Variationally fitting the total electron-electron interaction

TL;DR

This paper introduces a variationally consistent density fitting method for the electron-electron interaction energy in quantum chemistry, ensuring the fundamental variational principle is preserved across all electronic structure methods.

Contribution

It develops a new fitting approach that maintains the variational connection between the electron-electron energy and potentials, improving the theoretical consistency of density fitting in DFT.

Findings

New fitting equations satisfied at an energy saddle point

Ensures variational connection in all electronic structure methods

Improves theoretical robustness of density fitting

Abstract

Density fitting is used throughout quantum chemistry to simplify the electron-electron interaction energy (EE). A fundamental property of quantum chemistry, and DFT in particular, is that a variational principle connects the EE to a potential. Density fitting generally does not preserve this connection. Herein, we describe the construction of a robust EE that is variationally connected to fitted potentials in all electronic structure methods. For DFT, this results in new fitting equations which are satisfied at an energy saddle point in multidimensional fitting space.