First-Principles Insight into Pd-Doped C3N Monolayer as a Promising Scavenger for NO, NO2 and SO2

The adsorption and sensing behavior of three typical industrial toxic gases NO, NO2 and SO2 by the Pd modified C3N monolayer were studied in this work on the basic first principles theory. Meanwhile, the feasibility of using the Pd doped C3N monolayer (Pd-C3N) as a sensor and adsorbent for industrial toxic gases was discussed. First, the binding energies of two doping systems were compared when Pd was doped in the N-vacancy and C-vacancy sites of C3N to choose the more stable doping structure. The result shows that the doping system is more stable when Pd is doped in the N-vacancy site. Then, on the basis of the more stable doping model, the adsorption process of NO, NO2 and SO2 by the Pd-C3N monolayer was simulated. Observing the three gases adsorption systems, it can be found that the gas molecules are all deformed, the adsorption energy (Ead) and charge transfer (QT) of three adsorption systems are relatively large, especially in the NO2 adsorption system. This result suggests that the adsorption of the three gases on Pd-C3N belongs to chemisorption. The above conclusions can be further confirmed by subsequent deformable charge density (DCD) and density of state (DOS) analysis. Besides, through analyzing the band structure, the change in electrical conductivity of Pd-C3N after gas adsorption was studied, and the sensing mechanism of the resistive Pd-C3N toxic gas sensor was obtained. The favorable adsorption properties and sensing mechanism indicate that the toxic gas sensor and adsorbent prepared by Pd-C3N have great application potential. Our work may provide some guidance for the application of a new resistive sensor and gas adsorbent Pd-C3N in the field of toxic gas monitoring and adsorption.


Introduction
Nowadays, with the progress of the economy and the acceleration of industrialization, the problem of industrial waste gases is becoming more and more serious. The industrial production process produces a large number of industrial waste gases, and these waste gases' emission into the air will spread with the flow of the atmosphere, causing great harm to the environment and threatening the physical and mental health of the people [1,2]. NO, NO 2 and SO 2 are several typical toxic industrial waste gases. Hence, finding an effective method of detecting and adsorbing these toxic gases is of great significance to protect our living environment.
Since the typical two-dimensional (2D) material graphene was successfully synthesized, 2D nanomaterial, such as transition metal dihalogen compounds [3][4][5], silicene [6,7], germanene [8,9], and stannene [10,11], have attracted extensive attention in academia. The excellent properties of these 2D materials make them have broad application prospects in many areas [12][13][14][15]. Whereas, the zero-band gap characteristic of graphene limits its application in the nanoelectronics field [16,17]. Thus, researchers began to explore novel two-dimensional graphene-like materials, such as metal nitrides and carbides [18], III-V nitrides [19][20][21], etc. Among these new graphene-like materials, a planar honeycomb C 3 N monolayer which can be thought of as a 2 × 2 graphene supercell substituted by two N atoms is emerging [22,23]. C 3 N is a semiconductor, and one of its characteristics compared to graphene is its indirect band gap. Owing to the substitution of N atoms, compared with grapheme, the C 3 N monolayer has higher chemical activity and carrier mobility as well as better structural stability [24,25]. Therefore, C 3 N may have great application potential in gas sensing and adsorption fields [26,27]. Previous studies have shown that intrinsic C 3 N is inert to many toxic gases [28]. The adsorption capacity of nanomaterial with transition metal (TM) doping on gas molecules can be significantly improved due to significant electron hybridization between the TM atom and gas molecule [29][30][31]. Zhu et al. [32] found that the InN monolayer doped with Pd has a good application prospect in detecting and removing toxic gases CO and NO. Ma et al. [33] found that the Au, Pt, Pd and Ni modified MoS 2 monolayers have good sensing performance for CO and NO gases. Therefore, the doping of Pd may enhance the adsorption capacity of C 3 N to toxic gases NO, NO 2 and SO 2 . However, so far, few research has been executed in the adsorption properties of the TM doped C 3 N (TM-C 3 N) monolayer for toxic gases such as NO, NO 2 and SO 2 .
Based on first principles, the doping behavior of Pd on C 3 N and the adsorption properties of Pd-C 3 N for NO, NO 2 and SO 2 were studied in this study. Further, to study the adsorption properties and sensing mechanism of Pd-C 3 N for three kinds of toxic gases, the E ad , Q T , DCD, DOS and band structure were analyzed. The results show that NO, NO 2 and SO 2 can be stably adsorbed by Pd-C 3 N, which can be recognized as chemisorption. The adsorption properties and sensing mechanism of Pd-C 3 N for toxic gases obtained in this work provide a theoretical basis for further study of the toxic gas resistive sensor and adsorbent prepared by Pd-C 3 N.

