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Journal Articles SIAM Journal on Scientific Computing Year : 2022

Practical error bounds for properties in plane-wave electronic structure calculations

Abstract

We propose accurate computable error bounds for quantities of interest in plane-wave electronic structure calculations, in particular ground-state density matrices and energies, and interatomic forces. These bounds are based on an estimation of the error in terms of the residual of the solved equations, which is then efficiently approximated with computable terms. After providing coarse bounds based on an analysis of the inverse Jacobian, we improve on these bounds by solving a linear problem in a small dimension that involves a Schur complement. We numerically show how accurate these bounds are on a few representative materials, namely silicon, gallium arsenide and titanium dioxide.
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Dates and versions

hal-03408321 , version 1 (29-10-2021)
hal-03408321 , version 2 (18-06-2022)

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Cite

Eric Cancès, Geneviève Dusson, Gaspard Kemlin, Antoine Levitt. Practical error bounds for properties in plane-wave electronic structure calculations. SIAM Journal on Scientific Computing, 2022, 44 (5), ⟨10.1137/21M1456224⟩. ⟨hal-03408321v2⟩
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