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.

翻译：我们提出精确的可计算误差界限,以计算电子结构计算中感兴趣的数量,特别是地面国家密度矩阵和能量,以及交解力。这些界限以对解答方程式剩余部分的误差的估计为基础,然后有效地与可计算方程相近。在根据对雅各克人的分析提供粗糙的误差之后,我们通过在涉及Schur补充的小型层面解决线性问题来改进这些界限。我们用数字来显示这些界限对少数具有代表性的材料,即硅、砷化 ⁇ 和二氧化钛的准确程度。