Electronic structure of multiple vacancies in rutileTiO2by the equation-of-motion method

We report calculations of the electronic structure of a model of ${\mathrm{TiO}}_2$ which contains oxygen vacancies. The model uses the full tight-binding model of Vos. We use a screened Coulomb potential and a soft positive core to describe the oxygen vacancy. We study the electronic density of states as a function of the thickness of a layer of ${\mathrm{TiO}}_2$ and of the number of oxygen vacancies up to 10% vacancies. We show that the structure of the density of states in the neighborhood of the conduction-band edge cannot be even approximately described by a crystal-field calculation involving only a few metal ions near the vacancy. The evolution of the density of states as the layer is made thicker is described.