<i>Ab initio</i> calculation of ionic oxidation states in metal oxides

The concept of the oxidation state of ions is intuitive and useful for determining or predicting the stability, metallicity, and/or magnetism of metal oxides (as well as other materials). Determining the oxidation state of an ion is almost always a straightforward excercise in the use of the periodic table together with atomic electronegativities. However, calculating the charge state of an atom in a crystal, i.e., assigning electrons to atoms, is a notoriously difficult and ill-defined problem. After a brief discussion of some of the most popular approaches used for assigning electrons to atoms and their relative merits, we discuss the relation of oxidation state to the band structure, band occupancy and band symmetry in metal oxides and what is required and what it means to compute oxidation states from the band structure. Examples of insulating and metallic bulk metal oxides as well as superlattices and interfacial systems will illustrate the ideas.