Correlation Effects in Atoms. III. Four-Electron Systems

The binding energy of the ground state of four-electron systems is investigated in the framework of Hartree-Fock perturbation theory. First, we show that the original problem can be decoupled into a series of helium-like equations describing pair correlation between electrons. Then, the variational-perturbation method is applied to each of these equations through fifth order in energy. We have obtained for the correlation energies the values Ecorr(Be)=-0.0925 atomic units (a.u.) and Ecorr(B⁺)=-0.1096 a.u. The experimental numbers are Ecorrᵉˣᵖ(Be)=-0.0944 a.u. and Ecorrᵉˣᵖ(B⁺)=-0.1116 a.u.