Practical Error Bounds for Properties in Plane-Wave Electronic Structure Calculations

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