A self-consistent site-dependent DFT+U approach for defects in transition metal oxides

We propose a self-consistent site-dependent (SCSD) DFT+U approach for calculations of defects in transition-metal oxides. Defect formation in these materials induces local perturbations in the chemical environment of Hubbard sites around the defect that may not be properly described by applying a global U value on all sites as done in conventional DFT+U.
Here, U is treated as an intrinsic response property of the material and computed from first principles using density-functional perturbation theory. SCSD U values are obtained starting from a DFT ground state by an iteration of perturbing all inequivalent Hubbard sites followed by geometry relaxation with the determined U values until convergence of the geometry and U. Changes in U due to excess charge localization and lattice relaxation in defective structures are hence properly accounted for.
After discussing the approach, we highlight some results, showing that U values depend on the distance of the Hubbard site from the defect, its coordination number, its oxidation state, and on the magnetic properties of the material. This site-dependence is particularly important in the case of semiconductors, where filled localized defect states may form in the band gap, and strongly influences all properties related to defect energetics.