Ab initioevaluation of Coulomb and exchange parameters forDFT+Ucalculations

Abstract

Conventional density functional theory (DFT) fails for materials with strongly correlated electrons, such as late transition metal oxides. Large errors in the intra-atomic Coulomb and exchange interactions are the source of this failure. The $\mathrm{DFT}+\mathrm{U}$ method has provided a means, through empirical parameters, to correct these errors. Here, we present a systematic ab initio approach in evaluating the intra-atomic Coulomb and exchange terms, $U$ and $J$, respectively, in order to make the $\mathrm{DFT}+\mathrm{U}$ method a fully first-principles technique. The method is based on a relationship between these terms and the Coulomb and exchange integrals evaluated in the basis of unrestricted Hartree-Fock molecular orbitals that represent localized states of the extended system. We used this ab initio scheme to evaluate $U$ and $J$ for chromia $({\mathrm{Cr}}_{2}{\mathrm{O}}_{3})$. The resulting values are somewhat higher than those determined earlier either empirically or in constrained DFT calculations but have the advantage of originating from an ab initio theory containing exact exchange. Subsequent $\mathrm{DFT}+\mathrm{U}$ calculations on chromia using the ab initio derived $U$ and $J$ yield properties consistent with experiment, unlike conventional DFT. Overall, the technique developed and tested in this work holds promise in enabling accurate and fully predictive $\mathrm{DFT}+\mathrm{U}$ calculations of strongly correlated electron materials.