SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems

TL;DR

SPARC introduces a finite-difference, parallel implementation of Density Functional Theory that achieves high accuracy, efficient convergence, and scalable performance for extended systems, offering a competitive alternative to plane-wave methods.

Contribution

This work develops a novel finite-difference formulation and parallel implementation of DFT tailored for extended systems, demonstrating high accuracy and scalability.

Findings

High convergence rates in energy and forces compared to plane-wave results

Exponential convergence with respect to vacuum size for slabs and wires

Negligible 'egg-box' effect and drift in molecular dynamics

Abstract

As the second component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory (DFT) for extended systems. Specifically, employing a local formulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local force component, we develop a finite-difference framework wherein both the energy and atomic forces can be efficiently calculated to within desired accuracies in DFT. We demonstrate using a wide variety of materials systems that SPARC achieves high convergence rates in energy and forces with respect to spatial discretization to reference plane-wave result; exponential convergence in energies and forces with respect to vacuum size for slabs and wires; energies and forces that are consistent and display negligible `egg-box' effect; accurate properties of crystals, slabs, and wires; and negligible drift in molecular dynamics simulations. We also demonstrate that the weak and strong scaling behavior of SPARC is similar to well-established and optimized plane-wave implementations for systems consisting up to thousands of electrons, but with a significantly reduced prefactor. Overall, SPARC represents an attractive alternative to plane-wave codes for performing DFT simulations of extended systems.