On the calculation of phonons in real-space density functional theory

TL;DR

This paper introduces a precise and efficient real-space DFT approach for calculating phonons, applicable to diverse materials and system dimensions, verified by accurate phonon dispersion and density of states results.

Contribution

The authors develop a real-space finite-difference formulation for phonon calculations in DFT, compatible with both insulating and metallic systems of any dimensionality.

Findings

Accurate phonon dispersion curves matching planewave results

Effective for both bulk and semi-infinite systems

Applicable to orthogonal and non-orthogonal cells

Abstract

We present an accurate and efficient formulation for the calculation of phonons in real-space Kohn-Sham density functional theory. Specifically, employing a local exchange-correlation functional, norm-conserving pseudopotential in the Kleinman-Bylander representation, and local form for the electrostatics, we derive expressions for the dynamical matrix and associated Sternheimer equation that are particularly amenable to the real-space finite-difference method, within the framework of density functional perturbation theory. In particular, the formulation is applicable to insulating as well as metallic systems of any dimensionality, enabling the efficient and accurate treatment of semi-infinite and bulk systems alike, for both orthogonal and non-orthogonal cells. We also develop an implementation of the proposed formulation within the high-order finite-difference method. Through representative examples, we verify the accuracy of the computed phonon dispersion curves and density of states, demonstrating excellent agreement with established planewave results.