Self-consistent Hubbard parameters from density-functional perturbation theory in the ultrasoft and projector-augmented wave formulations

Abstract

The self-consistent evaluation of Hubbard parameters using linear-response theory is crucial for quantitatively predictive calculations based on Hubbard-corrected density-functional theory. Here, we extend a recently introduced approach based on density-functional perturbation theory (DFPT) for the calculation of the onsite Hubbard $U$ to also compute the intersite Hubbard $V$. DFPT allows us to reduce significantly computational costs, improve numerical accuracy, and fully automate the calculation of the Hubbard parameters by recasting the linear response of a localized perturbation into an array of monochromatic perturbations that can be calculated in the primitive cell. In addition, here we generalize the entire formalism from norm-conserving to ultrasoft and projector-augmented wave formulations, and to metallic ground states. After benchmarking DFPT against the conventional real-space Hubbard linear response in a supercell, we demonstrate the effectiveness of the present extended Hubbard formulation in determining the equilibrium crystal structure of ${\mathrm{Li}}_{x}\mathrm{Mn}{\mathrm{PO}}_{4}$ ($x=0,1$) and the subtle energetics of Li intercalation.