Computation Methods
All the theoretical calculations on the basic density functional theory (DFT) in this paper were carried out in the dispersion-corrected DMol 3 package [34,35]. The exchangecorrelation between electrons was handled by the Perdew-Burke-Ernzerhof (PBE) function under the generalized gradient approximation (GGA) to better describe the non-uniform electron density of the system which was closer to the experimental situation [36][37][38]. The DFT-D method, which was customized by Grimme, was used to understand van der Waals force and long-range interactions better [39]. We used DFT semi-core pseudopotential (DSSP) to handle the effects of core electron relativity and chose double numerical plus polarization (DNP) to calculate the density function of each model [40][41][42]. In terms of the setup of Monkhorst-Pack k-point mesh, 7 × 7 × 1 was set for geometric optimization and 10 × 10 × 1 for the calculation of static electronic structure [43]. The energy tolerance accuracy, maximum force, and displacement were severally set as 10 −5 Ha, 0.002 Ha/Å and 0.005 Å [44].
A 2 × 2 × 1 C 3 N supercell with 28 C atoms and 13 N atoms was built. In order to prevent the adjacent layers from interacting with each other, the vacuum region was set to 15 Å [45]. The lattice constant of the fully optimized C 3 N monolayer was calculated as 4.92 Å, which was basically consistent with the previous report (4.9 Å [46]). The Hirshfeld method was adopted to study the electronic behavior of atoms and molecules [47]. Meanwhile, charge transfer (Q T ) is defined to describe the electronic behavior of Pd doping and gas adsorption systems. A positive Q T value means the analyte acts as an electron donator, on the contrary, a negative Q T value means that the analyte acts as an electron acceptor [48].

Results and Discussions
3.1. Isolated Gas Molecules and Pd-C 3 N Monolayer Figure 1 displays the optimized structural models of the intrinsic C 3 N monolayer and three gas molecules NO, NO 2 and SO 2 . At the same time, Table 1 lists the geometrical parameters of the optimized three kinds of gas molecular configurations and Table 2 lists the single atom charges of gas molecules in the gas phase.  Figure 1 displays the optimized structural models of the intrinsic C3N monolayer and three gas molecules NO, NO2 and SO2. At the same time, Table 1 lists the geometrical parameters of the optimized three kinds of gas molecular configurations and Table 2 lists the single atom charges of gas molecules in the gas phase.  According to previous report, the metal atom can be stably adsorbed by the C3N monolayer with one C atom or one N atom deficiency (simplified as VC-C3N and VN-C3N below) due to the strong electrostatic attraction where electronic localization occurs [49]. Therefore, to obtain the most stable doping structure, priority was given to the Pd atom doping at the C-vacancy or N-vacancy site on the C3N monolayer. The two optimized doping configurations are shown in Figure 2. When Pd is doped at the C-vacancy site, the length of Pd-C and Pd-N is significantly different, which are 1.979 and 2.518 Å, respectively. However, when Pd is doped at the N-vacancy site, the three Pd-C bonds have basically the same length, 2.004, 2.006 and 2.008 Å, respectively. This result shows that the doping system with Pd doping at the N-vacancy site has better central symmetry. In this paper, the stability of the doping system is evaluated by binding energy (Eb), and the calculation formula is as follows:

Isolated Gas Molecules and Pd-C3N Monolayer
In the above formula, E Pd-C 3 N denotes the energy of the Pd-doped system, and E vacancy-C 3 N and E Pd denote the energy of the defective C3N and Pd atom, respectively. The binding energies of Pd doping at the C-vacancy site and N-vacancy site are −4.080 and

