The screened pseudo-charge repulsive potential in perturbed orbitals for band calculations by DFT+U

Abstract

The conventional linear response overestimates the U in DFT+U calculations for solids with fully occupied orbitals. Here, we demonstrate that the challenge arises from the incomplete cancellation of the electron–electron Coulomb repulsion energy under external perturbation. We applied the second charge response, denoted as the “pseudo-charge” model, to offset such residue effects. Counteracting between these two charge response-induced Coulomb potentials, the U parameters are self-consistently obtained by fulfilling the conditions for minimizing the non-Koopmans energy. Moreover, the pseudo-charge-induced repulsive potential shows a screening behavior related to the orbital occupation and is potentially in compliance with the screened exact exchange–correlation of electrons. The resultant U parameters are self-consistent solutions for improved band structure calculations by the DFT+U method. This work extends the validity of the linear response method to both partially and fully occupied orbitals and gives a reference for estimating the Hubbard U parameter prior to other advanced methods. The U parameters were determined in a transferability test using both PBE and hybrid density functional methods, and the results showed that this method is independent of the functional. The electronic structures determined from the hybrid-DFT+U^hybrid approach are provided. Comparisons are also made with the recently developed self-consistent hybrid-DFT+U_w method.