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). Oxygen vacancies leave behind two excess unpaired electrons per O_v, leading formally to the formation of two Ti ³⁺ 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 types (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 our results shows 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 ∼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.