Calculations were made of the electronic structure of a model of TiO2 which contained oxygen vacancies. The model used the full tight-binding model of Vos. A screened Coulomb potential and a soft positive core were used to describe the oxygen vacancy. The electronic density of states was studied as a function of the thickness of a layer of TiO2 and of the number of oxygen vacancies up to 10% vacancies. It was shown that the structure of the density of states in the neighborhood of the conduction-band edge could not be even approximately described by a crystal-field calculation involving only a few metal ions near to the vacancy. The evolution of the density of states as the layer was made thicker was described.

Electronic Structure of Multiple Vacancies in Rutile TiO2 by the Equation-Of-Motion Method. Halley, J.W., Michalewicz, M.T., Tit, N.: Physical Review B, 1990, 41[14], 10165-70