Ionic forces and stress tensor in all-electron DFT calculations using enriched finite element basis

TL;DR

This paper develops a method to accurately compute ionic forces and stress tensors in all-electron DFT calculations using an enriched finite element basis, improving computational efficiency and precision.

Contribution

It extends the formulation of configurational forces to the enriched finite element basis, including additional contributions from enrichment functions, and validates the approach through benchmark comparisons.

Findings

Accurate force and stress calculations match finite-difference results.

Benchmarking against Gaussian and LAPW+lo bases shows high accuracy.

Method enhances efficiency in all-electron DFT simulations.

Abstract

The enriched finite element basis -- wherein the finite element basis is enriched with atom-centered numerical functions -- has recently been shown to be a computationally efficient basis for systematically convergent all-electron DFT ground-state calculations. In this work, we present the expressions to compute variationally consistent ionic forces and stress tensor for all-electron DFT calculations in the enriched finite element basis. In particular, we extend the formulation of configurational forces in Motamarri & Gavini (Phys. Rev. B 2018) to the enriched finite element basis and elucidate the additional contributions arising from the enrichment functions. We demonstrate the accuracy of the formulation by comparing the computed forces and stresses for various benchmark systems with those obtained from finite-differencing the ground-state energy. Further, we also benchmark our calculations against Gaussian basis for molecular systems and against the LAPW+lo basis for periodic systems.