Ab initio electronic structure calculation of oxygen vacancies in rutile titanium dioxide

The electronic structure of rutile TiO_{2 - x} is studied using first-principles density functional theory (DFT) calculations. Nonstoichiometry in rutile TiO₂ due to defects in the form of oxygen vacancies leads to a considerable change in the electronic structure. In this paper, we calculate the band structure, density of states, and orbital energy distribution in a reduced (oxygen deficient) TiO_{2 - x} for different concentrations of oxygen vacancies (x). Energy levels are found to appear inside the forbidden energy region either as an isolated form of bands at different energy levels or merged with the conduction band depending on the value of x and the size of the super cells.