Correlated energy from radial density–energy relations
Here, we demonstrate that the radial distribution function can be mapped into a radial density–energy space and the relationship between the radial density and radial energy is linear for the ground and excited states of helium-like systems; the gradient of the resulting straight line delivers the e...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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The Royal Society
2023-03-01
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| Series: | Royal Society Open Science |
| Subjects: | |
| Online Access: | https://royalsocietypublishing.org/doi/10.1098/rsos.221402 |
| _version_ | 1797858291604258816 |
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| author | Adam L. Baskerville Conor Gray Hazel Cox |
| author_facet | Adam L. Baskerville Conor Gray Hazel Cox |
| author_sort | Adam L. Baskerville |
| collection | DOAJ |
| description | Here, we demonstrate that the radial distribution function can be mapped into a radial density–energy space and the relationship between the radial density and radial energy is linear for the ground and excited states of helium-like systems; the gradient of the resulting straight line delivers the energy of the state considered. To utilize this finding, a simple analytical expression for the total energy in terms of the density at the most probable nucleus–electron distance of the systems considered is derived using a fitting procedure. |
| first_indexed | 2024-04-09T21:10:58Z |
| format | Article |
| id | doaj.art-819d8ba046e146fd84135df4189c47e1 |
| institution | Directory Open Access Journal |
| issn | 2054-5703 |
| language | English |
| last_indexed | 2024-04-09T21:10:58Z |
| publishDate | 2023-03-01 |
| publisher | The Royal Society |
| record_format | Article |
| series | Royal Society Open Science |
| spelling | doaj.art-819d8ba046e146fd84135df4189c47e12023-03-28T20:17:14ZengThe Royal SocietyRoyal Society Open Science2054-57032023-03-0110310.1098/rsos.221402Correlated energy from radial density–energy relationsAdam L. Baskerville0Conor Gray1Hazel Cox2Department of Chemistry, School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QJ, UKDepartment of Chemistry, School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QJ, UKDepartment of Chemistry, School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QJ, UKHere, we demonstrate that the radial distribution function can be mapped into a radial density–energy space and the relationship between the radial density and radial energy is linear for the ground and excited states of helium-like systems; the gradient of the resulting straight line delivers the energy of the state considered. To utilize this finding, a simple analytical expression for the total energy in terms of the density at the most probable nucleus–electron distance of the systems considered is derived using a fitting procedure.https://royalsocietypublishing.org/doi/10.1098/rsos.221402energy–density relationradial densityenergy densitycorrelation energy |
| spellingShingle | Adam L. Baskerville Conor Gray Hazel Cox Correlated energy from radial density–energy relations Royal Society Open Science energy–density relation radial density energy density correlation energy |
| title | Correlated energy from radial density–energy relations |
| title_full | Correlated energy from radial density–energy relations |
| title_fullStr | Correlated energy from radial density–energy relations |
| title_full_unstemmed | Correlated energy from radial density–energy relations |
| title_short | Correlated energy from radial density–energy relations |
| title_sort | correlated energy from radial density energy relations |
| topic | energy–density relation radial density energy density correlation energy |
| url | https://royalsocietypublishing.org/doi/10.1098/rsos.221402 |
| work_keys_str_mv | AT adamlbaskerville correlatedenergyfromradialdensityenergyrelations AT conorgray correlatedenergyfromradialdensityenergyrelations AT hazelcox correlatedenergyfromradialdensityenergyrelations |