Accurate and stable numerical Hartree–Fock calculations for atoms. I. The 1s2 ground state of H−, He, Li+, and Be++

New techniques have been developed for atomic self‐consistent‐field calculations by numerical integration. For the origin and tail regions we present analytical expansions which can represent the solutions to high accuracy. For the numerical integration in the central region a five‐point generalization of the Numerov formula is used; the error term is of the order h10. While this formula is unstable if used in the customary way, stability is achieved by using a Gaussian elimination technique. The new procedures are tested on the ground state of the helium isoelectronic series; with 251 integration points all quantities are calculated with an inherent accuracy of better than 10–11.