Calculation of ns 2 configurations for the Helium isoelectronic series without matching

In the Hartree–Fock equations for the He isoelectronic series, the two‐point boundary conditions on one of the differential equations is replaced by initial conditions specified at large distances. [The condition Y ′(∞) = 0 replaces the condition Y (0) = 0.] This permits eigenvalues of ns 2 configurations to be determined as the zeros of a certain function arising from inward integrations, without having to match the solution with a corresponding outward integration. Calculations are performed for n = 1,2,3 for H − through Be 2+ . Resulting energy values and radial densities are presented. Agreement is found, to the eight significant figures calculated here, with the n = 1 results given by Roothaan and Soukup.