On preconditioning the self-consistent field iteration in real-space Density Functional Theory

TL;DR

This paper introduces a real-space approach for Fourier-space preconditioners in Density Functional Theory, improving computational efficiency and accuracy in self-consistent field iterations by solving sparse Helmholtz systems.

Contribution

It develops a novel real-space formulation for Fourier-space preconditioners, enabling efficient and accurate acceleration of DFT calculations with fewer computational steps.

Findings

Real-space method matches Fourier-space preconditioner accuracy.

Requires solving only one sparse Helmholtz system per iteration.

Significantly accelerates self-consistent field convergence.

Abstract

We present a real-space formulation for isotropic Fourier-space preconditioners used to accelerate the self-consistent field iteration in Density Functional Theory calculations. Specifically, after approximating the preconditioner in Fourier space using a rational function, we express its real-space application in terms of the solution of sparse Helmholtz-type systems. Using the truncated-Kerker and Resta preconditioners as representative examples, we show that the proposed real-space method is both accurate and efficient, requiring the solution of a single linear system, while accelerating self-consistency to the same extent as its exact Fourier-space counterpart.