ATLAS: A Real-Space Finite-Difference Implementation of Orbital-Free Density Functional Theory

TL;DR

This paper introduces a real-space finite-difference method and a direct energy-minimization scheme for orbital-free density functional theory, implemented in the ATLAS software, enabling efficient large-scale periodic system simulations with high accuracy.

Contribution

It develops a novel real-space finite-difference approach combined with energy minimization for OF-DFT, improving efficiency and stability over traditional methods.

Findings

Achieves high accuracy in large-scale periodic simulations.

Demonstrates efficiency and numerical stability in benchmark tests.

Successfully applied to systems of Mg, Al, and Al3Mg.

Abstract

Orbital-free density functional theory (OF-DFT) is a promising method for large-scale quantum mechanics simulation as it provides a good balance of accuracy and computational cost. Its applicability to large-scale simulations has been aided by progress in constructing kinetic energy functionals and local pseudopotentials. However, the widespread adoption of OF-DFT requires further improvement in its efficiency and robustly implemented software. Here we develop a real-space finite-difference method for the numerical solution of OF-DFT in periodic systems. Instead of the traditional self-consistent method, a powerful scheme for energy minimization is introduced to solve the Euler--Lagrange equation. Our approach engages both the real-space finite-difference method and a direct energy-minimization scheme for the OF-DFT calculations. The method is coded into the ATLAS software package and benchmarked using periodic systems of solid Mg, Al, and Al$_{3}$Mg. The test results show that our implementation can achieve high accuracy, efficiency, and numerical stability for large-scale simulations.