Coarse-graining Kohn-Sham Density Functional Theory

TL;DR

This paper introduces a real-space, coarse-grained approach to Kohn-Sham Density Functional Theory that accelerates defect analysis in materials while maintaining high accuracy, through a linear-scaling method and adaptive spatial approximation.

Contribution

It develops a novel coarse-graining scheme combining linear-scaling and spatial approximation for efficient DFT calculations of material defects.

Findings

Significant speed-up in defect analysis

Maintains accuracy comparable to traditional methods

Convergent solutions with respect to spatial approximation

Abstract

We present a real-space formulation for coarse-graining Kohn-Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps. First, we develop a linear-scaling method that enables the direct evaluation of the electron density without the need to evaluate individual orbitals. We achieve this by performing Gauss quadrature over the spectrum of the linearized Hamiltonian operator appearing in each iteration of the self-consistent field method. Building on the linear-scaling method, we introduce a spatial approximation scheme resulting in a coarse-grained Density Functional Theory. The spatial approximation is adapted so as to furnish fine resolution where necessary and to coarsen elsewhere. This coarse-graining step enables the analysis of defects at a fraction of the original computational cost, without any significant loss of accuracy. Furthermore, we show that the coarse-grained solutions are convergent with respect to the spatial approximation. We illustrate the scope, versatility, efficiency and accuracy of the scheme by means of selected examples.