## 3 Results and Discussion  
### Structures  
The calculated equilibrium bond lengths of Pd-ZGOi, 1 NO\({}_{2}\)-Pd-ZGOi, 2 NO\({}_{2}\)-Pd-ZGOi, 1H\({}_{2}\)S-Pd-ZGOi, and 2H\({}_{2}\)S-Pd-ZGOi (\(i=1,2,3,4\)) are listed in Table 1. The calculated Pd-Ga equilibrium bond lengths are 2.32 A and 2.37 A, respectively, for Pd-ZGO1 and Pd-ZGO4 structures; the calculated Pd-Zn equilibrium bond lengths are 2.57 A and 2.66 A, respectively, for Pd-ZGO2 and Pd-ZGO4 structures; the calculated Pd-O equilibrium bond length is 2.04 A for the Pd-ZGO3 structure. The equilibrium bond length of Pd-Ga or Pd-Zn is significantly larger than that of Pd-O (see Figure 1 and Table 1). This is because the valence electron for the O atom is negative, while it is positive for Pd, Ga, and Zn atoms. The Wigner-Seitz radii of Pd, Zn, Ga, and O atoms are 1.434 A, 1.217 A, 1.402 A, and 0.820 A, respectively. The bond length of Pd-Zn is larger than that of Pd-Ga because it is dominated by the Coulomb interaction. In other words, the electronic configurations of Zn and Ga are [Ar] 3d\({}^{10}\)4p\({}^{2}\) and [Ar] 3d\({}^{10}\)4s\({}^{2}\)4p\({}^{1}\), respectively. When the NO\({}_{2}\) molecule is adsorbed on the Pd-ZGO structure, the Pd atom is a bridge connecting the NO\({}_{2}\) molecule and the ZGO(111) surface. The calculated equilibrium bond length is completely different from \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**\(\pi\)NO\({}_{2}\)-Pd-ZGO\(i\)**} & \multicolumn{4}{c}{**Bond Length (Å)**} \\ \cline{2-5}  & **N-Pd** & **Pd-Ga** & **Pd-Zn** & **Pd-O** \\ \hline
1 NO\({}_{2}\)-Pd-ZGO1 & 2.01 & 2.53 & - & - \\
1 NO\({}_{2}\)-Pd-ZGO2 & 1.94 & 2.34 & - & 2.17 \\
1 NO\({}_{2}\)-Pd-ZGO3 & 1.96 & - & - & 2.10 \\
1 NO\({}_{2}\)-Pd-ZGO4 & 1.96 & 2.31 & 2.86 & 2.48 \\
2 NO\({}_{2}\)-Pd-ZGO1 & 2.04 & 2.04 & 2.51 & - & - \\
2 NO\({}_{2}\)-Pd-ZGO2 & 2.03 & 2.21 & 2.44 & 2.82 & 2.78 \\
2 NO\({}_{2}\)-Pd-ZGO3 & 2.11 & 2.05 & - & - & 2.15 \\
2 NO\({}_{2}\)-Pd-ZGO4 & 2.04 & 2.12 & 2.46 & - & - \\ \hline \multirow{2}{*}{**\(\pi\)H\({}_{2}\)S-Pd-ZGO\(i\)**} & \multicolumn{4}{c}{**Bond Length (Å)**} \\ \cline{2-5}  & **S-Pd** & **Pd-Ga** & **Pd-Zn** & **Pd-O** \\ \hline
1H\({}_{2}\)S-Pd-ZGO1 & 2.37 & 2.38 & - & - \\
1H\({}_{2}\)S-Pd-ZGO2 & 2.26 & 2.82 & 2.89 & 2.18 \\
1H\({}_{2}\)S-Pd-ZGO3 & 2.25 & 2.62 & - & 2.11 \\
1H\({}_{2}\)S-Pd-ZGO4 & 2.38 & 2.38 & - & - \\
2H\({}_{2}\)S-Pd-ZGO1 & 2.52 & 2.54 & 2.34 & - & - \\
2H\({}_{2}\)S-Pd-ZGO2 & 2.41 & 2.60 & 2.81 & 2.88 & 2.37 \\
2H\({}_{2}\)S-Pd-ZGO3 & 2.31 & 2.99 & - & - & 2.13 \\
2H\({}_{2}\)S-Pd-ZGO4 & 2.54 & 2.56 & 2.46 & - & - \\ \hline \end{tabular}
\end{table} 
Table 1: \(Cont.\)Pd-ZGOi. In the 1 NO\({}_{2}\)-Pd-ZGO1 structure, the bond length of Pd-Ga is 2.53 A, where it is 2.32 A in the absence of the NO\({}_{2}\) molecule without Pd atoms. Note that in the initial structure of 1 NO\({}_{2}\)-Pd-ZGO1, the distance between the NO\({}_{2}\) molecule and the surface Pd atom is 3.18 A. The electronic configuration of the Pd atom is [Kr]4d\({}^{9}\)5s1. This implies the attraction between Pd and N atoms. As a result, the bond length of N-Pd is reduced to 2.01 A, while the bond length for Pd-Ga is increased. Generally, the N-Pd bond lengths in nNO2-Pd-ZGOi are about 2 A. In the 1 NO\({}_{2}\)-Pd-ZGO2 and 1 NO\({}_{2}\)-Pd-ZGO4 structures, Pd atoms do not remain on the top of the Zn\({}_{3C}\) and O\({}_{4C}\) sites. Therefore, the calculated bond lengths change significantly, especially for the O\({}_{4C}\) site (see Figure 3). It seems that Pd atoms are attracted by Ga atoms on the ZGO(111) surface. In one and two NO\({}_{2}\) molecules attracted to Pd atoms, the results of 1 NO\({}_{2}\)-Pd-ZGO1 (1 NO\({}_{2}\)-Pd-ZGO3) and 2 NO\({}_{2}\)-Pd-ZGO1 (2 NO\({}_{2}\)-Pd-ZGO3) are similar, while Pd atoms are retained on the top of the Ga\({}_{3C}\) and O\({}_{3C}\) sites. When two NO\({}_{2}\) molecules are adsorbed into the Pd atom, the calculated bond length of N-Pd is larger. In the 2 NO\({}_{2}\)-Pd-ZGO4 structure, the interaction between the Pd and surface Zn (O) atom disappears.