Baskerville AL, Gray C, Cox H. Correlated energy from radial density-energy relations.
ROYAL SOCIETY OPEN SCIENCE 2023;
10:221402. [PMID:
36938537 PMCID:
PMC10014244 DOI:
10.1098/rsos.221402]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/30/2022] [Accepted: 02/13/2023] [Indexed: 06/18/2023]
Abstract
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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