## 2 Computational Details
An oxygen atom from a CO molecule perpendicular to the surface is adsorbed on Pd-ZGO\(i\) models, labeled as CO-Pd-ZGO\(i\) (where \(i\) = 1-4), as shown in the bottom panel of Figure 3. The initial distance from the adsorbed atom to the surface atom was set as the sum of the van der Waals radii of each of atom. Figure 1: The bulk ZnGa\({}_{2}\)O\({}_{4}\) crystal and top and side views of the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface. Surface atoms are labeled Ga\({}_{3c}\), Zn\({}_{3c}\), O\({}_{3c}\), and O\({}_{4c}\). Atoms are represented by spheres: Zn (gray, large), Ga (brown, medium-sized), and O (red, small). The adsorption of gas molecules on the surface of the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface causes a change in the work function \(\Delta\Phi\), resulting in a change between the resistance in the presence of the investigated gas (\(Rg\)) and the resistance in the reference gas (\(Ra\)) to measure the gas sensitivity. The gas sensitivity could be determined from the ratio of \(Rg/Ra\), and the work function change \(\Delta\Phi\) is given by [3]  
\[\Delta\Phi=\Delta X+kT\ln(Rg/Ra) \tag{1}\]  
where \(\Delta X\) denotes the change in electron affinity and \(kT\) denotes the product of the Boltzmann constant \(k\) and the temperature \(T\). Note that the work function \(\Phi\) is given by the following equation [21]:  
\[\Phi=E_{VAC}-E_{F} \tag{2}\]  
where \(E_{VAC}\) and \(E_{F}\) are the energies of a vacuum level and a Fermi level, respectively. Electrons in solids and molecules obey the Fermi-Dirac distribution. Electrons with the same quantum properties are forbidden to occupy the same energy state, while up to two electrons with opposite spins are allowed to occupy one energy state. The energy of the highest occupied state is known as the Fermi energy. Additionally, the limitations of the first-principles calculations do not allow the calculation of the absolute vacuum level because it depends on the periodic boundary conditions and surface terminations of the materials. The vacuum level here refers to the energy estimated from the planar average of  
Figure 2: Ball and stick structural representations of the optimized CO-\(Ci\), CO-\(Oi\) and CO-\(COi\) considered in this study. Atoms are represented by spheres: Zn (gray, large), Ga (brown, large), C (gray, medium-sized), and O (red, small). Bond lengths are given in Å.  
the potential of the periodic slabs in the vacuum region along the direction perpendicular to the surface of the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface. The gas adsorption on the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface that enables exothermic or endothermic reaction is also one of the serious issues affecting the sensitivity of the sensor. The adsorption energy \(\Delta\)E can be calculated through the equation:  
Figure 1.0  
where \(E_{ZGO-CO}\) is the total energy of a target molecule or a CO molecule adsorbed on the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface, and \(E_{ZGO}\) and \(E_{CO}\) are the total energies of a slab of ZnGa\({}_{2}\)O\({}_{4}\)(111) surface model and a free (isolated) CO molecule, respectively. Whether the adsorption energy is related to the work function is also an issue to be discussed in this study.