Correlated energy from radial density-energy relations

Area of Science:

• Quantum Chemistry
• Atomic Physics
• Computational Chemistry

Background:

• The radial distribution function is crucial for understanding electron-electron interactions in atomic systems.
• Accurate calculation of ground and excited state energies is fundamental in atomic physics.

Purpose of the Study:

• To explore a novel mapping of the radial distribution function into a radial density-energy space.
• To establish a new method for determining the energy of helium-like systems.

Main Methods:

• Mapping the radial distribution function to a radial density-energy space.
• Analyzing the linearity of the radial density-radial energy relationship.
• Deriving an analytical expression for total energy using a fitting procedure.

Main Results:

• A linear relationship between radial density and radial energy was identified for helium-like systems.
• The gradient of this linear relationship directly yields the energy of the considered state.
• A simple analytical expression for total energy was derived based on the density at the most probable nucleus-electron distance.

Conclusions:

• The developed radial density-energy space provides a new perspective on atomic structure.
• This method offers a straightforward approach to calculate energies of helium-like systems.
• The findings facilitate a deeper understanding of electron density and energy relationships in atoms.