Variationally consistent Hellmann–Feynman forces in the finite element formulation of Kohn–Sham density functional theory

Date
2023-01-01
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Source Title
Computer Methods in Applied Mechanics and Engineering
Print ISSN
0045-7825
Electronic ISSN
1879-2138
Publisher
Elsevier
Volume
403
Issue
Part A
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Language
en
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Abstract

Hellmann–Feynman forces are derived within the numerical framework of the finite element method for density functional theory in the Kohn–Sham formalism. The variational consistency of the force expressions in all-electron and pseudopotential settings are carefully examined, with a particular focus on the implications arising from different representations for interaction terms that are associated with electrostatics. Numerical investigations in nonperiodic systems which range from diatomic molecules to carbon allotropes demonstrate the systematic convergence that is offered by the finite element framework, not only for energy and force but also for geometric configuration and molecular statics parameters. A range of higher-order discretizations employing fixed meshes are invoked within these examples based on classical finite elements as well as on isogeometric analysis. Overall, this work contributes to recent advances which demonstrate the viability of the finite element method for carrying out ab initio molecular dynamics.

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