## 3 Results and Discussion
Figure 4 displays the lowest energy configurations for H\({}_{2}\)S on ZnGa\({}_{2}\)O\({}_{4}\)(111) surfaces. In Models S1 and S2, the sulfur atom of the H\({}_{2}\)S molecule adsorbed on the Ga\({}_{3c}\) and Zn\({}_{3c}\) atoms of the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface to yield S-Ga and S-Zn bonds with bond lengths of 2.46 A and 2.50 A, respectively. In Model S3, the H\({}_{2}\)S molecule adsorbed on the O\({}_{3c}\) atom of the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface and dissociated to HS\({}^{-}\) and H\({}^{+}\) ions to form H-O and S-Ga bonds with bond lengths of 0.97 A and 2.22 A, respectively. In Model S4, the H\({}_{2}\)S molecule moved away from the originally adsorbed O\({}_{4c}\) atom of the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface to form an S-Ga bond with a bond length of 2.46 A. In Models H1 and H2, the H\({}_{2}\)S molecules adsorbed on Ga\({}_{3c}\) and Zn\({}_{3c}\) atoms of the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface and dissociated to H\({}^{+}\) and HS\({}^{-}\) ions to form an H-O bond and an S-Ga bond with bond lengths of 0.97 A and 2.22 A, respectively. In Model H3, the hydrogen atom of the H\({}_{2}\)S molecule was adsorbed on the O\({}_{3c}\) atom of the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface to yield an H-O bond with a bond length of 1.25 A. In Model H4, the H\({}_{2}\)S molecule adsorbed on the O\({}_{4c}\) atom of the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface. However, its adsorption was unstable and therefore not ideal, with atomic distances of 3.12 A and 2.66 A for H-Ga and H-Zn, respectively. The vacuum energy, Fermi energy, work functions of ZnGa\({}_{2}\)O\({}_{4}\)(111) with and without H\({}_{2}\)S, and work function difference among H\({}_{2}\)S adsorption models are listed in Table 2. The work function difference among Models S1, S2, and S4 decreased when the H\({}_{2}\)S molecules adsorbed on the Ga\({}_{3c}\) and Zn\({}_{3c}\) atoms of the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface. The decrease in work function ranged from \(-\)0.31 to \(-\)1.66 eV, which concurs with the experimental results of other studies showing similar resistance responses of ZnO(Ga) samples to H\({}_{2}\)S [11]. Similarly, the H\({}_{2}\)S molecule preferred bonding with the Ga\({}_{3c}\) or Zn\({}_{3c}\) atom. Model S1 had the maximum work function difference of \(-\)1.66 eV, showing increased sensitivity for detecting H\({}_{2}\)S molecules. Models S3, H1, H2, H3, and H4 had positive work function differences,  
Figure 4: Top and side views of the most favorable configurations for H\({}_{2}\)S on the ZnGa\({}_{2}\)O\({}_{4}\)(111) surface. Atoms are represented by spheres: Zn (purple, large), Ga (brown, large), S (yellow, medium-sized), O (red, medium-sized), and H (white, small). Equilibrium bond lengths between molecular and surface atoms are given in Angstrom. possibly because of the heterolytic break of the H-S bond in the H\({}_{2}\)S, resulting in the tendency of forming H-O bonds on the surface of ZnGa\({}_{2}\)O\({}_{4}\). The H-S bond-breaking leading to the decrease of the H\({}_{2}\)S adsorption might explain the observed change in the decreased sensitivity for detecting H\({}_{2}\)S molecules, in agreement with the experimental observation [11].