## 3 Results and Discussion
The CO-O\(i\) have low adsorption energies, and ranged from \(-\)0.04 eV to \(-\)0.44 eV, showing less attraction between atoms. It is perhaps not surprising that the CO-O\(i\) have longer bond lengths than the CO-C\(i\). In the cases of the CO-CO\(i\), the CO-CO2 has the lowest adsorption energy of \(-\)1.55 eV and the CO-CO1 exhibits the second lowest adsorption energy of \(-\)1.28 eV. The oxygen atoms of CO molecules are more attractive to the Ga surface atoms of the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface than the carbon atoms of CO molecules. The gas sensing sensitivity of the various CO-C\(i\), CO-O\(i\), CO-CO\(i\), and CO-Pd-ZGO\(i\) configurations is intimately related to their surface resistances or work function changes. A common approach adopted in many studies is to analyze energies of the Fermi level and the vacuum level to determinate their work functions. We use the clean ZnGa\({}_{2}\)O\({}_{4}\)(111) surface as a reference state surface to calculate the work function of 3.91 eV, as shown in Table 1. In Table 1, it can be clearly seen that the Fermi energies of all models increase when a CO molecule is adsorbed on the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface. This is because a CO molecule adds extra electrons to the system, causing the increase of the Fermi energy. From Table 1, it is apparent that the vacuum energies of the only two models, i.e., the CO-C1 and CO-O1, are lower than the reference value (0.41 eV) of the vacuum level of the clean ZnGa\({}_{2}\)O\({}_{4}\)(111), leading to the small work functions. However, it is interesting to note that the bonding of carbon or oxygen atoms from CO molecules to Ga surface atoms on the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface decreases the vacuum energy level, which may explain why the Ga\({}_{3c}\) sites of adsorbed gas molecules have a great influence on the gas sensitivity. In the CO-C\(i\), the work function is proportional to the adsorption energy, while the CO-C1 model had the largest reduction with the work function change of \(-\)0.53 eV. In the CO-O\(i\), CO-O1 has the largest reduction with the work function change of \(-\)0.55 eV. Surprisingly, the work function change of CO-O1 is slightly higher than that of CO-C1 (\(-\)0.53 eV), which means that the Ga\({}_{3c}\) sites of adsorbed CO molecules have a great influence on the gas sensitivity. In the CO-CO\(i\), CO-CO2 has the largest reduction with the work function change of \(-\)0.49 eV, showing the oxygen atoms of CO molecules are more sensitive to the Ga surface atoms of the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface than the carbon atoms of CO molecules, corresponding to the work function change of \(-\)0.43 eV. Based on our previous study [5], we found that Pd atoms can be used to enhance the performance of ZnGa\({}_{2}\)O\({}_{4}\)-based gas sensors for detecting NO\({}_{2}\) and H\({}_{2}\)S. Here, we calculate the work function change and adsorption energy of the CO-Pd-ZGO\(i\) by following a similar procedure, as listed in Table 1. The work function changes of the CO-Pd-ZGO\(i\) range from \(-\)0.43 to \(-\)0.79 eV, making the latter 1.43 times larger than the former. Our results show that an increase in the work function changes can be used to improve the performance of the gas sensor. In addition, the adsorption energies of CO-Pd-ZGO\(i\) drop drastically and range from \(-\)1.58 to \(-\)3.36 eV, indicating CO molecules are catalyzed by Pd atoms to promote adsorption on the surface of ZnGa\({}_{2}\)O\({}_{4}\)(111) to enhance the work function change. In the CO-Pd-ZGO\(i\), CO-Pd-ZGO2 has the lowest adsorption energy of \(-\)3.36 eV. This implies that the existence of the Pd atom on the initial adsorbed site Zn\({}_{3c}\) of the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface is particularly attractive for CO molecules.