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

As the second component of SPARC (Simulation Package for Abinitio 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 iterat ion, and a reformulation of the non-local force component, we develop a finite-difference framework wherei n 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 energ y and forces with respect to spatial discretization to reference plane-wave result; exponential converge nce in energies and forces with respect to vacuum size for slabs and wires; energies and forces that are consis te t and display negligible ‘egg-box’ effect; accurate properties of crystals, slabs, and wires; and neglig ible drift in molecular dynamics simulations. We also demonstrate that the weak and strong scaling behavior o f SPARC is similar to well-established and optimized plane-wave implementations for systems consist i g 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.