Equation-of-motion method for the study of defects in insulators: Application to a simple model ofTiO2

We illustrate the advantages of an equation of motion technique for calculation of the electronic structure of oxides. The technique is described in some detail and applied to a simplified version of a tight-binding model of ${\mathrm{TiO}}_2$ due to Vos. We can determine the density of states of systems with arbitrary numbers of oxygen vacancies in this model with very modest expenditures of computer time. We discuss some physical implications of the results.