Helium Isoelectronic Series (NS)(2) Energy Levels by Numerical Hartree-Fock Solutions Without Matching.

In the Hartree-Fock equations for the He isoelectronic series, the 2-point boundary conditions on one of the differential equations is replaced by initial conditions specified at large distances. (The condition Y'((INFIN)) = 0 replaces the condition Y(0) = 0.) This permits eigenvalues of ns('2) configurations to be determined as the zeroes 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('++). 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 {Int. J. Quant. Chem. XV,449(1979) }.