Wavefunctions and correlation energies for two-, three-, and four-electron atoms

A recently developed method (the GF method) which is equivalent to optimizing the orbitals of a Slater determinant after spin projection has been applied to H^-, He, Li⁺, Be^{+ +}, Li, Be ⁺, B^{+ +}, Li^-, Be, B⁺, and C ^{+ +}. These wavefunctions, which can be given an independent particle interpretation, yield better energies than those of the Hartree-Fock method. For example, H^- and Li^- are correctly predicted to be stable in contradistinction with the Hartree-Fock results. The new correlation energies are tabulated and compared to the Hartree-Fock values. In the case of the two-electron systems the new wavefunctions are nearly at the radial limit, accounting for 93% to 97% of the radial correlation error present in the Hartree-Fock description.