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.

References in corpus (1)

• A robust and efficient line search for self-consistent field iterations

Cited by in corpus (4)

• Towards self-driving laboratories: The central role of density functional theory in the AI age
• An overview of a posteriori error estimation and post-processingmethods for nonlinear eigenvalue problems
• Algorithmic differentiation for plane-wave DFT: materials design, error control and learning model parameters
• Fully guaranteed and computable error bounds on the energy for periodic Kohn-Sham equations with convex density functionals