Gas
Bond Table 2. Single atom charges of gas molecules in the gas phase.
According to previous report, the metal atom can be stably adsorbed by the C 3 N monolayer with one C atom or one N atom deficiency (simplified as VC-C 3 N and VN-C 3 N below) due to the strong electrostatic attraction where electronic localization occurs [49]. Therefore, to obtain the most stable doping structure, priority was given to the Pd atom doping at the C-vacancy or N-vacancy site on the C 3 N monolayer. The two optimized doping configurations are shown in Figure 2. When Pd is doped at the C-vacancy site, the length of Pd-C and Pd-N is significantly different, which are 1.979 and 2.518 Å, respectively. However, when Pd is doped at the N-vacancy site, the three Pd-C bonds have basically the same length, 2.004, 2.006 and 2.008 Å, respectively. This result shows that the doping system with Pd doping at the N-vacancy site has better central symmetry. In this paper, the stability of the doping system is evaluated by binding energy (E b ), and the calculation formula is as follows: In the above formula, E Pd−C 3 N denotes the energy of the Pd-doped system, and E vacancy−C 3 N and E Pd denote the energy of the defective C 3 N and Pd atom, respectively. The binding energies of Pd doping at the C-vacancy site and N-vacancy site are −4.080 and −5.023 eV, respectively. This result indicates that Pd tends to be doped at the N-vacancy site, because the doping system at this time is more stable.
To further study the electronic behavior of Pd-C 3 N, we calculated DCD and DOS, as displayed in Figures 2 and 3, respectively. In the DCD of Figure 2, the areas with increased charge density are shown in red, while the areas with decreased charge density are shown in blue. As shown in Figure 2b, in the doping system where Pd doped is in the N-vacancy site, the charge density around Pd and C atoms decreases, while the charge density around N atoms increases. This result implies the electron-losing property of the Pd atom. In other words, the Pd atom transfers electrons to the VN-C 3 N monolayer. Meanwhile, the electron density between the Pd atom and C atom is very high, which suggests that a stable chemical bond in Pd-C is formed, so Pd can be stably adsorbed by VN-C 3 N. As can be seen from the total DOS of Pd-C 3 N, the spin up and spin down curves are highly symmetrical. This phenomenon shows that the doping system is not magnetic. Besides, the doping of Pd induces several impurity states, leading to some new peaks of total DOS after doping in the vicinity of −5.5, −4.0, 0.2, 1.0 and 2.0 eV. New peaks can be observed at the top of the valence band and at the bottom of the conduction band, indicating that Pd doping contributes greatly to the states near the Fermi energy. According to Figure 3b, huge hybridization occurs between Pd 4d orbital and C 2p orbital at multiple energy levels, such as −5.5, −2.7, −2 and 0.2 eV. This phenomenon confirms the previous conclusion that Pd can form a stable chemical bond with C and can be stably adsorbed by VN-C 3 N. Through the analysis of DCD and DOS, it can be concluded that the electronic behavior of VN-C 3 N has a significant change after doping with the Pd atom.
Nanomaterials 2021, 11, x FOR PEER REVIEW −5.023 eV, respectively. This result indicates that Pd tends to be doped at the N-vac site, because the doping system at this time is more stable. To further study the electronic behavior of Pd-C3N, we calculated DCD and DO displayed in Figures 2 and 3, respectively. In the DCD of Figure 2, the areas with incre charge density are shown in red, while the areas with decreased charge density are sh in blue. As shown in Figure 2b, in the doping system where Pd doped is in the N-vac site, the charge density around Pd and C atoms decreases, while the charge de around N atoms increases. This result implies the electron-losing property of the Pd a In other words, the Pd atom transfers electrons to the VN-C3N monolayer. Meanw the electron density between the Pd atom and C atom is very high, which suggests t stable chemical bond in Pd-C is formed, so Pd can be stably adsorbed by VN-C3N. A be seen from the total DOS of Pd-C3N, the spin up and spin down curves are highly metrical. This phenomenon shows that the doping system is not magnetic. Besides doping of Pd induces several impurity states, leading to some new peaks of total after doping in the vicinity of  −5.023 eV, respectively. This result indicates that Pd tends to be doped at the N-vacancy site, because the doping system at this time is more stable. To further study the electronic behavior of Pd-C3N, we calculated DCD and DOS, as displayed in Figures 2 and 3, respectively. In the DCD of Figure 2, the areas with increased charge density are shown in red, while the areas with decreased charge density are shown in blue. As shown in Figure 2b, in the doping system where Pd doped is in the N-vacancy site, the charge density around Pd and C atoms decreases, while the charge density around N atoms increases. This result implies the electron-losing property of the Pd atom. In other words, the Pd atom transfers electrons to the VN-C3N monolayer. Meanwhile, the electron density between the Pd atom and C atom is very high, which suggests that a stable chemical bond in Pd-C is formed, so Pd can be stably adsorbed by VN-C3N. As can be seen from the total DOS of Pd-C3N, the spin up and spin down curves are highly symmetrical. This phenomenon shows that the doping system is not magnetic. Besides, the doping of Pd induces several impurity states, leading to some new peaks of total DOS after doping in the vicinity of

