  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 O vacancy gives rise to a gap state lying 0.7 eV below the
conduction band edge, whose charge density is localised around the two of three
Ti atoms next to the vacancy. The Ti interstitial 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 O vacancy is 1.9 eV for
the O-poor chemical potential, and similar to that of the neutral Ti
interstitial, and has a lower formation energy for Ti interstitial under O-rich
conditions. This indicates that both the O vacancy and Ti interstitial are
relevant for oxygen deficiency in rutile TiO2 but the O vacancy will dominate
under O-rich conditions. This resolves the questions about defect localisation
and defect predominance in the literature.
