Factors determining surface oxygen vacancy formation energy in ternary spinel structure oxides with zinc

Spinel oxides are an important class of materials for heterogeneous catalysis including photocatalysis and electrocatalysis. The surface O vacancy formation energy (E_Ovac) is a critical quantity for catalyst performance because the surface of metal oxide catalysts often acts as a reaction site, for example, in the Mars-van Krevelen mechanism. However, experimental evaluation of E_Ovac is very challenging. We obtained the E_Ovac for (100), (110), and (111) surfaces of normal zinc-based spinel oxides ZnAl₂O₄, ZnGa₂O₄, ZnIn₂O₄, ZnV₂O₄, ZnCr₂O₄, ZnMn₂O₄, ZnFe₂O₄, and ZnCo₂O₄. The most stable surface is (100) for all compounds. The smallest E_Ovac for a surface is the largest in the (100) surface except for ZnCo₂O₄. For (100) and (110) surfaces, there is a good correlation, over all spinels, between the smallest E_Ovac for the surface and bulk formation energy, while the ionization potential correlates well in (111) surfaces. Machine learning over E_Ovac of all surface sites in all orientations and for all compounds to find the important factors, or descriptors, that decide the E_Ovac revealed that bulk and surface-dependent descriptors are the most important, namely the bulk formation energy, a Boolean descriptor of whether the surface is (111) or not, and the ionization potential, followed by geometrical descriptors that are different in each O site.