Auxiliary basis sets to approximate Coulomb potentials

TLDR: In this article, an approximate treatment of Coulomb operators based on the expansion of molecular electron densities in atom-centered auxiliary basis sets is proposed. But this approach is not suitable for all atoms and cannot be applied to all atoms.

Abstract: We demonstrate accuracy and computational efficiency resulting from an approximate treatment of Coulomb operators which is based on the expansion of molecular electron densities in atom-centered auxiliary basis sets. This is of special importance in density functional methods which separate the treatment of Coulomb and exchange-correlation terms. Auxiliary basis sets are optimized as much as possible for isolated atoms and then augmented for use in molecular electronic structure calculations. For molecules involving atoms up to Br this typically affects energies by only 10−4 au per atom, and computed structure constants by less than 0.1 pm in bond distances and 0.1° in bond angles.