DFT + U study of defects in bulk rutile TiO2

We present a systematic study of electronic gap states in defected titania using our implementation of the Hubbard-U approximation in the grid-based projector-augmented wave density functional theory code, GPAW. The defects considered are Ti interstitials, O vacancies, and H dopants in the rutile phase of bulk titanium dioxide. We find that by applying a sufficiently large value for the Hubbard-U parameter of the Ti 3d states, the excess electrons localize spatially at the Ti sites and appear as states in the band gap. At U=2.5 eV, the position in energy of these gap states are in fair agreement with the experimental observations. In calculations with several excess electrons and U=2.5 eV, all of these end up in gap states that are spatially localized around specific Ti atoms, thus effectively creating one Ti(3+) ion per excess electron. An important result of this investigation is that regardless of which structural defect is the origin of the gap states, at U=2.5 eV, these states are found to have their mean energies within a few hundredths of an eV from 0.94 eV below the conduction band minimum.