A generalization of the popular DFT+U method based on the extended Hubbard model that includes on-site and inter-site electronic interactions is presented. The generalized corrective Hamiltonian is designed to study systems for which electrons are not completely localized on atomic states and hybridization between orbitals from different sites plays an important role. The application of the the extended functional to archetypal Mott-chargetransfer (NiO) and covalently bonded insulators (Si and GaAs) deminstrates its versatility and the possiblity to obtain a unifying and equally accurate description for a broad range of very diverse systems.
