Numerical stability and efficiency of response property calculations in density functional theory

TL;DR

This paper analyzes the numerical stability of response property calculations in density functional theory and introduces a new, more stable and efficient method using a Schur complement approach, reducing computational costs.

Contribution

It presents a unified framework for gauge choices in response calculations and proposes a novel Schur complement method to enhance stability and efficiency.

Findings

Achieved around 40% reduction in Hamiltonian applications for complex materials.

Demonstrated improved numerical stability over existing gauge choices.

Validated the new method on transition metal alloy compounds.

Abstract

Response calculations in density functional theory aim at computing the change in ground-state density induced by an external perturbation. At finite temperature these are usually performed by computing variations of orbitals, which involve the iterative solution of potentially badly-conditioned linear systems, the Sternheimer equations. Since many sets of variations of orbitals yield the same variation of density matrix this involves a choice of gauge. Taking a numerical analysis point of view we present the various gauge choices proposed in the literature in a common framework and study their stability. Beyond existing methods we propose a new approach, based on a Schur complement using extra orbitals from the self-consistent-field calculations, to improve the stability and efficiency of the iterative solution of Sternheimer equations. We show the success of this strategy on nontrivial examples of practical interest, such as Heusler transition metal alloy compounds, where savings of around 40% in the number of required cost-determining Hamiltonian applications have been achieved.