## 3 Results and Discussion
### Adsorption Energies  
Table 2 also shows adsorption energies of the NO\({}_{2}\) and H\({}_{2}\)S molecules on the surface of ZGO with and without Pd atoms. It can be clearly seen that a NO\({}_{2}\) (H\({}_{2}\)S) molecule is adsorbed to the ZGO surface, which is endothermic by 0.64 eV (2.32 eV). In contrast with Pd atoms adsorbed on the surface of ZGO, i.e., Pd-ZGO\(i\), the NO\({}_{2}\) and H\({}_{2}\)S molecules on the surface of Pd-ZGO\(i\) have exothermic or negative adsorption energy. It should be noted that the spontaneous reaction occurs in the direction where the Gibbs free energy change, \(\Delta G\), decreases. The Gibbs free energy change consists of enthalpy change \(\Delta H\) and entropy change \(\Delta S\) by the following equation:  
\[\Delta G=\Delta H-T\Delta S\]  
The enthalpy change is defined as the sum of the internal energy change \(\Delta E\) and the product of the pressure \(P\) and volume change \(\Delta V\), as follows:  
\[\Delta H=\Delta E+P\Delta V\]  
Therefore, the Gibbs free energy change can be expressed by the following equation:  
\[\Delta G=\Delta E+P\Delta V-T\Delta S\]  
In our study, we ignored the contribution of entropy change, and the volume change in the Pd-ZGOi structures was negligible. The Gibbs free energy change can be further simplified as the internal energy change caused by the kinetic energy, potential energy, and chemical energy of the target system. The negative Gibbs free energy change, its negative internal energy change, or its negative adsorption energies, \(\Delta E\), provides a means of spontaneous physical and chemical changes to take place without any external help. On the contrary, the positive adsorption energy indicates that the corresponding endothermic process can be supported by the increase in temperature. A higher positive adsorption energy means that more energy is required from the outside world, which also indicates that the endothermic reaction does not occur easily. Our results on the surface of ZGO \begin{table}
\begin{tabular}{c c c c c} \hline
**Model** & \(\Phi_{S}\) (**eV**) & \(\Phi_{S,\text{gas}}\)(**eV**) & \(\Delta\Phi\) (**eV**) & \(\Delta E\) (**eV**) \\ \hline
1H\({}_{2}\)S-Pd-ZGO2 & - & 3.16 & \(-\)0.68 & \(-\)2.89 \\
1H\({}_{2}\)S-Pd-ZGO3 & - & 3.04 & \(-\)0.90 & \(-\)1.85 \\
1H\({}_{2}\)S-Pd-ZGO4 & - & 3.26 & \(-\)0.49 & \(-\)0.95 \\
2H\({}_{2}\)S-Pd-ZGO1 & - & 1.88 & \(-\)1.77 & \(-\)0.45 \\
2H\({}_{2}\)S-Pd-ZGO2 & - & 2.58 & \(-\)1.26 & \(-\)2.44 \\
2H\({}_{2}\)S-Pd-ZGO3 & - & 2.62 & \(-\)1.32 & \(-\)1.80 \\
2H\({}_{2}\)S-Pd-ZGO4 & - & 1.93 & \(-\)1.82 & \(-\)1.03 \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._show that the adsorption of NO\({}_{2}\) molecules on the surface is energetically more favorable than the adsorption of H\({}_{2}\)S molecules on the surface by 1.68 eV. Our results on NO\({}_{2}\) (H\({}_{2}\)S) molecules adsorbed on the surface of Pd-ZGOi show that the adsorption reaction is spontaneous and exothermic. Most importantly, the structures of Pd atoms remaining at the top of the Zn\({}_{3C}\) site, namely, 1 NO\({}_{2}\)-Pd-ZGO2, 2 NO\({}_{2}\)-Pd-ZGO2, 1H\({}_{2}\)S-Pd-ZGO2, and 2H\({}_{2}\)S-Pd-ZGO2, have the overall lowest adsorption energy for NO\({}_{2}\) and H\({}_{2}\)S molecules, regardless of the number of NO\({}_{2}\) and H\({}_{2}\)S molecules. It is interesting to note that the magnitudes of adsorption energy of 1 NO\({}_{2}\)-Pd-ZGO2 (\(-\)2.94 eV) and 2 NO\({}_{2}\)-Pd-ZGO2 (\(-\)3.72 eV) are larger than that of 1H\({}_{2}\)S-Pd-ZGO2 (\(-\)2.89 eV) and 2H\({}_{2}\)S-Pd-ZGO4 (\(-\)2.44 eV), showing that the surface of ZGO doped with palladium benefits the adsorption reaction to increase the amount of NO\({}_{2}\). However, the adsorption reaction on the surface of Pd-ZGOi is unfavorable for the increase in the amount of H\({}_{2}\)S. The largest adsorption energy occurs in the structures of the Pd atoms remaining on the top of the Zn\({}_{3C}\) site, but the largest work function difference occurs in the structures of Pd atoms remaining on the top of the Ga\({}_{3C}\) site.