Scaling reducibility of metal oxides

The reducibility of bulk metal oxides in which the cation is in its highest oxidation state (MgO, Sc2O3, Y2O3, TiO2, m-ZrO2, m-HfO2, CeO2, V2O5, Nb2O5, Ta2O5, WO3, CrO3, Al2O3, β-Ga2O3, SiO2, SnO2 and ZnO) has been studied by standard periodic density functional theory. We have defined and calculated descriptors able to describe and quantify semi-quantitatively the extent of reduction: electronic band gap, oxygen vacancy formation energy and electronic localization. We find that there is no single criterion for characterizing the reducibility. We discuss the advantages and limitations of each method, and we apply them to classify the materials with the PBE+U and B3LYP functionals. Typical irreducible oxides such as MgO show a large band gap, high oxygen vacancy formation energy and electronic localization of the reduction electrons forming and F-center, with a diamagnetic singlet electronic state. Reducible oxides such as TiO2 present small band gaps, small oxygen vacancy formation energy and electron localization of the reduction electrons in the cations, decreasing their oxidation state and presenting open-shell electronic states. Intermediate or ambivalent behavior is found for ZrO2, HfO2, β-Ga2O3, ZnO and SnO2.