Electron correlation energy in confined two-electron systems

TL;DR

This study calculates radial, angular, and total correlation energies for two-electron systems confined within an impenetrable sphere, revealing how these energies vary with confinement radius and atomic number.

Contribution

It provides accurate calculations of correlation energies for confined two-electron systems across different radii and atomic numbers, highlighting their behavior and limiting values.

Findings

Correlation energies approach Z-independent limits at small R.

Systems with Z > 1 show a maximum in correlation energy at intermediate R.

Angular correlation energy increases while radial decreases at certain R.

Abstract

Radial, angular and total correlation energies are calculated for four two-electron systems with atomic numbers Z=0-3 confined within an impenetrable sphere of radius R. We report accurate results for the non-relativistic, restricted Hartree-Fock and radial limit energies over a range of confinement radii from 0.05 - 10 a0. At small R, the correlation energies approach limiting values that are independent of Z while at intermediate R, systems with Z > 1 exhibit a characteristic maximum in the correlation energy resulting from an increase in the angular correlation energy which is offset by a decrease in the radial correlation energy.