Avoiding Negligible Shell Pairs and Quartets in Electronic Structure Calculations

Ellena K G Black; Andrew T B Gilbert; Simon C McKenzie; Peter M W Gill

doi:10.1021/acs.jpca.2c08408

Avoiding Negligible Shell Pairs and Quartets in Electronic Structure Calculations

J Phys Chem A. 2023 Jan 26;127(3):842-850. doi: 10.1021/acs.jpca.2c08408. Epub 2023 Jan 17.

Authors

Ellena K G Black¹, Andrew T B Gilbert², Simon C McKenzie¹, Peter M W Gill¹

Affiliations

¹ School of Chemistry, University of Sydney, Sydney, NSW2006, Australia.
² School of Computing, Australian National University, Canberra, ACT2601, Australia.

Abstract

We define a significant shell pair in an electronic structure calculation as one that generates at least one two-electron integral larger than a preset threshold. We define a significant shell quartet similarly. We then explore several methods for identifying nonsignificant pairs and quartets so that they can be avoided and computational efficiency improved. We find that the widely used Cauchy-Schwarz bound identifies most nonsignificant quartets but that the Hölder bound is slightly more powerful for identifying nonsignificant pairs.