Many-electron expansion: A density functional hierarchy for strongly correlated systems

Density functional theory (DFT) is the de facto method for the electronic structure of weakly correlated systems. But for strongly correlated materials, common density functional approximations break down. Here, we derive a many-electron expansion (MEE) in DFT that accounts for successive one-, two-...

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Main Authors: Zhu, Tianyu, de Silva, Piotr, van Aggelen, Helen, Van Voorhis, Troy
Other Authors: Massachusetts Institute of Technology. Department of Chemistry
Format: Article
Language:English
Published: American Physical Society 2016
Online Access:http://hdl.handle.net/1721.1/103119
https://orcid.org/0000-0003-2061-3237
https://orcid.org/0000-0002-4985-7350
https://orcid.org/0000-0001-7111-0176
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author Zhu, Tianyu
de Silva, Piotr
van Aggelen, Helen
Van Voorhis, Troy
author2 Massachusetts Institute of Technology. Department of Chemistry
author_facet Massachusetts Institute of Technology. Department of Chemistry
Zhu, Tianyu
de Silva, Piotr
van Aggelen, Helen
Van Voorhis, Troy
author_sort Zhu, Tianyu
collection MIT
description Density functional theory (DFT) is the de facto method for the electronic structure of weakly correlated systems. But for strongly correlated materials, common density functional approximations break down. Here, we derive a many-electron expansion (MEE) in DFT that accounts for successive one-, two-, three-, ... particle interactions within the system. To compute the correction terms, the density is first decomposed into a sum of localized, nodeless one-electron densities (ρ_{i}). These one-electron densities are used to construct relevant two- (ρ_{i}+ρ_{j}), three- (ρ_{i}+ρ_{j}+ρ_{k}), ... electron densities. Numerically exact results for these few-particle densities can then be used to correct an approximate density functional via any of several many-body expansions. We show that the resulting hierarchy gives accurate results for several important model systems: the Hubbard and Peierls-Hubbard models in 1D and the pure Hubbard model in 2D. We further show that the method is numerically convergent for strongly correlated systems: applying successively higher order corrections leads to systematic improvement of the results. MEE thus provides a hierarchy of density functional approximations that applies to both weakly and strongly correlated systems.
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spelling mit-1721.1/1031192022-10-01T22:06:34Z Many-electron expansion: A density functional hierarchy for strongly correlated systems Zhu, Tianyu de Silva, Piotr van Aggelen, Helen Van Voorhis, Troy Massachusetts Institute of Technology. Department of Chemistry Zhu, Tianyu de Silva, Piotr van Aggelen, Helen Van Voorhis, Troy Density functional theory (DFT) is the de facto method for the electronic structure of weakly correlated systems. But for strongly correlated materials, common density functional approximations break down. Here, we derive a many-electron expansion (MEE) in DFT that accounts for successive one-, two-, three-, ... particle interactions within the system. To compute the correction terms, the density is first decomposed into a sum of localized, nodeless one-electron densities (ρ_{i}). These one-electron densities are used to construct relevant two- (ρ_{i}+ρ_{j}), three- (ρ_{i}+ρ_{j}+ρ_{k}), ... electron densities. Numerically exact results for these few-particle densities can then be used to correct an approximate density functional via any of several many-body expansions. We show that the resulting hierarchy gives accurate results for several important model systems: the Hubbard and Peierls-Hubbard models in 1D and the pure Hubbard model in 2D. We further show that the method is numerically convergent for strongly correlated systems: applying successively higher order corrections leads to systematic improvement of the results. MEE thus provides a hierarchy of density functional approximations that applies to both weakly and strongly correlated systems. National Science Foundation (U.S.) (NSF (CHE-1464804)) David & Lucile Packard Foundation (grant) 2016-06-16T18:25:32Z 2016-06-16T18:25:32Z 2016-05 2016-04 2016-05-19T22:00:13Z Article http://purl.org/eprint/type/JournalArticle 2469-9950 2469-9969 http://hdl.handle.net/1721.1/103119 Zhu, Tianyu, Piotr de Silva, Helen van Aggelen, and Troy Van Voorhis. Phys. Rev. B 93, 201108 (2016). ©2016 American Physical Society. https://orcid.org/0000-0003-2061-3237 https://orcid.org/0000-0002-4985-7350 https://orcid.org/0000-0001-7111-0176 en http://dx.doi.org/10.1103/PhysRevB.93.201108 Physical Review B Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society
spellingShingle Zhu, Tianyu
de Silva, Piotr
van Aggelen, Helen
Van Voorhis, Troy
Many-electron expansion: A density functional hierarchy for strongly correlated systems
title Many-electron expansion: A density functional hierarchy for strongly correlated systems
title_full Many-electron expansion: A density functional hierarchy for strongly correlated systems
title_fullStr Many-electron expansion: A density functional hierarchy for strongly correlated systems
title_full_unstemmed Many-electron expansion: A density functional hierarchy for strongly correlated systems
title_short Many-electron expansion: A density functional hierarchy for strongly correlated systems
title_sort many electron expansion a density functional hierarchy for strongly correlated systems
url http://hdl.handle.net/1721.1/103119
https://orcid.org/0000-0003-2061-3237
https://orcid.org/0000-0002-4985-7350
https://orcid.org/0000-0001-7111-0176
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