Exact Density Functional Obtained via the Levy Constrained Search
A stochastic minimization method for a real-space wavefunction, Ψ(r ,r ...r ), constrained to a chosen density, ρ(r), is developed. It enables the explicit calculation of the Levy constrained search F[ρ]=min <Ψ|T+V |Ψ>, that gives the exact functional of density functional theory. This general...
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| Veröffentlicht in: | The journal of physical chemistry letters Jg. 9; H. 17; S. 4910 |
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| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
United States
06.09.2018
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| ISSN: | 1948-7185, 1948-7185 |
| Online-Zugang: | Weitere Angaben |
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| Zusammenfassung: | A stochastic minimization method for a real-space wavefunction, Ψ(r
,r
...r
), constrained to a chosen density, ρ(r), is developed. It enables the explicit calculation of the Levy constrained search F[ρ]=min
<Ψ|T+V
|Ψ>, that gives the exact functional of density functional theory. This general method is illustrated in the evaluation of F[ρ] for densities in one dimension with a soft-Coulomb interaction. Additionally, procedures are given to determine the first and second functional derivatives δF/δρ(r) and δ
F/δρ(r)δρ(r'). For a chosen external potential, v(r), the functional and its derivatives are used in minimizations over densities to give the exact energy, E
, without needing to solve the Schrödinger equation. |
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| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 1948-7185 1948-7185 |
| DOI: | 10.1021/acs.jpclett.8b02332 |