Ionic forces and stress tensor in all-electron density functional theory calculations using an enriched finite-element basis

Nelson D. Rufus and Vikram Gavini
Phys. Rev. B 106, 085108 – Published 5 August 2022

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 density functional theory (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 [P. Motamarri and V. Gavini, Phys. Rev. B 97, 165132 (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 the Gaussian basis for molecular systems and against the linearized augmented plane wave with local orbitals basis for periodic systems.

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  • Received 11 May 2022
  • Revised 13 July 2022
  • Accepted 14 July 2022

DOI:https://doi.org/10.1103/PhysRevB.106.085108

©2022 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Nelson D. Rufus

  • Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA

Vikram Gavini

  • Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA and Department of Materials Science & Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA

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Vol. 106, Iss. 8 — 15 August 2022

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