Defects on ${\mathrm{TiO}}_2$ (110) surfaces

We present self-consistent ab initio total-energy calculations on ${\mathrm{TiO}}_2$ (110) surfaces for which the atomic geometry has been relaxed to equilibrium. For stoichiometric supercells we find no surface states in the bulk band gap, in accord with experiment. Oxygen vacancies on the surface give rise to Ti 3d-like surface states at the edge of the bulk conduction band. The relaxations of the atoms at the surface were found to be substantial, and those induced by a vacancy were localized in its vicinity. Bulk vacancies introduce states about 0.3 eV below the edge of the bulk conduction band.