On nearsightedness in metallic systems for $\mathcal{O}(N)$ Density Functional Theory calculations: A case study on Aluminum

Abstract

We investigate the locality of electronic interactions in aluminum as a function of smearing/electronic temperature in the context of $\mathcal{O}(N)$ Density Functional Theory calculations. Specifically, we determine the convergence in energy and atomic forces with truncation region size for smearing of $0.001-0.15$ Ha. We find exponential convergence accompanied by a rate that increases sub-linearly with smearing, with truncation region sizes of $48-64$ Bohr required to achieve chemical accuracy for typical smearing values of $0.001-0.01$ Ha. This translates to $\mathcal{O}(N)$ scaling for systems larger than $\mathcal{O}(1000)$ atoms.

12 pages, 5 Figures, 1 Table

References in corpus (5)

• Nearsightedness of Electronic Matter
• SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems
• SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters
• 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 (10)

• SQDFT: Spectral Quadrature method for large-scale parallel $\mathcal{O}(N)$ Kohn-Sham calculations at high temperature
• Symmetry-adapted real-space density functional theory for cylindrical geometries: application to large X (X=C, Si, Ge, Sn) nanotubes
• Equation of state of warm-dense boron nitride combining computation, modeling, and experiment
• Transversal flexoelectric coefficient for nanostructures at finite deformations from first principles
• Properties of carbon up to 10 million kelvin from Kohn-Sham density functional theory molecular dynamics
• On the calculation of the stress tensor in real-space Kohn-Sham Density Functional Theory
• Real-space formulation of the stress tensor for $\mathcal{O}(N)$ density functional theory: application to high temperature calculations
• Assessment of localized and randomized algorithms for electronic structure
• Ab-initio investigation of finite size effects in rutile titania nanoparticles with semilocal and nonlocal density functionals
• M-SPARC: MATLAB-Simulation Package for Ab-initio Real-space Calculations