Fully relativistic ab initio extended Hubbard interactions: energy gaps, force, and electron-phonon couplings

Ab initio computational methods that incorporate both self-consistent on-site and inter-site Hubbard corrections have been shown to treat local and non-local Coulomb interactions on an equal footing. The Hubbard parameters needed for these corrections are obtained directly from a Hartree-Fock-based formalism within the self-consistent field procedure. This approach enables efficient calculations with only a moderate increase in computational cost compared to other correction schemes. Meanwhile, accounting for the extended Hubbard interaction effectively alleviates the well-known self-interaction error of exchange-correlation functionals such as the local density approximation and generalized gradient approximation. As a result, both electronic structures and their corresponding lattice dynamical properties can be computed accurately. Furthermore, when extended to a noncollinear form that includes spin-orbit coupling, this approach has demonstrated GW-level accuracy for materials like topological insulators. We also confirmed that Hubbard corrections can make a substantial contribution to phenomena governed by electron-phonon interaction, including carrier mobility and optical absorption.