Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations

TL;DR

This paper introduces an efficient adaptive local basis set for Kohn-Sham DFT that accurately computes atomic forces and enables scalable molecular dynamics, demonstrated on various physical systems with minimal Pulay force contributions.

Contribution

The paper extends the adaptive local basis set framework to include force calculations and molecular dynamics, showing near-linear scaling and high accuracy with few basis functions per atom.

Findings

Forces computed with the basis set are accurate compared to planewave results.

Force calculations scale nearly linearly with system size.

Pulay forces are small and decrease with basis completeness.

Abstract

Recently, we have proposed the adaptive local basis set for electronic structure calculations based on Kohn-Sham density functional theory in a pseudopotential framework. The adaptive local basis set is efficient and systematically improvable for total energy calculations. In this paper, we present the calculation of atomic forces, which can be used for a range of applications such as geometry optimization and molecular dynamics simulation. We demonstrate that, under mild assumptions, the computation of atomic forces can scale nearly linearly with the number of atoms in the system using the adaptive local basis set. We quantify the accuracy of the Hellmann-Feynman forces for a range of physical systems, benchmarked against converged planewave calculations, and find that the adaptive local basis set is efficient for both force and energy calculations, requiring at most a few tens of basis functions per atom to attain accuracy required in practice. Since the adaptive local basis set has implicit dependence on atomic positions, Pulay forces are in general nonzero. However, we find that the Pulay force is numerically small and systematically decreasing with increasing basis completeness, so that the Hellmann-Feynman force is sufficient for basis sizes of a few tens of basis functions per atom. We verify the accuracy of the computed forces in static calculations of quasi-1D and 3D disordered Si systems, vibration calculation of a quasi-1D Si system, and molecular dynamics calculations of H$_2$ and liquid Al-Si alloy systems, where we find excellent agreement with independent benchmark results in literature.