Adsorption and Sensing of CO 2 , CH 4 and N 2 O Molecules by Ti-Doped HfSe 2 Monolayer Based on the First-Principle

: With the continuous emission of greenhouse gases, the greenhouse effect is becoming more and more serious. CO 2 , CH 4 , and N 2 O are three typical greenhouse gases, and in order to limit their emissions, it is imperative that they are accurately monitored. In this paper, the doping behavior of Ti on the surface of HfSe 2 is investigated, based on the ﬁrst-nature principle. Additionally, the parameters of adsorption energy and the transfer charges of Ti − HfSe 2 for CO 2 , CH 4 , and N 2 O are calculated and compared, while the sensing characteristics of Ti − HfSe 2 are analyzed. The results show that the structure is most stable when Ti is located above the lower-layer Se atom. The CO 2 and N 2 O adsorption systems with large adsorption energies and transfer charges are a chemical adsorption, while the CH 4 system is a physical adsorption with small adsorption energies and transfer charges. In addition, Ti − HfSe 2 has a good sensitivity and recovery time for CO 2 at 298 K, which is feasible for industrial application. All the contents of this paper provide theoretical guidance for the implementation of Ti − HfSe 2 as a gas-sensitive material for the detection of greenhouse gas components.


Introduction
With the development of the industry, the environmental impact of greenhouse gases is increasing and the global extreme climate problems caused by greenhouse gases have attracted the attention of countries around the world [1][2][3]. Due to the economy and population growth, anthropogenic greenhouse gas emission has been rising since the beginning of the industrial era. Meanwhile, the concentrations of carbon dioxide (CO 2 ), methane (CH 4 ), and nitrous oxide (N 2 O) have reached their current highest levels [4]. In order to limit carbon emissions, it is necessary to monitor each emission source.
Currently, greenhouse gases are mainly monitored by means of gas sensors, which include electrochemical gas sensors [5], semiconductor gas sensors [6], infrared gas sensors [7], and new nano-gas sensors. Compared with other gas sensors, the new nano-gas sensors have a specific surface area close to the theoretical extremes, excellent semiconductor properties, and abundant active sites, which lead to the advantages of smaller size and higher accuracy and broaden the application fields of sensors greatly [8,9]. Gassensitive material is at the core of nano gas sensors, which mainly includes metal oxide semiconductors [10][11][12], carbon nanotubes [13][14][15][16], graphene [17][18][19], and transition metal dichalcogenides (TMDs) [20][21][22][23]. Among them, TMDs are a new two-dimensional layered nanomaterial with the chemical formula MX 2 , where M stands for transition metal elements (Mo, W, Ti, Hf, etc.) and X stands for sulfur group elements (S, Se, and Te). Its structure includes three layers, in which two layers of X atoms are sandwiching a single layer of M atoms in between [24]. Compared with graphene, TMDs have greater potential for gas adsorption and sensing because of their certain band gap [25]. However, since TMD sheets tend to form a dense stacking structure during the formation of the conductive network, their sensitivity and recovery time at room temperature still need to be improved. Some studies have shown that doping the surface of adsorbent materials with metals such as Ti, Mn, Ag, and Pt can improve the adsorption performance of adsorbent materials [26,27]. As a representative material in TMDs, MoS 2 has received much attention for its application in gas sensors [28]. Li et al. studied the adsorption properties of Mn-doped MoS 2 for dissolved gases in transformer oil [29], and Zhang et al. investigated the adsorption properties of Ti-doped MoS 2 on CF 4 , C 2 F 6 , and COF 2 [30].
However, there are other TMDs with good adsorption properties that have rarely been investigated. HfSe 2 has a larger work function than MoS 2 , which makes HfSe 2 less prone to losing electrons. At the same time, HfSe 2 experiences a more violent reaction when exposed to air, indicating a strong interaction between HfSe 2 and air. Above all, HfSe 2 is very suitable for gas sensors [31]. Cui et al. studied the adsorption properties of Pt-doped HfSe 2 on SO 2 and SOF 2 , as well as Pd-doped HfSe 2 on SO 2 and NO 2 [32,33]; the results indicate that HfSe 2 has great adsorption and sensing properties. As a commonly used doping metal, Ti is often used to dope the surface of nanomaterials to improve their properties [34][35][36]. At present, the research for Ti−doped HfSe 2 is not clear enough, so this paper establishes the Ti−doped HfSe 2 model based on the first-principle to obtain the most stable structure of Ti−HfSe 2 and investigates the adsorption performance of Ti−HfSe 2 by analyzing the adsorption energy, transfer of electrons, and other adsorption parameters of CO 2 , CH 4 , and N 2 O adsorption systems. Meanwhile, this paper also calculates the sensitivity and recovery time of Ti−HfSe 2 for the three gases to evaluate the feasibility of Ti−HfSe 2 as a gas-sensitive material. This study can provide a theoretical basis for the application of Ti−doped HfSe 2 nanomaterials in gas sensors.

