Pd-GaSe and Pd₃-GaSe Monolayers: Two Promising Candidates for Detecting Dissolved Gases in Transformer Oil

Abstract

In this paper, the adsorption behaviors of three gases (H₂, CO, and C₂H₂) decomposed by the transformer oil on Pd-GaSe and Pd₃-GaSe monolayers were calculated by density functional theory. Compared with Pd single-atom doping, Pd₃ 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 (H₂, CO, and C₂H₂) than the intrinsic GaSe monolayer. Compared with Pd-GaSe, Pd₃-GaSe showed stronger adsorption property for the three gases. Analysis of frontier molecular orbitals and recovery characteristics shows that 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 be used as a disposable resistive sensor for CO. Pd₃-GaSe is a kind of sensing material suitable for disposable resistance sensors for CO and C₂H₂. 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.

1. 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 H₂, CO, C₂H₂, 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, two-dimensional (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 MoS₂ monolayer can remarkably improve the adsorption performance for C₂H₆ and C₂H₄ 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 H₂, O₂, NO₂, and H₂O, and found that monolayer GaSe has a wide application prospect as O₂ and NO₂ 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 SF₆ 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 HfSe₂ has good adsorption performance for NO₂ and SO₂ 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 MoS₂ monolayer, and found that Rh₃-MoS₂ has the best stability and the best electronic behavior [34]. For the above reasons, the Pd₃ cluster doping method is adopted in this paper. Therefore, this paper studies the adsorption behavior of Pd monatomic doped GaSe molecules and Pd₃ cluster-doped GaSe molecules on dissolved gases in transformer oil, and compares the adsorption performance of the two materials.

2. Computation Methods

In this study, all microscopic calculations based on density functional theory (DFT) were performed in Dmol³ 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]

$${\mathrm{E}}_{\mathrm{b}}={\mathrm{E}}_{{\mathrm{Pd}}_{\mathrm{n}}-\mathrm{GaSe}}-{\mathrm{E}}_{\mathrm{GaSe}}-\mathrm{n}·{\mathrm{E}}_{\mathrm{Pd}}$$

(1)

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].

$${\mathrm{E}}_{\mathrm{ad}}={\mathrm{E}}_{{\mathrm{Pd}}_{\mathrm{n}}-\mathrm{GaSe}/\mathrm{gas}}-\left({\mathrm{E}}_{{\mathrm{Pd}}_{\mathrm{n}}-\mathrm{GaSe}}+{\mathrm{E}}_{\mathrm{gas}}\right)$$

(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.

$${\mathrm{Q}}_{\mathrm{T}}={\mathrm{Q}}_{\mathrm{after}}-{\mathrm{Q}}_{\mathrm{before}}$$

(3)

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].

3. Results and Discussion

3.1. Structures of Characteristic Gases, Pd-GaSe, and Pd₃-GaSe Monolayers

Figure 1 and Figure 2 show the optimized dissolved gas molecular structures in transformer oil and the optimized GaSe monolayer, respectively. The H₂ molecule and C₂H₂ molecule have a symmetrical structure. The length of H–H bond in H₂ 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 C₂H₂ 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 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.

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.

3.2. H₂ Adsorption

The adsorption properties, charge transfer, and E_ad of H₂ on Pd-GaSe and Pd₃-Gase monolayers are shown in Figure 7 and Figure 8, and

Table 1. Adsorption characteristic parameters of H₂ adsorption.

