 eV, −2.9 eV, and −7.1 eV, and hybridization between orbitals causes strong orbital interactions. Based on the TDOS distribution of the Pd 3 -GaSe/C 2 H 2 system shown in Figure 12d, the overall TDOS shifted significantly to the left after adsorption, indicating that its electrical conductivity was significantly enhanced. As can be seen from the PDOS distribution in Figure 12e, obvious orbital hybridization exists in Pd-4d and C-2p orbitals at 0.1 eV, −1.1 eV, −4.5 eV, and −7.5 eV. It means that chemical bonds are formed between Pd atom and C atom. From the above analysis, it can be seen that Pd 3 -GaSe monolayer shows strong adsorption of C 2 H 2 . In conclusion, after Pd n (n is 1 or 3) doping, the adsorption performance of the system for C 2 H 2 is significantly enhanced, and various data show that Pd 3 cluster doped with GaSe monolayer have better adsorption performance of C 2 H 2 than Pd-GaSe system.

Frontier Orbital Theory Analysis
To further elucidate the changes in the conductivity of Pd-GaSe and Pd 3 -GaSe monolayers caused by gas adsorption, the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) were calculated according to the frontier molecular orbital (FMO) theory. The relationship between band gap and conductivity is shown as follows: where k B and T represent Boltzmann constant and temperature respectively. According to the formula, the narrower the band gap means that it has greater conductivity when the temperature is constant. Thus, the narrower the band gap, the easier the electron transfer. Refer to Figure 13a, LUMO and HOMO are mostly distributed around Pd atoms in the Pd-GaSe system. After gas molecule adsorption, LUMO and HOMO distribution of the Pd-GaSe/H 2 system does not change much compared with that before adsorption, meaning that the interaction force between gas and adsorption material is weak after H 2 adsorption. In Pd-GaSe/CO and Pd-GaSe/C 2 H 2 systems, LUMO is mainly distributed in Pd-GaSe monolayer, HOMO is mainly distributed in the vicinity of gas molecules and Pd atoms. After the adsorption of the three gas molecules, the band gaps of the adsorption systems all increase, indicating that the conductivity of the adsorption systems decreases after gas adsorption. Since the band gap increase of Pd-GaSe/C 2 H 2 system is not obvious, the sensitivity of the sensor to C 2 H 2 detection is limited. Therefore, Pd-GaSe can be used as a semiconductor sensor to detect H 2 and CO.
In Figure 13b, before gas adsorption, LUMO and HOMO are mainly distributed around the Pd 3 group before gas adsorption, which indicated that there is a high electron concentration in the vicinity of the Pd 3 cluster. After gas adsorption, HOMO of the system is mainly distributed near gas molecules and Pd 3 cluster. Except for the Pd 3 -GaSe/H 2 system, the LUMO of the other two systems is rarely distributed near the gas and Pd 3 cluster. Compared with Pd 3 -GaSe, the band gap of Pd 3 -GaSe/C 2 H 2 system decreased significantly, indicating that the electrical conductivity increased significantly after adsorption. However, the band gaps of Pd 3 -GaSe/H 2 and Pd 3 -GaSe/CO systems increased and the conductivity decreased after gas adsorption. Therefore, Pd 3 -GaSe can be used as a sensor material to detect these three gases.
is mainly distributed near gas molecules and Pd3 cluster. Except for the Pd3-GaSe/H2 system, the LUMO of the other two systems is rarely distributed near the gas and Pd3 cluster. Compared with Pd3-GaSe, the band gap of Pd3-GaSe/C2H2 system decreased significantly, indicating that the electrical conductivity increased significantly after adsorption. However, the band gaps of Pd3-GaSe/H2 and Pd3-GaSe/CO systems increased and the conductivity decreased after gas adsorption. Therefore, Pd3-GaSe can be used as a sensor material to detect these three gases.

Analysis of Recovery Time
As an important index, recovery time is used to indicate the desorption capacity of gas-sensitive materials to characteristic gases, which can be obtained by the following equation: In the above formula, A and T represent the attempt frequency and temperature, A is constant and equal to 10 12 s −1 . [30,58,59] KB represents Boltzmann constant (8.62 × 10 −5 eV/K). Ea represents the energy to be overcome in the desorption process, and its value can be considered to be equal to Ead. Figure 14 shows the recovery time of the three gas

