On basis set optimisation in quantum chemistry

TL;DR

This paper introduces new criteria for constructing optimal atomic basis sets in quantum chemistry, comparing their effectiveness through numerical tests on a simplified model of molecular dissociation.

Contribution

It proposes and evaluates two novel criteria for basis set optimization based on the density matrix and energy, with numerical validation on a toy model.

Findings

Both criteria effectively optimize basis sets in the toy model.

The energy-based criterion shows better performance in certain cases.

The density matrix criterion provides a complementary approach.

Abstract

In this article, we propose general criteria to construct optimal atomic centered basis sets in quantum chemistry. We focus in particular on two criteria, one based on the ground-state one-body density matrix of the system and the other based on the ground-state energy. The performance of these two criteria are then numerically tested and compared on a parametrized eigenvalue problem, which corresponds to a one-dimensional toy version of the ground-state dissociation of a diatomic molecule.