## 4 Conclusions  
The adsorption energy and work function change of CO on the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface have been investigated using first-principles calculations. Our results show that a single CO molecule on clean and Pd-doped ZnGa\({}_{2}\)O\({}_{4}\)(111) surfaces exhibit maximum work function changes of \(-\)0.55 eV and \(-\)0.79 eV, respectively, indicating Pd-doped ZnGa\({}_{2}\)O\({}_{4}\)-based gas sensors can improve sensitivity to detect CO molecules. The adsorption energies for a single CO molecule on the clean and Pd-doped ZnGa\({}_{2}\)O\({}_{4}\)(111) surface have the lowest adsorption energy of \(-\)1.88 eV and \(-\)3.36 eV, respectively, which means that CO molecules are catalyzed by Pd atoms to promote adsorption on the surface of ZnGa\({}_{2}\)O\({}_{4}\)(111) to \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Models** & \(E_{VAC}\) **(eV)** & \(E_{F}\) **(eV)** & \(\Phi_{S.CO}\) **(eV)** & \(\Phi_{S}\) **(eV)** & \(\Delta\Phi\)**(eV)** & \(\Delta\)**E **(eV)** \\ \hline ZnGa\({}_{2}\)O\({}_{4}\)(111) & 0.41 & \(-\)3.50 & - & 3.91 & - & - \\ CO-C1 & 0.23 & \(-\)3.15 & 3.38 & - & \(-\)0.53 & \(-\)1.88 \\ CO-C2 & 0.51 & \(-\)3.28 & 3.79 & - & \(-\)0.11 & \(-\)0.68 \\ CO-C3 & 0.63 & \(-\)3.37 & 4.00 & - & 0.09 & \(-\)0.17 \\ CO-C4 & 0.49 & \(-\)3.23 & 3.72 & - & \(-\)0.18 & \(-\)0.70 \\ CO-O1 & 0.16 & \(-\)3.20 & 3.36 & - & \(-\)0.55 & \(-\)0.44 \\ CO-O2 & 0.53 & \(-\)3.24 & 3.77 & - & \(-\)0.13 & \(-\)0.25 \\ CO-O3 & 0.69 & \(-\)3.29 & 3.98 & - & 0.07 & \(-\)0.04 \\ CO-O4 & 0.58 & \(-\)3.26 & 3.84 & - & \(-\)0.07 & \(-\)0.21 \\ CO-CO1 & 0.42 & \(-\)3.06 & 3.48 & - & \(-\)0.43 & \(-\)1.28 \\ CO-CO2 & 0.21 & \(-\)3.21 & 3.42 & - & \(-\)0.49 & \(-\)1.55 \\ CO-CO3 & 0.24 & \(-\)3.41 & 3.65 & - & \(-\)0.26 & \(-\)0.15 \\ CO-CO4 & 0.34 & \(-\)3.47 & 3.81 & - & \(-\)0.09 & \(-\)0.17 \\ Pd-ZGO1 & 0.65 & \(-\)3.00 & - & 3.65 & - & - \\ Pd-ZGO2 & 0.76 & \(-\)3.08 & - & 3.84 & - & - \\ Pd-ZGO3 & 0.65 & \(-\)3.29 & - & 3.94 & - & - \\ Pd-ZGO4 & 0.67 & \(-\)3.08 & - & 3.75 & - & - \\ CO-Pd- & & \(-\)0.30 & \(-\)3.16 & 2.86 & - & \(-\)0.79 & \(-\)1.58 \\ ZGO1 & 0.20 & \(-\)2.96 & 3.16 & - & \(-\)0.68 & \(-\)3.36 \\ CO-Pd- & & & & & & \\ ZGO3 & \(-\)0.02 & \(-\)3.21 & 3.19 & - & \(-\)0.75 & \(-\)2.78 \\ CO-Pd- & & & & & & \\ CO-Pd- & & & & & & \\ ZGO4 & 0.40 & \(-\)2.92 & 3.32 & - & \(-\)0.43 & \(-\)2.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calculated vacuum energy \(E_{VAC}\), Fermi energy \(E_{F}\), work function with CO molecules \(\Phi_{S.CO}\), and without CO molecules \(\Phi_{S}\), work function changes \(\Delta\Phi\), and adsorption energy \(\Delta\)E of ZnGa\({}_{2}\)O\({}_{4}\)(111), CO-Ci, CO-Oi, CO-COi, Pd-ZGOi, and CO-Pd-ZGOi. All energies are presented in eV. enhance the work function change. This result also leads that the adsorption energy of CO molecules is positively correlated with the sensitivity or the work function change of CO on the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface. Our calculations for work function change for gas sensor applications overcome many issues encountered in potential energy barrier for electrons caused by gas adsorption on the ZnGa\({}_{2}\)O\({}_{4}\) surface and offers promising applications in next-generation sensing technologies, including not only adsorption energy indicating a spontaneous reaction progression, but also designing high-performance single-atom catalysts (SACs), such as the recently demonstrated catalytic CO oxidation on MgAl\({}_{2}\)O\({}_{4}\)-supported iridium single atoms [22]. [PERSON] and [PERSON] contributed equally to this work; conceptualization, [PERSON] and [PERSON]; methodology, C.-A.P. ; validation, C.-A.P. ; formal analysis, [PERSON]-[PERSON], [PERSON], [PERSON] and [PERSON]; investigation, C.-A.P. ; writing--original draft preparation, [PERSON], [PERSON], [PERSON] and [PERSON]; writing--review and editing, [PERSON]-C.T., [PERSON]-W.H. and P.-L.L. ; supervision, [PERSON]-H.H., C.-C.C. and P.-L.L. All authors have read and agreed to the published version of the manuscript.