Adsorption Analysis of Pd-C 3 N Monolayer to NO, NO 2 , SO 2
In order to fully compare various possible configurations of the three gas adsorption systems and find the most stable one for analysis, NO, NO 2 and SO 2 were placed in different directions on top of the Pd-C 3 N monolayer. Adsorption energy (E ad ) can describe the energy change of each adsorption structure, so it can be used to assess the stability of the system after adsorption of gas. The calculation formula of E ad is as below: In the above formula, E Pd−C 3 N/gas and E Pd−C 3 N respectively represent the energy before and after the adsorption of gas by Pd-C 3 N, and E gas represents the energy of the isolated gas molecule. The adsorption energies of the three gas adsorption systems are all negative, suggesting that the gas adsorption process of Pd-C 3 N is accompanied by the release of heat. Choose the structure with the lowest E ad , that is, the most stable configuration for subsequent works (as displayed in Figure 4). To understand the mechanism of charge transfer better, deformed charge density (DCD) is also described in Figure 4. Meanwhile, Tables 3 and 4 show the specific characteristic parameters of the three gas adsorption systems.

Adsorption Analysis of Pd-C3N Monolayer to NO, NO2, SO2
In order to fully compare various possible configurations of the three gas adsorption systems and find the most stable one for analysis, NO, NO2 and SO2 were placed in different directions on top of the Pd-C3N monolayer. Adsorption energy (Ead) can describe the energy change of each adsorption structure, so it can be used to assess the stability of the system after adsorption of gas. The calculation formula of Ead is as below: In the above formula, E Pd-C 3 N/gas and E Pd-C 3 N respectively represent the energy before and after the adsorption of gas by Pd-C3N, and E gas represents the energy of the isolated gas molecule. The adsorption energies of the three gas adsorption systems are all negative, suggesting that the gas adsorption process of Pd-C3N is accompanied by the release of heat. Choose the structure with the lowest Ead, that is, the most stable configuration for subsequent works (as displayed in Figure 4). To understand the mechanism of charge transfer better, deformed charge density (DCD) is also described in Figure 4. Meanwhile, Tables 3 and 4 show the specific characteristic parameters of the three gas adsorption systems.   In the NO adsorption system, the NO molecule is adsorbed on top of the Pd atom and perpendicular to the C 3 N plane. When NO is adsorbed, the N-O bond elongates from 1.164 to 1.188 Å, indicating that the NO molecule has certain activity during the adsorption process. The E ad of the NO adsorption system is −1.83 eV, so the adsorption of NO by the Pd-C 3 N monolayer can be identified as chemisorption. Meanwhile, according to the DCD in Figure 4a, the charge density near N atoms and O atoms increases. From the molecular point of view, NO has a 0.122 e negative charge, indicating the electron-receiving property of NO. During the interaction with the Pd-C 3 N monolayer, NO obtains 0.122 e from it. According to Figure 4b,c, NO 2 and SO 2 tend to be adsorbed on one side of the Pd dopant in the Pd-C 3 N monolayer rather than on the top. In addition, the adsorbed NO 2 and SO 2 molecules are negatively charged, which means that they both act as electron acceptors to absorb 0.407 e and 0.177 e from the Pd-C 3 N monolayer, respectively. In the NO 2 adsorption Nanomaterials 2021, 11, 1267 6 of 11 system, the N-O bond elongates to 1.281 Å compared to the 1.210 Å in the isolated phase. At the same time, the O-N-O bond angle of the NO 2 molecule in the adsorption system decreases from 133.487 • in the gas phase to 111.674 • . This significant deformation indicates that NO 2 has obvious geometric activation during its interaction with the Pd dopant. Besides, the charge density near the N atom in the NO 2 adsorption system decreases, while the charge density near the O atom increases. In addition, the E ad of the NO 2 adsorption system is −2.74 eV, which indicates that NO 2 has an ideal chemisorption on the surface of Pd-C 3 N, which is supported by large Q T (−0.407 e) and geometric deformation. In the SO 2 adsorption system, the S-O bond elongates from 1.480 to 1.495 Å, while the O-S-O bond angle decreases from 119.970 • to 119.932 • , suggesting that SO 2 is activated when interacting with the surface of Pd-C 3 N. The E ad of the SO 2 adsorption system is −1.61 eV, Q T is −0.177 e, which can be used to identify the adsorption as chemisorption. Previous reports have shown that E ad of the intrinsic C 3 N monolayer adsorption system for NO, NO 2 and SO 2 is −0.248, −0.840 and −0.584 eV, respectively [28]. Comparing to the results in this study, it can be found that the adsorption capacity of Pd-C 3 N for NO, NO 2 and SO 2 was significantly higher than that of intrinsic C 3 N. At the same time, the adsorption process of three kinds of gas molecules by the Pd-C 3 N monolayer is accompanied by a relatively large charge transfer, which indicates that the adsorption of gas will lead to the redistribution of electrons in the whole system and change the electronic behavior of Pd-C 3 N. To further explore the electronic behavior of Pd-C 3 N during the adsorption of NO, NO 2 and SO 2 , DOS is analyzed in the following.

