Electronic Structure of Partially Reduced Rutile TiO2(110) Surface: Where Are the Unpaired Electrons Located?

When an oxygen atom is removed from the surface of rutile TiO2(110), to make an oxygen vacancy, two unpaired electrons are left in the oxide. We perform density functional calculations with on-site repulsion (DFT + U) to find where these electrons are located. If U <= 2.5 eV, they are delocalized. If 3.0 <= U <= 6.0 eV, they are both localized on different Ti atoms, reducing them (formally) from Ti4+ to Ti3+. The energy of vacancy formation depends on the location of this pair of reduced Ti atoms. Three kinds of states have low energies that are very close to each other. In these states, the electrons are located on the five-coordinated Ti atoms at the surface and on Ti atoms below the surface. Previous calculations proposed that the unpaired electrons reduced two Ti atoms located near the vacancy. We find that this state has higher energy than all other states examined here.