Hubbard-corrected density functional perturbation theory with ultrasoft pseudopotentials

TL;DR

This paper introduces a formalism for density functional perturbation theory (DFPT) based on DFT+U with ultrasoft pseudopotentials, enabling efficient phonon and dielectric calculations for systems with localized electrons.

Contribution

The authors develop a new DFPT formalism compatible with DFT+U and ultrasoft pseudopotentials, allowing accurate vibrational property calculations for correlated and metallic systems.

Findings

Successfully applied to CoO and LiCoO₂

Accurately captures vibrational properties of localized electrons

Avoids computationally intensive frozen-phonon calculations

Abstract

We present in full detail a newly developed formalism enabling density functional perturbation theory (DFPT) calculations from a DFT+$U$ ground state. The implementation includes ultrasoft pseudopotentials and is valid for both insulating and metallic systems. It aims at fully exploiting the versatility of DFPT combined with the low-cost DFT+$U$ functional. This allows to avoid computationally intensive frozen-phonon calculations when DFT+$U$ is used to eliminate the residual electronic self-interaction from approximate functionals and to capture the localization of valence electrons e.g. on $d$ or $f$ states. In this way, the effects of electronic localization (possibly due to correlations) are consistently taken into account in the calculation of specific phonon modes, Born effective charges, dielectric tensors and in quantities requiring well converged sums over many phonon frequencies, as phonon density of states and free energies. The new computational tool is applied to two representative systems, namely CoO, a prototypical transition metal monoxide and LiCoO$_2$, a material employed for the cathode of Li-ion batteries. The results show the effectiveness of our formalism to capture in a quantitatively reliable way the vibrational properties of systems with localized valence electrons.