Electron correlation energy in confined two-electron systems

Radial, angular and total correlation energies are calculated for four two-electron systems with atomic numbers Z=0–3Z=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 0.05–10a00.05–10a0. At small R, the correlation energies approach limiting values that are independent of Z while at intermediate R  , systems with Z⩾1Z⩾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.