DOS Analysis of NO, NO 2 and SO 2 Adsorption Systems
DOS is an important parameter for studying the electronic behavior of the interaction between gas and the Pd-C 3 N surface. According to Figure 5, the total DOS (TDOS) of the three adsorption systems shift to the right in different degrees compared with the Pd-C 3 N monolayer, and some new peaks appear nearby the Fermi level. In the TDOS of NO adsorption system, novel peaks appear in the vicinity of −1, −0.1 and 2 eV, while in NO 2 and SO 2 adsorption systems, the new peaks appear in the vicinity of −1.5, −0.3 and 0.3 eV. Besides, there are multiple activated states in the gas molecules due to the interaction between it and the surface of the Pd dopant. Then, the orbital hybridization of these activated states with Pd 4d results in new peaks in the TDOS of the three adsorption systems. In particular, the activated states of gas molecules lead to a certain degree of deformation of the states at the top of the conduction band and the bottom of the valence band, which indicates that the adsorption of gas will affect the electronic behavior of Pd-C 3 N.
tween it and the surface of the Pd dopant. Then, the orbital hybridization of these acti-vated states with Pd 4d results in new peaks in the TDOS of the three adsorption systems. In particular, the activated states of gas molecules lead to a certain degree of deformation of the states at the top of the conduction band and the bottom of the valence band, which indicates that the adsorption of gas will affect the electronic behavior of Pd-C3N.
Atomic DOS (PDOS) is shown in Figure 5. In the NO adsorption system, the N 2p and O 2p orbitals of activated NO have certain hybridization with Pd 4d orbitals at −8, −7, 0 (Fermi level) and 2.2 eV. According to the atomic DOS of the NO2 adsorption system, the Pd 4d orbital is strongly hybridized with N 2p and O 2p orbitals around −8, −7.2 and 2 eV, resulting in a relatively large charge transfer between NO2 and Pd-C3N. In the atomic DOS of SO2 adsorption system, S 2p, O 2p and Pd 4d orbital have strong hybridization at energy levels of −6.3, −2.5, −0.2 and 2 eV, indicating that there is a good orbital interaction between SO2 and Pd dopant. The strong hybridization between the atomic orbitals of the three gas molecules and Pd 4d orbital again confirms that NO, NO2 and SO2 can be stably adsorbed by Pd-C3N.
In summary, the strong interaction between three gases and Pd-C3N during gas adsorption process significantly affects the electronic behavior of Pd-C3N.

