Mapping of Extended Hubbard Interactions to GW Self-Energy

We present a mapping from the extended Hubbard interactions to the local and non-local static self-energy of the GW approximation. Thanks to the mapping and the proper treatment of position-dependent screening of charge for the Hubbard interactions, we show that the recently developed self-consistent pseudohybrid functional method for the on-site (U) and inter-site (V) Hubbard interactions within the density functional theory (DFT+U+V) is an efficient and accurate method for descriptions of various physical properties of solids. We provide several examples proving the relevance of this method for descriptions of dielectric screenings of solids, (i) quasiparticle band gaps, effective mass, and absorption spectra of covalent semiconductors, silicon (3 dimensional) and monolayer black phosphorus (2 dimensional), and (ii) optical phonon frequency of a correlated insulator, NiO.