Variations of the Hartree–Fock fractional-spin error for one electron
Fractional-spin errors are inherent in all current approximate density functionals, including Hartree–Fock theory, and their origin has been related to strong static correlation effects. The conventional way to encode fractional-spin calculations is to construct an ensemble density that scales betwe...
| Main Authors: | , , , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
AIP Publishing
2021
|
| _version_ | 1797083777230438400 |
|---|---|
| author | Burton, HGA Marut, C Daas, TJ Gori-Giorgi, P Loos, P-F |
| author_facet | Burton, HGA Marut, C Daas, TJ Gori-Giorgi, P Loos, P-F |
| author_sort | Burton, HGA |
| collection | OXFORD |
| description | Fractional-spin errors are inherent in all current approximate density functionals, including Hartree–Fock theory, and their origin has been related to strong static correlation effects. The conventional way to encode fractional-spin calculations is to construct an ensemble density that scales between the high-spin and low-spin densities. In this article, we explore the variation of the Hartree–Fock fractional-spin (or ghost-interaction) error in one-electron systems using restricted and unrestricted ensemble densities and the exact generalized Hartree–Fock representation. By considering the hydrogen atom and H+2 cation, we analyze how the unrestricted and generalized Hartree–Fock schemes minimize this error by localizing the electrons or rotating the spin coordinates. We also reveal a clear similarity between the Coulomb hole of He-like ions and the density depletion near the nucleus induced by the fractional-spin error in the unpolarized hydrogen atom. Finally, we analyze the effect of the fractional-spin error on the Møller–Plesset adiabatic connection, excited states, and functional- and density-driven errors. |
| first_indexed | 2024-03-07T01:46:13Z |
| format | Journal article |
| id | oxford-uuid:98858739-45de-4c91-80c2-db3bb26c384d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:46:13Z |
| publishDate | 2021 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | oxford-uuid:98858739-45de-4c91-80c2-db3bb26c384d2022-03-27T00:07:28ZVariations of the Hartree–Fock fractional-spin error for one electronJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:98858739-45de-4c91-80c2-db3bb26c384dEnglishSymplectic ElementsAIP Publishing2021Burton, HGAMarut, CDaas, TJGori-Giorgi, PLoos, P-FFractional-spin errors are inherent in all current approximate density functionals, including Hartree–Fock theory, and their origin has been related to strong static correlation effects. The conventional way to encode fractional-spin calculations is to construct an ensemble density that scales between the high-spin and low-spin densities. In this article, we explore the variation of the Hartree–Fock fractional-spin (or ghost-interaction) error in one-electron systems using restricted and unrestricted ensemble densities and the exact generalized Hartree–Fock representation. By considering the hydrogen atom and H+2 cation, we analyze how the unrestricted and generalized Hartree–Fock schemes minimize this error by localizing the electrons or rotating the spin coordinates. We also reveal a clear similarity between the Coulomb hole of He-like ions and the density depletion near the nucleus induced by the fractional-spin error in the unpolarized hydrogen atom. Finally, we analyze the effect of the fractional-spin error on the Møller–Plesset adiabatic connection, excited states, and functional- and density-driven errors. |
| spellingShingle | Burton, HGA Marut, C Daas, TJ Gori-Giorgi, P Loos, P-F Variations of the Hartree–Fock fractional-spin error for one electron |
| title | Variations of the Hartree–Fock fractional-spin error for one electron |
| title_full | Variations of the Hartree–Fock fractional-spin error for one electron |
| title_fullStr | Variations of the Hartree–Fock fractional-spin error for one electron |
| title_full_unstemmed | Variations of the Hartree–Fock fractional-spin error for one electron |
| title_short | Variations of the Hartree–Fock fractional-spin error for one electron |
| title_sort | variations of the hartree fock fractional spin error for one electron |
| work_keys_str_mv | AT burtonhga variationsofthehartreefockfractionalspinerrorforoneelectron AT marutc variationsofthehartreefockfractionalspinerrorforoneelectron AT daastj variationsofthehartreefockfractionalspinerrorforoneelectron AT gorigiorgip variationsofthehartreefockfractionalspinerrorforoneelectron AT loospf variationsofthehartreefockfractionalspinerrorforoneelectron |