The Shirley reduced basis: a reduced order model for plane-wave DFT

TL;DR

The Shirley reduced basis (SRB) offers a k-independent, efficient reduced order model for plane-wave DFT calculations, significantly reducing computational costs while maintaining accuracy for complex electronic structures.

Contribution

We introduce a novel k-independent transformation of the DFT eigenproblem using the SRB, enabling faster calculations with minimal loss of accuracy.

Findings

Reduces computational cost by over 5x for reduced systems

Improves performance by 1.67x in molecular dynamics contexts

Converges to plane-wave solutions with proper orthogonal decomposition

Abstract

The Shirley reduced basis (SRB) represents the periodic parts of Bloch functions as linear combi- nations of eigenvectors taken from a coarse sample of the Brillouin zone, orthogonalized and reduced through proper orthogonal decomposition. We describe a novel transformation of the self-consistent density functional theory eigenproblem from a plane-wave basis with ultra-soft pseudopotentials to the SRB that is independent of the k-point. In particular, the number of operations over the space of plane-waves is independent of the number of k-points. The parameter space of the transformation is explored and suitable defaults are proposed. The SRB is shown to converge to the plane-wave solution. For reduced dimensional systems, reductions in computational cost, compared to the plane-wave calculations, exceed 5x. Performance on bulk systems improves by 1.67x in molecular dynamics-like contexts. This robust technique is well-suited to efficient study of systems with strin- gent requirements on numerical accuracy related to subtle details in the electronic band structure, such as topological insulators, Dirac semi-metals, metal surfaces and nanostructures, and charge transfer at interfaces with any of these systems. The techniques used to achieve a k-independent transformation could be applied to other computationally expensive matrix elements, such as those found in density functional perturbation theory and many-body perturbation theory.