The effect of electron localization on the electronic structure and migration barrier of oxygen vacancies in rutile

By applying the on-site Coulomb interaction (Hubbard term U) to the Ti d orbital, the influence of electron localization on the electronic structure as well as the transport of oxygen vacancies (V_O) in rutile was investigated. With U = 4.5 eV, the positions of defect states in the bandgap were correctly reproduced. The unbonded electrons generated by taking out one neutral oxygen atom are spin parallel and mainly localized on the Ti atoms near V_O, giving rise to a magnetic moment of 2 μ_B, in agreement with the experimental finding. With regard to the migration barrier of V_O, surprisingly, we found that U = 4.5 eV only changed the value of the energy barrier by ±0.15 eV, depending on the diffusion path. The most probable diffusion path (along ) is the same as that calculated by using the traditional GGA functional. To validate the GGA + U method itself, a hybrid functional with a smaller supercell was used, and the trend of the more probable diffusion path was not changed. In this regard, the traditional GGA functional might still be reliable in the study of intrinsic-defect transportation in rutile. Analyzing the atomic distortion and density of states of the transition states for different diffusion paths, we found that the anisotropy of the diffusion could be rationalized according to the various atomic relaxations and the different positions of the valence bands relative to the Fermi level of the transition states.