Density functional theory and a projector-augmented wave method were applied to study defected TiO2(110) surface. Three types of a single oxygen vacancy created in surface and in sub-surface layers were examined. The variation of the vacancy formation energy and the changes in structural and electronic properties of oxygen-deficient rutile surface were investigated as a function of the vacancy depth. It was found that the formation of bridging and sub-bridging O vacancies in odd layers of the slab was favored over even layers.

Energetics of Oxygen Vacancies at Rutile TiO2(110) Surface. Pabisiak, T., Kiejna, A.: Solid State Communications, 2007, 144[7-8], 324-8