Structure	The Length of Band (Å)		Adsorption Distance (Å)	Atom	Charge (e)	QT (e)	Ead (eV)
GaSe/H2	H1-H2	0.751	3.504	H1	0.001	0.002	−0.544
				H2	0.001
Pd-GaSe/H2	H1-H2	0.822	1.820	H1	0.058	0.108	−0.58
				H2	0.050
				Pd	−0.249
Pd3-GaSe/H2	H1-H2	0.847	1.726	H1	0.100	0.199	−0.943
				H2	0.099
				Pd1	−0.153
				Pd2	−0.336
				Pd3	−0.161

. Some data of H₂ adsorption by intrinsic GaSe monolayer are also listed in Table 1. From the data in Table 1, the adsorption energy of H₂ on GaSe monolayer is −0.544 eV, H₂ on Pd-GaSe monolayer is −0.58 eV, and H₂ on Pd₃-GaSe monolayer is −0.943 eV. It is worth noting that the adsorption distance of GaSe/H₂ system (3.504 Å) is almost twice that of Pd-GaSe/H₂ system (1.820 Å), but the adsorption energy of both systems is close. It can be noted that the Q_T of Pd-GaSe/H₂ system (0.108 e) is obviously more than that of GaSe/H₂ 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/H₂ system is smaller than that of GaSe/H₂ 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 H₂. The doping method of Pd₃ cluster significantly enhances the system’s adsorption performance for H₂, which belongs to chemical adsorption. Isolated H₂ 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 Pd₃-GaSe monolayer is obviously deformed during the adsorption process, and all three Pd atoms have shifted in different degrees. Pd cluster capture H₂, which indicates that there is a strong interaction between them. Mulliken atomic population analysis of H₂ molecule shows that 0.108 e electrons are transferred to Pd-GaSe monolayer and 0.199 e electrons are transferred to Pd₃-GaSe monolayer after H₂ adsorption. The results show that the doping method of Pd₃ cluster brings greater charge transfer amount than the doping method of Pd. Figure 7c and Figure 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 H₂ adsorption, indicating that the electron orbit changed, but TDOS changed little during the adsorption process. The results indicate that H₂ has weak interaction with Pd-GaSe. TDOS shown in Figure 8d shows that after H₂ was adsorbed by Pd₃-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 H₂ 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 Pd₃-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 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.

3.3. CO Adsorption

Parameters and structures related to CO adsorption are shown in Figure 9 and Figure 10, and

Table 2. Adsorption characteristic parameters of CO adsorption.

Structure	The Length of Bond (Å)		Adsorption Distance (Å)	Atom	Charge (e)	QT (e)	Ead (eV)
GaSe/CO	C-O	1.141	3.804	C	0.111	0.006	−0.545
				O	−0.105
Pd-GaSe/CO	C-O	1.158	1.921	C	0.307	0.163	−1.587
				O	−0.144
				Pd	−0.334
Pd3-GaSe/CO	C-O	1.180	2.003	C	0.373	0.187	−2.427
				O	−0.186
				Pd1	−0.203
				Pd2	−0.206
				Pd3	−0.165

. 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 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 Pd₃-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 Pd₃-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 Pd₃-Gase monolayer, 0.187 e electrons were transferred from CO molecule to Pd₃-GaSe monolayer. In the DCD diagrams of Figure 9c and Figure 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.

Figure 9d,e show the DOS distribution of the Pd-GaSe system. After CO adsorption, the overall TDOS changes little and a new peak appears near −8.5 eV. The hybridization of the Pd-4d orbital, C-2p orbital, and O-2p orbital at −1.1 eV and −5.8 eV caused TDOS to rise around −1.1 eV and −5.8 eV. Figure 10d,e show the DOS distribution of the Pd₃-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 Pd₃-GaSe monolayer. The results show that both Pd-GaSe monolayer and Pd₃-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 Pd₃-Gase monolayer has better adsorption performance for CO.

3.4. C₂H₂ Adsorption

Figure 11 and Figure 12, and

Table 3. Adsorption characteristic parameters of C₂H₂ adsorption.

