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We propose accurate computable error bounds for quantities of interest inplane-wave electronic structure calculations, in particular ground-statedensity matrices and energies, and interatomic forces. These bounds are basedon an estimation of the error in terms of the residual of the solved equations,which is then efficiently approximated with computable terms. After providingcoarse bounds based on an analysis of the inverse Jacobian, we improve on thesebounds by solving a linear problem in a small dimension that involves a Schurcomplement. We numerically show how accurate these bounds are on a fewrepresentative materials, namely silicon, gallium arsenide and titaniumdioxide.

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