Shaw, R.A. orcid.org/0000-0002-9977-0835 (2020) The completeness properties of Gaussian‐type orbitals in quantum chemistry. International Journal of Quantum Chemistry, 120 (17). e26264. ISSN 0020-7608
Abstract
In this work, I extend results on the convergence of Gaussian basis sets in quantum chemistry, previously shown for ground‐state hydrogenic wavefunctions, to orbitals of arbitrary angular momentum. I give rigorous proofs of their asymptotic behavior, and demonstrate for methods with regular potential operators—in particular, Hartree–Fock and Kohn–Sham density functional theory—that the assumption of completeness is correct under fairly lenient conditions. The final result under the correct norm is that the convergence in energy follows urn:x-wiley:00207608:media:qua26264:qua26264-math-0001, where M is the number of Gaussians and k is a positive constant, generalizing previous results due to Kutzelnigg. This then yields prescriptions for accelerated convergence using even‐tempered Gaussians, which could be used as initial guesses in future basis set optimizations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 Wiley Periodicals LLC. This is an author-produced version of a paper subsequently published in International Journal of Quantum Chemistry. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | analysis; basis sets; completeness; Gaussians; orbitals; quantum chemistry |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > Department of Chemistry (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 08 Jan 2021 16:24 |
Last Modified: | 19 Jun 2021 00:38 |
Status: | Published |
Publisher: | Wiley |
Refereed: | Yes |
Identification Number: | 10.1002/qua.26264 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:169598 |