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

Eric Cancès (1, 2) , Geneviève Dusson (3) , Gaspard Kemlin (1, 2) , Antoine Levitt (1, 2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MATHERIALS - MATHematics for MatERIALS
3 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

We propose accurate computable error bounds for quantities of interest in 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.

Domaines: Analyse numérique [math.NA]; Science des matériaux [cond-mat.mtrl-sci]

Eric Cancès, Geneviève Dusson, Gaspard Kemlin, Antoine Levitt. Practical error bounds for properties in plane-wave electronic structure calculations. 2021. ⟨hal-03408321v1⟩