Computation Details
Density functional theory (DFT) is a method for studying multi-electron systems that uses the electron density as the fundamental physical quantity to describe the system [37]. In the field of gas sensing, DFT is also a very effective research tool [38]. The calculations in this paper were all performed in the DMol3 module of Materials Studio based on DFT [39]. In this paper, a 3×3 monolayer HfSe 2 supercell containing 16 Hf atoms and 18 Se atoms was constructed. A vacuum layer with a thickness of 15 Å was built to prevent the interaction of periodic HfSe 2 crystals in the upper layer. The Perdew-Burke-Ernzerhof (PBE) functional within generalized gradient approximation (GGA) was used to deal with the exchange correlation interaction between electrons, while the Tkatchenko and Scheffler (TS) method was used to describe the van der Waals interactions, using Double Numerical Polarization (DNP) as the atomic orbital basis group [40], and the global orbital cut-off radius was 5 Å. To simplify the process, a DFT semi-core pseudopotential (DSPP) containing relativistic effects was used. The Monkhorst-Pack k-point mesh of 3 × 3 × 1 was used to geometrically optimize the structure in the paper, and the convergence criteria were set as follows: the tolerance accuracy, the maximum force, and the maximum displacement were 10 −5 Ha, 0.002 Ha/Å, and 0.005 Å, respectively.

Results and Discussions
Firstly, in this paper, the geometry of the gas molecules is optimized. The optimized gas molecules are shown in Figure 1. In Figure 1

Analysis of Ti−HfSe 2 Monolayer
For the structure of Ti doped on the surface of HfSe 2 , three possible doping sites are considered: the sites above the upper-layer Se atom, the Hf atom, and the lower-layer Se atom. The doping sites are shown in Figure 2. The binding energy E bind of the Ti atom doped on the surface of HfSe 2 is calculated by Equation (1) [41]: in which E Ti−HfSe2 , E Ti , and E HfSe2 denote the total energy of Ti−HfSe 2 , the energy of Ti atoms, and the total energy of monolayer HfSe 2 , respectively. Obviously, the lowest binding energy corresponds to the most stable configuration (MSC). Table 1 indicates the parameters of Ti atoms at different doping sites. Combined with the results of geometry optimization of the adsorption system, it can be found that the geometrical optimization results for the doping site above the upper-layer Se layer is consistent with the doping site above Hf, and both doping sites are not the MSC. When the doping site is above the lower-layer Se, the binding energy is biggest, reaching −5.001 eV, indicating that Ti forms the MSC on the HfSe 2 surface. The structure of MSC is shown in Figure 3. The huge binding energy also makes Ti bond with the upper Se layer. Figure 4 shows the electron density difference (EDD) of Ti-HfSe 2 , where the blue area indicates electron accumulation, and the yellow area indicates electron depletion. One can see that the electron depletion area is mainly concentrated around the Ti atom, and the electron accumulation area is mainly concentrated on the Ti-Se bond, which indicates that Ti transfers 1.034e of electrons to HfSe 2 .   The density of states (DOS) and partial density of states (PDOS) before and after Ti doping are shown in Figure 5. From Figure 5a, the DOS of the adsorbed material shifts to a lower energy overall, and the shape of the DOS of the adsorbed material is partially changed, with new peaks near −14eV and −5eV after Ti doping. Additionally, the Ti atoms have a great effect on the DOS in the part above the Fermi level, which leads to a higher peak of Ti−HfSe 2 at −1eV to 2eV than the peak of HfSe 2 pristine. Figure 5b shows the PDOS of the adsorbed material, where Ti 3d orbitals hybridize highly in the range of −6eV to 2eV, with Hf 6s, 5p, and 5d orbitals and Se 4p orbitals producing a strong hybridization. This also indicates that Ti forms a very stable structure with the HfSe 2 surface, and the strong electronic orbital hybridization also leads to the formation of chemical bonds between Ti and Se, which is consistent with the previous analysis.

