Communication: Curing basis set overcompleteness with pivoted Cholesky decompositions

TL;DR

The paper introduces a pivoted Cholesky decomposition method to prune over-complete basis sets in electronic structure calculations, improving stability and reducing computational cost while maintaining accuracy.

Contribution

It presents a novel basis set pruning technique using pivoted Cholesky decomposition, enabling more efficient and stable electronic structure calculations with minimal loss of accuracy.

Findings

Achieves 9-28% reduction in basis functions depending on the basis set size.

Maintains accuracy close to standard augmented basis sets.

Reduces computational cost in electronic structure calculations.

Abstract

The description of weakly bound electronic states is especially difficult with atomic orbital basis sets. The diffuse atomic basis functions that are necessary to describe the extended electronic state generate significant linear dependencies in the molecular basis set, which may make the electronic structure calculations ill-convergent. We propose a method where the over-complete molecular basis set is pruned by a pivoted Cholesky decomposition of the overlap matrix, yielding an optimal low-rank approximation that is numerically stable; the pivot indices determining a reduced basis set that is complete enough to describe all the basis functions in the original over-complete basis. The method can be implemented either by a simple modification to the usual canonical orthogonalization procedure, which hides the excess functions and yields fewer efficiency benefits, or by generating custom basis sets for all the atoms in the system, yielding significant cost reductions in electronic structure calculations. The pruned basis sets from the latter choice allow accurate calculations to be performed at a lower cost even at the self-consistent field level, as illustrated on a solvated (H2O)24- anion. Our results indicate that the Cholesky procedure allows one to perform calculations with accuracies close to standard augmented basis sets with cost savings which increase with the size of the basis set, ranging from 9% fewer functions in single-{\zeta} basis sets to 28% fewer functions in triple-{\zeta} basis sets.