Hybrid exchange-correlation energy functionals for strongly correlated electrons: Applications to transition-metal monoxides

For the treatment of strongly correlated electrons, the corresponding Hartree-Fock exchange energy is used instead of the local density approximation (LDA) or generalized gradient approximation (GGA) functional, as suggested recently [P. Nov\'ak et al., Phys. Status Solidi B 243, 563 (2006)]. If this is done only inside the atomic spheres, using an augmented plane wave scheme, a significant simplification and reduction of computational cost is achieved with respect to the usual but costly implementation of the Hartree-Fock formalism in solids. Starting from this, we construct exchange-correlation energy functionals of the hybrid form like B3PW91, PBE0, etc. These functionals are tested on the transition-metal monoxides MnO, FeO, CoO, and NiO, and the results are compared with the LDA, GGA, $\mathrm{LDA}+U$, and experimental ones. The results show that the proposed method, which does not contain any system-dependent input parameter, gives results comparable or superior to the ones obtained with $\mathrm{LDA}+U$ which is designed to improve significantly over the LDA and GGA results for systems containing strongly correlated electrons. The computational efficiency, similar to the $\mathrm{LDA}+U$ one, and accuracy of the proposed method show that it represents a very good alternative to $\mathrm{LDA}+U$.