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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...

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Detalles Bibliográficos
Autores principales: Baskerville, Adam L., Gray, Conor, Cox, Hazel
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10014244/
https://www.ncbi.nlm.nih.gov/pubmed/36938537
http://dx.doi.org/10.1098/rsos.221402
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author Baskerville, Adam L.
Gray, Conor
Cox, Hazel
author_facet Baskerville, Adam L.
Gray, Conor
Cox, Hazel
author_sort Baskerville, Adam L.
collection PubMed
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.
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spelling pubmed-100142442023-03-16 Correlated energy from radial density–energy relations Baskerville, Adam L. Gray, Conor Cox, Hazel R Soc Open Sci Chemistry 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. The Royal Society 2023-03-15 /pmc/articles/PMC10014244/ /pubmed/36938537 http://dx.doi.org/10.1098/rsos.221402 Text en © 2023 The Authors. https://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, provided the original author and source are credited.
spellingShingle Chemistry
Baskerville, Adam L.
Gray, Conor
Cox, Hazel
Correlated energy from radial density–energy relations
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 Chemistry
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10014244/
https://www.ncbi.nlm.nih.gov/pubmed/36938537
http://dx.doi.org/10.1098/rsos.221402
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