Analysis of Recovery Time
As an important index, recovery time is used to indicate the desorption capacity of gassensitive materials to characteristic gases, which can be obtained by the following equation: In the above formula, A and T represent the attempt frequency and temperature, A is constant and equal to 10 12 s −1 . [30,58,59] K B represents Boltzmann constant (8.62 × 10 −5 eV/K). E a represents the energy to be overcome in the desorption process, and its value can be considered to be equal to E ad . Figure 14 shows the recovery time of the three gas molecules on the Pd-GaSe and Pd 3 -GaSe systems at 298 K, 398 K, and 498 K. The recovery time of H 2 in Pd-GaSe is very short, and the adsorptive H 2 will soon break away from the binding of the material, indicating that Pd-GaSe is not suitable as H 2 scavenger. When the temperature is 398 K, the recovery time of H 2 on Pd 3 -GaSe is 0.87 s, and when the temperature is 298 K, the recovery time is 8780 s (2.4 h), meaning that Pd 3 -GaSe is an ideal gas sensitive material for the detection of H 2 . CO is difficult to desorption on the two adsorption systems at three temperatures, which means that there is a strong interaction between adsorbent and gas molecule. Therefore, both doping structures can be used as disposable CO scavengers. At 298 K, C 2 H 2 is difficult to desorption from Pd-GaSe monolayer, but the recovery time is 16.7 s when the temperature rises to 498 K. Pd-GaSe has a strong adsorption of C 2 H 2 at room temperature, and the recovery time is very short at high temperature. However, after adsorption of C 2 H 2 , the increase of conductivity is not obvious. Therefore Pd-GaSe is more suitable as a reusable C 2 H 2 scavenger than for detecting C 2 H 2 . However, the desorption time of C 2 H 2 on Pd 3 -GaSe is very long, and Pd 3 -GaSe can be used as a one-time scavenger of C 2 H 2 .
CO scavengers. At 298 K, C2H2 is difficult to desorption from Pd-GaSe monolayer, but the recovery time is 16.7 s when the temperature rises to 498 K. Pd-GaSe has a strong adsorption of C2H2 at room temperature, and the recovery time is very short at high temperature. However, after adsorption of C2H2, the increase of conductivity is not obvious. Therefore Pd-GaSe is more suitable as a reusable C2H2 scavenger than for detecting C2H2. However, the desorption time of C2H2 on Pd3-GaSe is very long, and Pd3-GaSe can be used as a onetime scavenger of C2H2.

Conclusions
In this study, the adsorption behaviors of Pd-GaSe and Pd3-GaSe monolayers on three gases (H2, CO, and C2H2) decomposed by the transformer oil were studied using DFT calculations. The results show that Pd mono-atom doping and Pd3 cluster doping can improve the adsorption capacity of the materials to the three gases compared with the intrinsic GaSe monolayer. The adsorption performance of Pd3-GaSe for three gases is better than that of Pd-GaSe. All three kinds of adsorption of Pd3-GaSe are chemical adsorption. It is speculated that the increase in the number of doped Pd atoms changes the original structure and charge distribution to a greater extent, more obviously enhances the conductivity, and thus enhances the adsorption performance of the gas. Through the analysis of DOS, the above viewpoint is also proved. By analyzing the frontier molecular orbitals and recovery characteristics, Pd3-GaSe can be used as an ideal gas sensitive material for H2 detection because of its good desorption properties and obvious conductivity changes. Pd-GaSe can also be used as a disposable resistive sensor for CO. Pd3-GaSe is a sensing material suitable for the disposable resistive sensor for CO and C2H2. Therefore, Pd-GaSe and Pd3-GaSe monolayers have great application potential in gas detection and adsorption, and are of important significance to the safe operation of power equipment.

Conclusions
In this study, the adsorption behaviors of Pd-GaSe and Pd 3 -GaSe monolayers on three gases (H 2 , CO, and C 2 H 2 ) decomposed by the transformer oil were studied using DFT calculations. The results show that Pd mono-atom doping and Pd 3 cluster doping can improve the adsorption capacity of the materials to the three gases compared with the intrinsic GaSe monolayer. The adsorption performance of Pd 3 -GaSe for three gases is better than that of Pd-GaSe. All three kinds of adsorption of Pd 3 -GaSe are chemical adsorption. It is speculated that the increase in the number of doped Pd atoms changes the original structure and charge distribution to a greater extent, more obviously enhances the conductivity, and thus enhances the adsorption performance of the gas. Through the analysis of DOS, the above viewpoint is also proved. By analyzing the frontier molecular orbitals and recovery characteristics, Pd 3 -GaSe can be used as an ideal gas sensitive material for H 2 detection because of its good desorption properties and obvious conductivity changes. Pd-GaSe can also be used as a disposable resistive sensor for CO. Pd 3 -GaSe is a sensing material suitable for the disposable resistive sensor for CO and C 2 H 2 . Therefore, Pd-GaSe and Pd 3 -GaSe monolayers have great application potential in gas detection and adsorption, and are of important significance to the safe operation of power equipment.

Data Availability Statement:
The data is available on the request from corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.