## 2 Computational Details  
The work functions of NO\({}_{2}\) and H\({}_{2}\)S adsorbed on Pd-decorated ZnGa\({}_{2}\)O\({}_{4}\)(111) (Pd-ZGO) surfaces were systematically studied. All calculations were performed by using the density functional theory as implemented in the Vienna ab initio simulation package (VASP) [19; 20] with the exchange correlation function described by generalized gradient approximation (GGA) and the Perdew-Wang (PW91) correction [21; 22]. The crystal structure of ZnGa\({}_{2}\)O\({}_{4}\) is displayed in Figure 1a. We used a conventional crystal structure containing 56 atoms, i.e., 8 Zn, 16 Ga, and 32 O atoms. The cutoff energy was set to 500 eV, and the self-consistent total energy criterion was \(10^{-5}\) eV/unit cell. To understand the work function changes when NO\({}_{2}\) (H\({}_{2}\)S) is adsorbed on Pd-ZGO surfaces, we built a supercell containing 112 atoms to simulate ZnGa\({}_{2}\)O\({}_{4}\)(111) surfaces with a vacuum of 20 A, which should be wide enough to decouple the nearest surface interaction. This preferred Ga-Zn-O-terminated surface was selected from the previous study on ZnGa\({}_{2}\)O\({}_{4}\), and its surface energy was 0.01 eV/A\({}^{2}\)[23]. In order to describe the effect of changes in the work function of the NO\({}_{2}\) and H\({}_{2}\)S on the surface of Pd-ZGO, we firstly calculated the work function \(\Phi_{S}\) using the following formula [24]:  
\[\Phi_{S}=E_{VAC}-E_{F}\]  
where \(\Phi_{S}\) is the work function of ZnGa\({}_{2}\)O\({}_{4}\)(111) surface. \(E_{VAC}\) and \(E_{F}\) are the energy of the vacuum and the Fermi energy, respectively. Second, we constructed four adsorption models of Pd atoms, denoted as Pd-ZGO\(i\) (\(i\) = 1,2,3,4). Here, the superscripts 1, 2, 3, and 4 in Pd-ZGO, respectively, indicate the positions of the initial adsorbed sites Ga\({}_{3C}\), Zn\({}_{3C}\), O\({}_{3C}\), and O\({}_{4C}\) on the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface, as shown in Figure 1b. The initial distance from the Pd atom to the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface was set as the sum of the van der Waals radii of the Pd atom and Ga (Zn or O)  
Figure 1: Left and right panels illustrate bulk ZnGa\({}_{2}\)O\({}_{4}\) crystal structure and top view of the adsorption sites O\({}_{3C}\), Zn\({}_{3C}\), O\({}_{4C}\), and Ga\({}_{3C}\) on ZnGa\({}_{2}\)O\({}_{4}\)(111) surface, respectively. These sites are labeled for the adsorption sites of the Pd atom. surface atoms, as shown in Figure 2. Third, we considered one NO\({}_{2}\) (H\({}_{2}\)S) molecule and two NO\({}_{2}\) (H\({}_{2}\)S) molecules adsorbed on the surface Pd atoms and compared the corresponding results of the calculated work functions in the second step, denoted as _n_NO\({}_{2}\)-Pd-ZGO_i_ and _n_H\({}_{2}\)S-Pd-ZGO_i (_n_ = 1,2; \(i\) = 1,2,3,4). Here, \(n\) represents the number of molecules. All supercells were fully relaxed until the force attraction on each atom was less than 0.001 eV/A, and a 3 \(\times\) 3 \(\times\) 1 Monkhorst-Pack grid was used. The initial distance from NO\({}_{2}\) (H\({}_{2}\)S) molecules to Pd surface atoms was also set to the sum of the van der Waals radii of N (S) from the NO\({}_{2}\) (H\({}_{2}\)S) molecules and the Pd surface atoms. The van der Waals distances of H, N, O, S, Zn, Ga, and Pd atom were 1.20 A, 1.55 A, 1.52 A, 1.80 A 1.39 A, 1.87 A, and 1.63 A, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Pd-ZGO\(i\)**} & \multicolumn{3}{c}{**Bond Length (Å)**} \\ \cline{2-4}  & **Pd-Ga** & **Pd-Zn** & **Pd-O** \\ \hline Pd-ZGO1 & 2.32 & - & - \\ Pd-ZGO2 & - & 2.57 & - \\ Pd-ZGO3 & - & - & 2.04 \\ Pd-ZGO4 & 2.37 & 2.66 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calculated equilibrium bond length (Å) for the Pd-ZGO_i_, _n_NO\({}_{2}\)-Pd-ZGO_i_, and _n_H\({}_{2}\)S-Pd-ZGO_i_ structures. Figure 2: Side view of the Pd atom on ZnGa\({}_{2}\)O\({}_{4}\)(111) surface.