Structure	The Length of Bond (Å)		Bond Angle (°)		Adsorption Distance (Å)	Atom	Charge (e)	QT (e)	Ead (eV)
GaSe/C2H2	C1-C2	1.212	H1-C1-C2	179.704	3.593	C1	−0.123	0.004	−0.700
						C2	−0.127
	C1-H1	1.072	C1-C2-H2	179.283		H1	0.126
	C2-H2	1.072				H2	0.128
Pd-GaSe/C2H2	C1-C2	1.261	H1-C1-C2	155.279	2.108	C1	−0.062	0.100	−1.307
						C2	−0.060
	C1-H1	1.079	C1-C2-H2	155.552		H1	0.111
						H2	0.111
	C2-H2	1.079				Pd	−0.296
Pd3-GaSe/C2H2	C1-C2	1.337	H1-C1-C2	131.730	2.018	C1	−0.026	0.178	−2.757
						C2	−0.035
						H1	0.119
	C1-H1	1.097	C1-C2-H2	131.258		H2	0.120
						Pd1	−0.212
	C2-H2	1.096				Pd2	−0.204
						Pd3	−0.208

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 can be seen, in Pd₃-GaSe/C₂H₂ system, deformation of the C₂H₂ molecule is more severe, which may be related to the stronger reaction between adsorbent and C₂H₂. The adsorption energy of Pd-GaSe/C₂H₂ and Pd₃-GaSe/C₂H₂ 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 C₂H₂ were significantly increased, and the change of adsorption energy of Pd₃-GaSe/C₂H₂ system was particularly obvious, which also verified the previous conjecture. Moreover, from the adsorption model, it can be seen that Pd₃-GaSe has a strong adsorption effect on C₂H₂. After adsorption, three Pd atoms shift obviously and capture C₂H₂, but the monolayer of Pd-GaSe does not change obviously. In the Pd-GaSe/C₂H₂ system, Pd atom carries 0.296 e electrons after C₂H₂ 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 Pd₃-GaSe/C₂H₂ system, accepting electrons from gas molecules and GaSe monolayer. As can be seen from the DCD diagrams in Figure 11c and Figure 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.

DOS distribution of Pd-GaSe/C₂H₂ system is shown in Figure 11d,e. After adsorption of C₂H₂, 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 Pd₃-GaSe/C₂H₂ 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 Pd₃-GaSe monolayer shows strong adsorption of C₂H₂. In conclusion, after Pd_n (n is 1 or 3) doping, the adsorption performance of the system for C₂H₂ is significantly enhanced, and various data show that Pd₃ cluster doped with GaSe monolayer have better adsorption performance of C₂H₂ than Pd-GaSe system.

3.5. 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:

$$\mathsf{\sigma }\propto \exp (-{\mathrm{E}}_{\mathrm{g}} /2{\mathrm{k}}_{\mathrm{B}}\mathrm{T})$$

(4)

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/H₂ system does not change much compared with that before adsorption, meaning that the interaction force between gas and adsorption material is weak after H₂ adsorption. In Pd-GaSe/CO and Pd-GaSe/C₂H₂ 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/C₂H₂ system is not obvious, the sensitivity of the sensor to C₂H₂ detection is limited. Therefore, Pd-GaSe can be used as a semiconductor sensor to detect H₂ and CO.

In Figure 13b, before gas adsorption, LUMO and HOMO are mainly distributed around the Pd₃ group before gas adsorption, which indicated that there is a high electron concentration in the vicinity of the Pd₃ cluster. After gas adsorption, HOMO of the system 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.

3.6. 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:

$$\mathsf{\tau } ={ \mathrm{A}}^{-1}{\mathrm{e}}^{\left(-{\mathrm{E}}_{\mathrm{a}}/{\mathrm{K}}_{\mathrm{B}}\mathrm{T}\right)}$$

(5)

In the above formula, A and T represent the attempt frequency and temperature, A is constant and equal to 10¹² 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 Pd₃-GaSe systems at 298 K, 398 K, and 498 K. The recovery time of H₂ in Pd-GaSe is very short, and the adsorptive H₂ will soon break away from the binding of the material, indicating that Pd-GaSe is not suitable as H₂ scavenger. When the temperature is 398 K, the recovery time of H₂ on Pd₃-GaSe is 0.87 s, and when the temperature is 298 K, the recovery time is 8780 s (2.4 h), meaning that Pd₃-GaSe is an ideal gas sensitive material for the detection of H₂. 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, 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 one-time scavenger of C₂H₂.

4. 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.