## 3 Results and Discussion
### Adsorption Behavior of the Pd-InN Monolayer  
With the relaxed Pd-InN monolayer, we implemented the adsorption of CO and NO molecules onto the surface and plotted the most stable configurations in Figures 3 and 4, respectively, in which the electron localization function (ELF) is also depicted to display the bonding behavior in the adsorbed systems. Figure 1: Configuration (**a**) and EDD (**b**) of the Pd-InN monolayer. The black values are bond lengths while the red value is the charge of the Pd dopant. In EDD, the green and rosy regions represent electron accumulation and depletion, respectively. The isosurface is set to 0.005 eV/Å\({}^{3}\). Figure 4: The most stable configuration (**a**), ELF (**b**) and EDD (**c**) for NO adsorption on the Pd-InN monolayer. Other settings are same as Figure 3.  
Figure 3: The most stable configuration (**a**), ELF (**b**) and EDD (**c**) for CO adsorption on the Pd-InN monolayer. The setting in EDD is same as Figure 2. The black values are bond length while the red value is the charge of the Pd dopant. Figure 2: Total DOS (**a**) and partial DOS (**b**) of Pd-InN. The dash line is the Fermi level. As can be seen in Figure 3a, in the CO system the CO molecule was vertically adsorbed on the top of the Pd dopant by the C-end position, forming the Pd-C bond (shown in Figure 3b) measured at 1.89 A. At the same time, the C\(\equiv\)O bond on the inner of the CO molecule elongated to 1.16 A from 1.14 A for the gas phase, while the Pd-N and Pd-In bonds were prolonged to 2.09 and 3.01 A, respectively. These deformations indicate the activation effect on the geometries of the CO molecule and the Pd-InN monolayer during adsorption [32]. The calculated \(E_{\text{ad}}\) for CO adsorption is \(-\)2.12 eV, much larger than that in a pristine InN system (\(-\)0.223 eV), as reported in Reference [15], indicating the enhanced adsorption performance of Pd-doping on the nano-surface. After adsorption, the CO molecule accepts 0.121 e from the Pd-InN surface, in which the Pd dopant loses 0.004 e, which indicates that Pd behaves as a media bridging the charge-transfer from the InN layer to the CO molecule. Such an amount of charge-transfer (0.117 e) is larger than that in a pristine InN system as well, confirming the enhancement in surface reactivity of the InN monolayer after Pd-doping. The electron hybridization between Pd and C atoms according to the dense electron accumulation and depletion on the Pd-C bond is visible in Figure 3b. From Figure 3c, where the EDD is shown, we can observe strong electron accumulation on the CO molecule and electron depletion on the Pd dopant, which is in line with the Hirshfeld method. Apart from that, electron depletion appears on the Pd-In and Pd-N bonds, suggesting their weakened binding force, which accords with their elongation. When it comes to the NO system, as shown in Figure 4a, the most stable configuration for NO adsorption is same as that for CO adsorption. The N atom was oriented to the Pd dopant, forming a new Pd-N bond of 1.86 A, as displayed in Figure 4b. Meanwhile, the C=O bond elongated to 1.17 A from 1.16 A for the isolated molecule, while in the Pd-InN monolayer the Pd-N bond shortened to 2.05 A after adsorption. This may attribute to the predominant protrusion of the N atom in the InN layer. Along with such deformation, the Pd-In bonds were broken as well. However, the electron hybridization between the Pd dopant and the N atom of the NO molecule remained quite strong, as seen in ELF. The \(E_{\text{ad}}\) (\(-\)1.65 eV) and \(Q_{\text{T}}\) (\(-\)0.093) in the NO system were not as large as those in CO system, indicating the relatively weak interaction here, but it was still larger than that in the pristine InN system (\(-\)0.380 eV) [15]. Based on the Hirshfeld method, the NO molecule performed an electron-accepting property, but the Pd dopant contributed most of the charge-transfer (0.061 e) to the gas species. Thus, we assume that the binding force of Pd-N for NO adsorption will be stronger than that of Pd-C for CO adsorption.