SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters

TL;DR

SPARC introduces an accurate, efficient finite-difference DFT framework for isolated clusters, demonstrating exponential convergence, reliable forces, and scalable parallel performance, offering a competitive alternative to plane-wave methods.

Contribution

This work presents the first finite-difference formulation and parallel implementation of DFT specifically optimized for isolated clusters, with improved accuracy and efficiency.

Findings

Exponential convergence of energy and forces with domain size.

Systematic convergence to plane-wave results with mesh refinement.

Scalable parallel performance comparable to established plane-wave codes.

Abstract

As the first 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 isolated clusters. Specifically, utilizing a local reformulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local component of the force, we develop a framework using the finite-difference representation that enables the efficient evaluation of energies and atomic forces to within the desired accuracies in DFT. Through selected examples consisting of a variety of elements, we demonstrate that SPARC obtains exponential convergence in energy and forces with domain size; systematic convergence in the energy and forces with mesh-size to reference plane-wave result at comparably high rates; forces that are consistent with the energy, both free from any noticeable `egg-box' effect; and accurate ground-state properties including equilibrium geometries and vibrational spectra. In addition, for systems consisting up to thousands of electrons, SPARC displays weak and strong parallel scaling behavior that is similar to well-established and optimized plane-wave implementations, but with a significantly reduced prefactor. Overall, SPARC represents an attractive alternative to plane-wave codes for practical DFT simulations of isolated clusters.