Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
117 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
5 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Communication: Curing basis set overcompleteness with pivoted Cholesky decompositions (1911.10372v2)

Published 23 Nov 2019 in physics.chem-ph, physics.atm-clus, and physics.comp-ph

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.

Summary

We haven't generated a summary for this paper yet.