Calculation of point defects in rutile TiO2 by the screened-exchange hybrid functional

The formation energies of the oxygen vacancy and titanium interstitial in rutile TiO2 were calculated by the screened-exchange (sX) hybrid density functional method, which gives a band gap of 3.1 eV, close to the experimental value. The oxygen vacancy gives rise to a gap state lying 0.7 eV below the conduction band edge, whose charge density is localized around the two of three Ti atoms next to the vacancy. The Ti interstitial (Ti-int) generates four defect states in the gap, whose unpaired electrons lie on the interstitial and the adjacent Ti 3d orbitals. The formation energy for the neutral oxygen vacancy is 1.9 eV for the O-poor chemical potential. The neutral Ti interstitial has a lower formation energy than the O vacancy under O-poor conditions. This indicates that both the O vacancy and Tiint are relevant for oxygen deficiency in rutile TiO2 but the O vacancy will dominate under O-rich conditions. This resolves questions about defect localization and defect predominance in the literature.