Band Structure Analysis of NO, NO2 and SO2 Systems
To further study the change in electrical conductivity of Pd-C3N after adsorbing gas, we calculated and analyzed the band structure of three adsorption systems ( Figure 6). In the band structure, the energy interval with zero energy state density between the con- Atomic DOS (PDOS) is shown in Figure 5. In the NO adsorption system, the N 2p and O 2p orbitals of activated NO have certain hybridization with Pd 4d orbitals at −8, −7, 0 (Fermi level) and 2.2 eV. According to the atomic DOS of the NO 2 adsorption system, the Pd 4d orbital is strongly hybridized with N 2p and O 2p orbitals around −8, −7.2 and 2 eV, resulting in a relatively large charge transfer between NO 2 and Pd-C 3 N. In the atomic DOS of SO 2 adsorption system, S 2p, O 2p and Pd 4d orbital have strong hybridization at energy levels of −6.3, −2.5, −0.2 and 2 eV, indicating that there is a good orbital interaction between SO 2 and Pd dopant. The strong hybridization between the atomic orbitals of the three gas molecules and Pd 4d orbital again confirms that NO, NO 2 and SO 2 can be stably adsorbed by Pd-C 3 N.
In summary, the strong interaction between three gases and Pd-C 3 N during gas adsorption process significantly affects the electronic behavior of Pd-C 3 N.

Band Structure Analysis of NO, NO 2 and SO 2 Systems
To further study the change in electrical conductivity of Pd-C 3 N after adsorbing gas, we calculated and analyzed the band structure of three adsorption systems ( Figure 6). In the band structure, the energy interval with zero energy state density between the conduction band and the valence band is called the band gap [50,51]. The narrower the band gap, the more easily the electron can be excited across the band gap, the higher the conductivity. According to Figure 6a, the band gap of the Pd-C 3 N monolayer is 0.203 eV, which is much narrower than that of C 3 N (0.44 eV [52]). Besides, the band structure of the doping system does not have an impurity state beyond the Fermi level. Thus, C 3 N doped with the Pd atom still has semiconductor property. In the band structure of NO and SO 2 adsorption systems (Figure 6b,d), the new impurity level surpassing the Fermi energy appears at the top of the valence band, causing a zero band gap for both systems. Therefore, the adsorption of NO and SO 2 can be deemed to strong p-type doping for Pd-C 3 N [53]. According to Figure 6, the band gap of NO and SO 2 adsorption system is 0 eV, while that of NO 2 adsorption system is 0.091 eV. It can be seen that the band gaps of these three adsorption systems are much narrower than that of Pd-C 3 N. This result shows that the conductivity of Pd-C 3 N is observably improved after adsorbing gas, especially after adsorbing NO and SO 2 . Through calculating and analyzing the band structure of the three adsorption systems, it is helpful to further understand the sensing mechanism of the resistive chemical sensor prepared by Pd-C 3 N. (c)

Band Structure Analysis of NO, NO2 and SO2 Systems
To further study the change in electrical conductivity of Pd-C3N after adsorbing gas, we calculated and analyzed the band structure of three adsorption systems ( Figure 6). In the band structure, the energy interval with zero energy state density between the conduction band and the valence band is called the band gap [50,51]. The narrower the band gap, the more easily the electron can be excited across the band gap, the higher the conductivity. According to Figure 6a, the band gap of the Pd-C3N monolayer is 0.203 eV, which is much narrower than that of C3N (0.44 eV [52]). Besides, the band structure of the doping system does not have an impurity state beyond the Fermi level. Thus, C3N doped with the Pd atom still has semiconductor property. In the band structure of NO and SO2 adsorption systems (Figure 6b,d), the new impurity level surpassing the Fermi energy appears at the top of the valence band, causing a zero band gap for both systems. Therefore, the adsorption of NO and SO2 can be deemed to strong p-type doping for Pd-C3N [53]. According to Figure 6, the band gap of NO and SO2 adsorption system is 0 eV, while that of NO2 adsorption system is 0.091 eV. It can be seen that the band gaps of these three adsorption systems are much narrower than that of Pd-C3N. This result shows that the conductivity of Pd-C3N is observably improved after adsorbing gas, especially after adsorbing NO and SO2. Through calculating and analyzing the band structure of the three adsorption systems, it is helpful to further understand the sensing mechanism of the resistive chemical sensor prepared by Pd-C3N.

Conclusions
The adsorption performance and sensing mechanism of the Pd-C 3 N monolayer for three kinds of industrial toxic gases NO, NO 2 and SO 2 were explored based on first principles. The DCD, DOS and band structure were considered to study the change in