Optimization of atomic density-fitting basis functions for molecular two-electron integral approximations

TL;DR

This paper presents a new procedure for optimizing atomic density-fitting basis functions to improve the accuracy and stability of two-electron integral approximations across all elements, enhancing computational quantum chemistry methods.

Contribution

A general optimization method for atomic density-fitting basis functions that balances accuracy and numerical stability for all elements in a scalar-relativistic framework.

Findings

Optimized auxiliary basis sets match wavefunction basis sets for all 102 elements.

The procedure improves the accuracy of two-electron integral approximations.

The method ensures numerical stability in density-fitting calculations.

Abstract

A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the product densities, modeling their contribution to the exchange and second-order correlation energy, and a simple weighted error measure is minimized. Generally-contracted Gaussian auxiliary basis sets are optimized to match the wavefunction basis sets [D. N. Laikov, Theor. Chem. Acc. 138, 40 (2019)] for all 102 elements in a scalar-relativistic approximation [D. N. Laikov, J. Chem. Phys. 150, 061102 (2019)].