Robust variational fitting: Gáspár's variational exchange can accurately be treated analytically

Abstract

Efficient density-functional calculations require the Kohn–Sham potential be fitted to a linear-combination-of-atomic-orbitals form. This approximation is completely consistent with the very high accuracy associated with traditional quantum chemistry provided the approximations are treated variationally, i.e. in a way that is compatible with the variational principle. Robust fits correct the energy through first order in the fitting error, thereby allowing variational determination of the fits as well as the orbitals. Robust variational fitting is reviewed for the Coulomb problem. Robust variational resolution-of-the-identity fitting methods are derived for use in all nondensity-functional ab initio calculations. Robust variational fitting of the interaction between any two charge distributions is derived for density functional calculations. A robust, variational, divide-and-conquer treatment of the Gáspár–Kohn–Sham potential is developed.