Straightforward and accurate automatic auxiliary basis set generation for molecular calculations with atomic orbital basis sets

TL;DR

This paper introduces a simple, stable, and automatic method for generating auxiliary basis sets for density fitting in quantum chemistry, applicable to various atomic basis functions, and demonstrates its effectiveness with Gaussian basis sets.

Contribution

The authors propose a novel automated auxiliary basis set generation scheme using pivoted Cholesky decomposition, applicable to any atomic basis type, improving accuracy and efficiency in quantum chemical calculations.

Findings

Negligible errors in Hartree-Fock and MP2 energies using the new scheme.

Effective with Gaussian basis sets of at least polarized triple-zeta quality.

Promising potential for application with Slater-type and numerical atomic orbitals.

Abstract

Density fitting (DF), also known as the resolution of the identity (RI), is a widely used technique in quantum chemical calculations with various types of atomic basis sets - Gaussian-type orbitals, Slater-type orbitals, as well as numerical atomic orbitals - to speed up density functional, Hartree-Fock, and post-Hartree-Fock calculations. Traditionally, custom auxiliary basis sets are hand-optimized for each orbital basis set; however, some automatic schemes have also been suggested. In this work, we propose a simple yet numerically stable automated scheme for forming auxiliary basis sets with the help of a pivoted Cholesky decomposition, which is applicable to any type of atomic basis function. We exemplify the scheme with proof-of-concept calculations with Gaussian basis sets and show that the proposed approach leads to negligible DF/RI errors in Hartree-Fock (HF) and second-order M{\o}ller-Plesset (MP2) total energies of the non-multireference part of the W4-17 test set when used with orbital basis sets of at least polarized triple-$\zeta$ quality. The results are promising for future applications employing Slater-type orbitals or numerical atomic orbitals, as well as schemes based on the use of local fitting approaches. Global fitting approaches can also be used, in which case the high-angular-momentum functions produced by the present scheme can be truncated to minimize the computational cost.