Distribution of Ti3+ Surface Sites in Reduced TiO2

We describe a DFT+U study of the (110) rutile surface with oxygen vacancies (O-v's)(2) Oxygen vacancies leave behind two excess unpaired electrons per O-v, leading formally to the formation of two Ti3+ ions. We investigate the location of the Ti3+ ions within the first three surface layers. In total, we obtained 49 unique solutions of possible Ti3+ pairs, to examine the stability of all Ti type (e.g., five-coordinated surface Ti, six-coordinated surface Ti, subsurface sites etc). Our results show that subsurface sites are preferred but that many configurations are close in energy within up to 0.3-0.4 eV of each other. In contrast to findings in previous work, we show that sites directly adjacent to the O-v's are unstable. Analysis of out results show that the two Ti3+ ions within a pair behave independently of each other, as there are little electronic interactions between the excess electrons associated with these sites. We also examined the migration of Ti3+ sites from the surface into the bulk and find the surface locations to be preferred by similar to 0.5 eV relative to the bulk. Our systematic results provide a comprehensive picture of excess electrons that indicates that they are not trapped or localized at specific sites but are distributed across several sites due to nearly degenerate Ti3(+) states.