A systematic study of polarons due to oxygen vacancy formation at the rutile TiO ₂(110) surface by GGA+U and HSE06 methods

The polaronic nature of excess electrons accompanying an oxygen vacancy in a TiO ₂(110) surface has been studied by several theoretical approaches. According to previous studies, DFT+U and hybrid functional methods predict different sites of localization of the polarons. In this paper, we conducted a thorough comparison of the results obtained by GGA+U (generalized gradient approximation+HubbardU) and HSE06 (Heyd-Scuseria-Ernzerhof hybrid functional) approximations. Considering initial symmetry breaking in the geometry optimization process, we show that regardless of the approximations used, electrons localize at two particular subsurface Ti sites in a state with mixed d _x2-y2/d _z2 character in the global coordinate frame with a spatial extent of the order of 7 Å. The lowest state of the polarons is a singlet, but the triplet is only about 0.1meV higher in energy. Our results agree with previous experiments and calculations, wherever available. We stress that the hybrid functional has been first applied on this surface with a realistic coverage of oxygen vacancies corresponding to the experimental situation (∼12.5%).