Higher-order finite-difference formulation of periodic Orbital-free Density Functional Theory

TL;DR

This paper introduces a real-space, higher-order finite-difference approach to periodic Orbital-free Density Functional Theory, enabling scalable, accurate large-scale simulations with linear scaling and rapid convergence.

Contribution

It develops a novel real-space, higher-order finite-difference formulation for OF-DFT with a self-consistent fixed-point method and parallel implementation for large-scale computations.

Findings

Higher-order finite differences improve convergence rates.

Fixed-point iteration converges rapidly and benefits from extrapolation.

Results agree with plane-wave methods for benchmark examples.

Abstract

We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we develop a generalized framework for performing OF-DFT simulations with different variants of the electronic kinetic energy. In particular, we propose a self-consistent field (SCF) type fixed-point method for calculations involving linear-response kinetic energy functionals. In this framework, evaluation of both the electronic ground-state as well as forces on the nuclei are amenable to computations that scale linearly with the number of atoms. We develop a parallel implementation of this formulation using the finite-difference discretization. We demonstrate that higher-order finite-differences can achieve relatively large convergence rates with respect to mesh-size in both the energies and forces. Additionally, we establish that the fixed-point iteration converges rapidly, and that it can be further accelerated using extrapolation techniques like Anderson's mixing. We validate the accuracy of the results by comparing the energies and forces with plane-wave methods for selected examples, including the vacancy formation energy in Aluminum. Overall, the suitability of the proposed formulation for scalable high performance computing makes it an attractive choice for large-scale OF-DFT calculations consisting of thousands of atoms.