First-principlesDFT+GWstudy of oxygen vacancies in rutileTiO2

We perform first-principles calculations of the quasiparticle defect states, charge transition levels, and formation energies of oxygen vacancies in rutile titanium dioxide. The calculations are done within the recently developed combined $\mathrm{DFT}+GW$ formalism, including the necessary electrostatic corrections for the supercells with charged defects. We find the oxygen vacancy to be a negative $U$ defect, where $U$ is the defect electron addition energy. For Fermi level values below $\ensuremath{\sim}2.8$ eV (relative to the valence-band maximum), we find the $+2$ charge state of the vacancy to be the most stable, while above $2.8$ eV we find that the neutral charge state is the most stable.