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 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. Program summary Program title: SPARC Catalogue identifier: AFBR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBR_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: GNU GPL v3 No. of lines in distributed program, including test data, etc.: 93822 No. of bytes in distributed program, including test data, etc.: 1386659 Distribution format: tar.gz Programming language: C/C++. Computer: Any system with C/C++ compiler. Operating system: Linux. RAM: Problem dependent. Ranges from 80 GB to 800 GB for a system with 2500 electrons. Classification: 7.3. External routines: PETSc 3.5.3 (http://www.mcs.anl.gov/petsc), MKL 11.2 (https://software.intel.com/en-us/intel-mkl), and MVAPICH2 2.1 (http://mvapich.cse.ohio-state.edu/). Does the new version supersede the previous version?: Yes Nature of problem: Calculation of the static and dynamic properties of isolated and extended systems in the framework of KohnSham Density Functional Theory (DFT). Solution method: High-order finite-difference discretization. Local reformulation of the electrostatics in terms of the electrostatic potential and pseudocharge densities. Application of Bloch-periodic and zero-Dirichlet boundary conditions on the orbitals in the direction of periodicity and vacuum, respectively. Application of periodic and Dirichlet boundary conditions on the electrostatic potential in the direction of periodicity and vacuum, respectively. Integration over the Brillouin zone for extended systems using the MonkhorstPack grid. Calculation of the electronic ground-state using the Chebyshev polynomial filtered self-consistent field iteration in conjunction with Anderson based extrapolation/mixing schemes. Reformulation of the non-local component of the force. Geometry optimization using the PolakRibiere variant of non-linear conjugate gradients with secant line search. NVE molecular dynamics using the leapfrog method. Parallelization via domain decomposition and over Brillouin zone integration. Reasons for new version: To enable the study of extended systems like crystals, slabs, and wires using SPARC. Summary of revisions: Incorporated the ability to study the static and dynamic properties of crystals, slabs, and wires. Restrictions: System size less than similar to 4000 electrons. Local Density Approximation (LDA). Troullier-Martins pseudopotentials without relativistic or non-linear core corrections. Domain has to be cuboidal. Running time: Problem dependent. Timing results for selected examples provided in the paper. (C) 2017 Elsevier B.V. All rights reserved.