On the calculation of the stress tensor in real-space Kohn-Sham Density Functional Theory

TL;DR

This paper introduces a new, accurate, and efficient real-space formulation for calculating the stress tensor in Kohn-Sham DFT, improving accuracy and convergence for various simulation types.

Contribution

The authors derive a linear-scaling, real-space stress tensor formulation compatible with arbitrary unit cell symmetry and improve accuracy of stress calculations by up to three orders of magnitude.

Findings

High convergence rates with respect to spatial discretization

Excellent agreement with planewave reference results

Significant accuracy improvements in stress computation

Abstract

We present an accurate and efficient formulation of the stress tensor for real-space Kohn-Sham Density Functional Theory (DFT) calculations. Specifically, while employing a local formulation of the electrostatics, we derive a linear-scaling expression for the stress tensor that is applicable to simulations with unit cells of arbitrary symmetry, semilocal exchange-correlation functionals, and Brillouin zone integration. In particular, we rewrite the contributions arising from the self energy and the nonlocal pseudopotential energy to make them amenable to the real-space finite-difference discretization, achieving up to three orders of magnitude improvement in the accuracy of the computed stresses. Using examples representative of static and dynamic calculations, we verify the accuracy and efficiency of the proposed formulation. In particular, we demonstrate high rates of convergence with spatial discretization, consistency between the computed energy and stress tensor, and very good agreement with reference planewave results.