Robust and variational fitting: Removing the four-center integrals from center stage in quantum chemistry

We are interested in developing very fast and very accurate first-principles molecular dynamics. The approach that we are developing is robust and variational fitting. Fitting can be used effectively in quantum chemistry in many ways beyond optimizing and generating molecular orbitals, provided the fits are variational, i.e. compatible with the variational principle. Robust-variational fits, in addition to being variational, correct the target function to first order in the error made due to fitting. Thus robust and variational fits and fitting-basis sets can be generated in the same manner that molecular orbitals and atomic-basis sets are generated. Robust-variational resolution-of-the-identity methods are described as well as methods for analytically treating Kohn-Sham exchange and the case of canted spins in a general treatment of magnetism and with the spin-orbit interaction. Published by Elsevier Science B.V.