Adsorption Properties of Ti−HfSe 2 Monolayer
The CO 2 , CH 4 , and N 2 O molecules are placed on the Ti−HfSe 2 surface in different ways, and these structures are geometrically optimized to finally find the MSC. Through several attempts, it can be found that the MSC exists when the gas molecule is located above the Ti atom. For the CO 2 gas molecule, two adsorption structures are selected: parallel and perpendicular close to the Ti−HfSe 2 surface. For the CH 4 molecule, two adsorption configurations are chosen: C atom perpendicular to the Ti atom and H atom perpendicular to the Ti atom. Due to the asymmetric structure of the N 2 O gas molecule, there are three adsorption structures: parallel close to the Ti−HfSe 2 surface and perpendicular to the Ti−HfSe 2 surface with N and O atoms, respectively. Combined with the simulation results, the lowest energy adsorption structure can be obtained as shown in Figure 6. In order to further analyze the adsorption characteristics of the gas on the Ti−HfSe 2 monolayer, the energy change in the adsorption process of the gas molecules on the Ti−HfSe 2 surface is taken as the adsorption energy in this paper. The adsorption energy E ad of the gas adsorption process is shown in Equation (2) [42]: in which E Ti−HfSe2/gas , E Ti−HfSe2 , and E gas denote the total energy of the system after gas adsorption, the energy of the layer Ti−HfSe 2 , and the total energy of the gas molecules, respectively. The charge transfer ∆Q of the adsorption system is calculated by the Mulliken method, and the expression is as shown in Equation (3): in which Q 1 and Q 2 denote the charge of gas molecules after and before adsorption. If ∆Q > 0, this indicates that the gas molecule loses electrons during the adsorption process; if ∆Q < 0, this indicates that the gas molecule gains electrons during the adsorption process.
The calculation results are shown in Table 2. The equation for the EDD is shown in Equation (4): in which ρ gas/Ti−HfSe2 , ρ gas , and ρ Ti−HfSe2 denote the electron density of the adsorption system after adsorption of gas molecules, individual gas molecules, and Ti−HfSe 2 , respectively. The EDD is shown in Figure 7 based on the calculated results, where the blue area indicates electron accumulation, and the yellow area indicates electron depletion. For the CO 2 adsorption system, the large adsorption energy leads to a significant change in the structure of CO 2 , with the C-O bond length elongated from 1.178 Å to 1.207 Å and 1.350 Å, and with the angle changed to 132.734 • . The Ti-Se bond in Ti−HfSe 2 increased by about 0.126 Å, following adsorption. In the CH 4 adsorption system, the C-H bond in CH 4 near Ti−HfSe 2 increased by 0.009 Å, and the Ti-Se bond length changed by 0.001 Å. The whole system is almost unchanged, which also indicates that CH 4 adsorption on Ti−HfSe 2 surface is not effective. There are no bonds formed during the adsorption process, indicating that the adsorption process is a physical adsorption and the main force is Van der Waals (VDW). From the EDD of the CH 4 adsorption system, the electron depletion region is concentrated on the surface of H atoms in CH 4 , and the electron accumulation region is concentrated near the C atoms. The trace electron transferring amount of 0.107e also confirms the weak interaction between CH 4 and Ti−HfSe 2 . The N 2 O adsorption system changes significantly during the adsorption process, with the Ti-Se bond elongating by 0.032 Å to 0.130 Å, attracted by N 2 O. From the EDD, it can be seen that a large electron accumulation region is formed near N and O atoms, and a large electron depletion region exists near Ti atoms, indicating that there is a large amount of charge transfer during the adsorption process, further verifying the strong adsorption performance of Ti−HfSe 2 on N 2 O. The CO 2 and N 2 O adsorption systems have large adsorption energies and transfer charges, and both create new bonds during the adsorption process, indicating that these adsorption processes are chemical adsorptions, rebuilding the electron arrangement.

