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

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.

33 pages, 12 figures, 5 tables

References in corpus (5)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Recent progress with large-scale ab initio calculations: the CONQUEST code
• Parallel Self-Consistent-Field Calculations via Chebyshev-Filtered Subspace Acceleration
• Periodic Pulay method for robust and efficient convergence acceleration of self-consistent field iterations
• Augmented Lagrangian formulation of Orbital-Free Density Functional Theory

Cited by in corpus (40)

• DFT-FE -- A massively parallel adaptive finite-element code for large-scale density functional theory calculations
• SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems
• Design and Analysis of Machine Learning Exchange-Correlation Functionals via Rotationally Invariant Convolutional Descriptors
• DFT-FE 1.0: A massively parallel hybrid CPU-GPU density functional theory code using finite-element discretization
• SQDFT: Spectral Quadrature method for large-scale parallel $\mathcal{O}(N)$ Kohn-Sham calculations at high temperature
• Cyclic Density Functional Theory : A route to the first principles simulation of bending in nanostructures
• Symmetry-adapted real-space density functional theory for cylindrical geometries: application to large X (X=C, Si, Ge, Sn) nanotubes
• Chebyshev polynomial filtered subspace iteration in the Discontinuous Galerkin method for large-scale electronic structure calculations
• Nonlocal Kinetic Energy Density Functionals for Isolated Systems via Local Density Approximation Kernels
• On nearsightedness in metallic systems for $\mathcal{O}(N)$ Density Functional Theory calculations: A case study on Aluminum
• Electronic structure study of screw dislocation core energetics in Aluminum and core energetics informed forces in a dislocation aggregate
• On preconditioning the self-consistent field iteration in real-space Density Functional Theory
• Strain engineering of Janus transition metal dichalcogenide nanotubes: An ab intio study
• On the calculation of the stress tensor in real-space Kohn-Sham Density Functional Theory
• Ab initio framework for systems with helical symmetry: theory, numerical implementation and applications to torsional deformations in nanostructures
• Density functional theory method for twisted geometries with application to torsional deformations in group-IV nanotubes
• GPU acceleration of local and semilocal density functional calculations in the SPARC electronic structure code
• Real-space formulation of the stress tensor for $\mathcal{O}(N)$ density functional theory: application to high temperature calculations
• On real-space Density Functional Theory for non-orthogonal crystal systems: Kronecker product formulation of the kinetic energy operator
• Torsional strain engineering of transition metal dichalcogenide nanotubes: An ab initio study
• Implementation of Perdew-Zunger self-interaction correction in real space using Fermi-Löwdin orbitals
• On the bending of rectangular atomic monolayers along different directions: an ab initio study
• Ab-initio investigation of finite size effects in rutile titania nanoparticles with semilocal and nonlocal density functionals
• Torsional moduli of transition metal dichalcogenide nanotubes from first principles
• The phase stability of large-size nanoparticle alloy catalysts at ab initio quality using a nearsighted force-training approach
• Elastic properties of Janus transition metal dichalcogenide nanotubes from first principles
• Solving the electronic structure problem for over 100,000 atoms in real-space
• Ab initio study on the electromechanical response of Janus transition metal dihalide nanotubes
• Real-space density kernel method for Kohn-Sham density functional theory calculations at high temperature
• SPARC: Simulation Package for Ab-initio Real-space Calculations
• Assessing the source of error in the Thomas-Fermi-von Weizsäcker density functional
• Subspace recursive Fermi-operator expansion strategies for large-scale DFT eigenvalue problems on HPC architectures
• M-SPARC: MATLAB-Simulation Package for Ab-initio Real-space Calculations
• Partition of unity finite element method for quantum mechanical materials calculations
• Finite-element methods for noncollinear magnetism and spin-orbit coupling in real-space pseudopotential density functional theory
• Chemical bonding in large systems using projected population analysis from real-space density functional theory calculations
• Symmetry-Adapted Tight-Binding Electronic Structure Analysis of Carbon Nanotubes with Defects, Kinks, Twist, and Stretch
• Machine learning based prediction of the electronic structure of quasi-one-dimensional materials under strain
• Transversal flexoelectric coefficients for fifty select atomic monolayers from first principles
• Generalization of Stoney's equation for flexoelectric thin films on elastic substrates