The use of the “+U” correction in describing defect states at metal oxide surfaces: oxygen vacancies on CeO₂ and TiO₂, and Li-doping of MgO

There are many examples of defects in strongly-correlated metal oxides for which density functional theory predicts electronic structures that qualitatively disagree with experimental data. This behaviour arises from the self-interaction error inherent to standard density functionals, and is demonstrated by both p- and n-type systems where the defect state is a small polaron associated with host lattice atoms. An approximate correction is to describe the electron—electron interactions in the orbitals of interest within the DFT+U formalism. This gives improved descriptions for systems where the states of interest are well represented by atomic-like orbitals. The qualitative failure of standard DFT and corresponding improvement achieved with DFT+U is illustrated for cases where the defect state is primarily associated with localised cation f and d states (O vacancies in CeO₂ and TiO₂) and anion p states (Li-doped MgO).