DOS of Adsorption System
To further analyze the interaction between gas molecules and the surface of the adsorbent material, the DOS and PDOS of three gas adsorption systems are investigated in this section, and the results are shown in Figure 8. From Figure 8, the DOS and PDOS change to different degrees after the adsorption of gas by Ti−HfSe 2 . The CO 2 adsorption system is shown in Figure 8a. The structure of CO 2 is changed after adsorption and the positions of the different peaks of the DOS of CO 2 are changed, which leads to three new peaks at −21 eV, −8.5 eV, and −6.5 eV for CO 2 /Ti−HfSe 2 . In addition, in the range from −1eV to 0eV, the Ti 3d orbitals, and the C 2p orbitals and O 2p orbitals overlap highly, forming a strong hybridization. This also confirms the bonding between Ti atoms and C and O atoms, respectively, making the structure of CO 2 gas molecules change. The adsorption effect is obvious; the adsorption is a chemical adsorption. Figure 8b shows the DOS and PDOS of the CH 4 adsorption system. It can be seen that the DOS of CH 4 is changed in position and peaks during the adsorption process, which leads to two new peaks in the DOS of the adsorption system at −15 eV and −7.5 eV. It can also be seen that the other parts almost overlap with the DOS of before adsorption, indicating that the interaction between CH 4 molecules and the Ti−HfSe 2 surface is weak, and only a small amount of charge is transferred during the adsorption process. Meanwhile, the Ti 3d orbitals only have a small overlap with the C 2p and H 1s orbitals. The trace amount of hybridization also indicates that Ti−HfSe 2 is less effective in the adsorption of CH 4 . In the N 2 O adsorption system, the DOS of the system changed significantly after adsorption, generating new peaks at −20 eV, −10 eV, −7.5 eV, −6.5 eV, and −3 eV, and the newly generated peaks were caused by the adsorbed N 2 O. There is an obvious overlap between the Ti 3d orbitals and the N 2p and O 2p orbitals near the Fermi level, indicating a strong hybridization between these orbitals and a strong adsorption of N 2 O by Ti−HfSe 2 , an adsorption which is sufficient to change the structure of N 2 O. It also indicates that Ti is bonded to N and O atoms. The adsorption is chemisorption, and the main force is an intermolecular force.
osensors 2022, 10, x FOR PEER REVIEW 8 of (c) From Figure 8, the DOS and PDOS change to different degrees after the adsorpti of gas by Ti−HfSe2. The CO2 adsorption system is shown in Figure 8a. The structure CO2 is changed after adsorption and the positions of the different peaks of the DOS of C are changed, which leads to three new peaks at −21 eV, −8.5 eV, and −6.5 eV CO2/Ti−HfSe2. In addition, in the range from −1eV to 0eV, the Ti 3d orbitals, and the C orbitals and O 2p orbitals overlap highly, forming a strong hybridization. This also co firms the bonding between Ti atoms and C and O atoms, respectively, making the str ture of CO2 gas molecules change. The adsorption effect is obvious; the adsorption i chemical adsorption. Figure 8b shows the DOS and PDOS of the CH4 adsorption syste

