Large-Z atoms in the strong-interaction limit of DFT: Implications for gradient expansions and for the Lieb-Oxford bound

Kimberly J. Daas, Derk P. Kooi, Tarik Benyahia, Michael Seidl, Paola Gori-Giorgi*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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Abstract

We numerically study the strong-interaction limit of the exchange-correlation functional for neutral atoms and Bohr atoms as the number of electrons increases. Using a compact representation, we analyze the second-order gradient expansion, comparing it with the one for exchange (weak interaction limit). The two gradient expansions, at strong and weak interaction, turn out to be very similar in magnitude but with opposite signs. We find that the point-charge plus continuum model is surprisingly accurate for the gradient expansion coefficient at strong coupling, while generalized gradient approximations, such as Perdew-Burke-Ernzerhof (PBE) and PBEsol, severely underestimate it. We then use our results to analyze the Lieb-Oxford bound from the point of view of slowly varying densities, clarifying some aspects on the bound at a fixed number of electrons.

Original languageEnglish
Article number234114
Pages (from-to)1-12
Number of pages12
JournalJournal of Chemical Physics
Volume159
Issue number23
Early online date19 Dec 2023
DOIs
Publication statusPublished - 21 Dec 2023

Bibliographical note

Special collection

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Funding Information:
This work was funded by the Netherlands Organisation for Scientific Research under Vici Grant No. 724.017.001. We thank Nathan Argaman, Antonio Cancio, and Kieron Burke for the data of the exchange energy of Bohr atoms and for insightful discussions on the gradient expansion and Stefan Vuckovic for discussions on the droplet data for the LO bound. We are especially grateful to Mathieu Lewin for suggesting to look at counterexamples of the kind of Eq. .

Publisher Copyright:
© 2023 Author(s).

Funding

This work was funded by the Netherlands Organisation for Scientific Research under Vici Grant No. 724.017.001. We thank Nathan Argaman, Antonio Cancio, and Kieron Burke for the data of the exchange energy of Bohr atoms and for insightful discussions on the gradient expansion and Stefan Vuckovic for discussions on the droplet data for the LO bound. We are especially grateful to Mathieu Lewin for suggesting to look at counterexamples of the kind of Eq. .

FundersFunder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek724.017.001
Nederlandse Organisatie voor Wetenschappelijk Onderzoek

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