First-principles embedded-cluster calculations of the neutral and charged oxygen vacancy at the rutile TiO2(110) surface

We perform full-potential screened-hybrid density-functional theory calculations to compare the thermodynamic stability of neutral and charged states of the surface oxygen vacancy at the rutile TiO2(110) surface. Solidstate (QM/MM) embedded-cluster calculations are employed to account for the strong TiO2 polarization response to the charged defect states. Similarly to the situation for the bulk O vacancy, the +2 charge state V-O(2+) is found to be energetically by far the most stable. Only for Fermi-level positions very close to the conduction band, small polarons may at best be trapped by the charged vacancy. The large decrease in the V-O(2+) formation energy with decreasing Fermi-level position indicates strongly enhanced surfaceOvacancy concentrations for p-doped samples.