Gas sensor Analyzation of Ti−HfSe 2
The sensitivity of this material and the recovery time after adsorption of each gas are analyzed to evaluate the possibility of Ti−HfSe 2 as a resistive gas sensor.
The sensitivity of gas-sensitive materials can be obtained by detecting the change in conductivity of the material before and after adsorption of gas, and the band gap is the main factor that determines the conductivity of the material. Furthermore, there is a quantitative relationship between conductivity (σ) and band gap (B g ), as in Equation (5) [43,44]: in which A is a constant, k is Boltzmann constant, and T(K) denotes the thermodynamic temperature.
The relationship between sensitivity (S) and conductivity (σ) of the gas-sensitive material is shown in Equation (6): (6) in which σ gas and σ pure denote the conductivity of the adsorption system and Ti−HfSe 2 , respectively. The change in conductivity of Ti−HfSe 2 after adsorbing different gases can be approximated by calculating the change in band gap of each system. When the band gap of the material increases, it is more difficult to excite electrons in the material from the valence band to the conduction band, leading to a decrease in the conductivity of the material; conversely, the conductivity of the material increases.
The band structures of CO 2 , CH 4 , and N 2 O after adsorption are shown in Figure 9. From Equations (5) and (6), the sensitivities of Ti−HfSe 2 for CO 2 , CH 4 , and N 2 O at room temperature are 73.34, 123.63, and 1013.97, respectively, which indicates that the conductivity of Ti−HfSe 2 has changed significantly after adsorbing three gases above with a high sensitivity. Therefore, Ti−HfSe 2 can meet the application requirements of gas detection. In addition, the desorption performance is also an important index for evaluating gas sensors and is often expressed in terms of the recovery time (τ), which is the time for the gas to desorb from the material surface, and is expressed as shown in Equation (7) [45,46]: in which A is the attempt frequency with a value of 10 12 s −1 , k is the Boltzmann constant, T(K) denotes the thermodynamic temperature, and E g (eV) denotes the potential barrier; the value of the potential barrier of the desorption process can be considered as the absolute value of the adsorption energy E ad . When the potential barrier is large, the desorption process on the material surface becomes very difficult, and heating is often used to speed up the desorption process.
The recovery time for different gases at different temperatures is shown in Table 3. The recovery times for CO 2 , CH 4 , and N 2 O at room temperature are 38.024 s, 4.852 × 10 −4 s, and 1.312 × 10 11 s, respectively. CO 2 has a fast recovery time at room temperature, which allows Ti−HfSe 2 to be recycled quickly to meet the practical use requirements of gas sensors. Therefore, Ti−HfSe 2 has significant advantages in terms of gas-sensitive properties and practicality. For the CH 4 adsorption system, the recovery time reaches milliseconds at room temperature due to its weaker adsorption energy, and the recovery time is too fast for the gas sensor to detect the gas. The recovery time of N 2 O at room temperature is longer, at 1.312 × 10 11 s. Even when heated to 398 K, the recovery time is still long, indicating that N 2 O is strongly adsorbed and Ti−HfSe 2 can be used as an adsorbent for this gas to reduce its emission.

Conclusions
In this paper, the doping model of Ti on the HfSe 2 surface is constructed and CO 2 , CH 4 , and N 2 O are adsorbed by Ti−HfSe 2 . The results show that the MSC of Ti−HfSe 2 is when Ti is located above the upper-layer Se atoms of HfSe 2 and that Ti−HfSe 2 has a good adsorption performance for CO 2 and N 2 O. Furthermore, the sensitivity and recovery time of Ti−HfSe 2 to CO 2 are great, which allows Ti−HfSe 2 to be used to detect CO 2 . Conversely, Ti−HfSe 2 is not suitable for detecting CH 4, due to its fast recovery time. Due to the excellent adsorption and excessive recovery time of N 2 O, Ti−HfSe 2 can be considered as an adsorbent for N 2 O.