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

TL;DR

This paper extends a density-functional perturbation theory approach to compute Hubbard parameters, including inter-site V, for ultrasoft and projector-augmented wave methods, improving efficiency and applicability to metals.

Contribution

It generalizes the DFPT-based Hubbard parameter calculation to ultrasoft and PAW formulations and includes inter-site V, enabling more accurate and efficient electronic structure calculations.

Findings

DFPT accurately computes Hubbard U and V parameters.

The method is validated against real-space linear response.

Application to LiMnPO4 demonstrates improved structural and energetic predictions.

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 on-site Hubbard $U$ to also compute the inter-site Hubbard $V$. DFPT allows 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 Li$_x$MnPO$_4$ (x=0,1) and the subtle energetics of Li intercalation.