Correlated energy from radial density–energy relations. Issue 3 (15th March 2023) - Baskerville, Adam L.; Gray, Conor; Cox, Hazel
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.