Spectral quadrature for the first principles study of crystal defects: Application to magnesium

TL;DR

This paper introduces a parallel finite-difference spectral quadrature method within DFT for non-periodic systems, enabling efficient simulation of defects in magnesium alloys with linear scaling and accurate force calculations.

Contribution

It develops a novel parallel finite-difference spectral quadrature framework for non-periodic DFT calculations, demonstrating linear scaling and application to defect studies in magnesium alloys.

Findings

Binding energies of defects are anisotropic and cell size dependent.

The framework scales linearly with the number of atoms.

Simulations show favorable binding of defects.

Abstract

We present an accurate and efficient finite-difference formulation and parallel implementation of Kohn-Sham Density (Operator) Functional Theory (DFT) for non periodic systems embedded in a bulk environment. Specifically, employing non-local pseudopotentials, local reformulation of electrostatics, and truncation of the spatial Kohn-Sham Hamiltonian, and the Linear Scaling Spectral Quadrature method to solve for the pointwise electronic fields in real-space and the non-local component of the atomic force, we develop a parallel finite difference framework suitable for distributed memory computing architectures to simulate non-periodic systems embedded in a bulk environment. Choosing examples from magnesium-aluminum alloys, we first demonstrate the convergence of energies and forces with respect to spectral quadrature polynomial order, and the width of the spatially truncated Hamiltonian. Next, we demonstrate the parallel scaling of our framework, and show that the computation time and memory scale linearly with respect to the number of atoms. Next, we use the developed framework to simulate isolated point defects and their interactions in magnesium-aluminum alloys. Our findings conclude that the binding energies of divacancies, Al solute-vacancy and two Al solute atoms are anisotropic and are dependent on cell size. Furthermore, the binding is favorable in all three cases.