Consolidated Configuration-Interaction Perturbation Method: The Ground State of Beryllium

Abstract

A method is developed for consolidating the configuration‐interaction method and Rayleigh–Schrödinger perturbation theory. The technique requires the existence of a more or less conventional unperturbed Hamiltonian but not its eigenfunctions. The method depends crucially upon a particular partitioning of terms among perturbed and unperturbed parts of the full Hamiltonian expressed in spectral representation, and leads to having some perturbation denominators significantly different from the Rayleigh–Schrödinger ones. The beryllium ground‐state energy was calculated as a test. An hydrogeniclike basis was obtained by interacting the Shull–Löwdin discrete Laguerres over an appropriate one‐electron Hamiltonian. A single screening constant was employed and a rather unique method was used to treat the (zero‐order) degeneracy of the ${\text{|\hspace{0.17em}1s}}^2{\text{2s}}^2〉$ and ${\text{|\hspace{0.17em}1s}}^2{\text{2p}}^2〉$ functions. Some two‐electron integrals were calculated by the method of Jones and Brooks and others by modifying the formula of Brown. The value − 14.659 a.u. was obtained for the ground‐state energy. This compares well with values obtained by more involved techniques. An analysis of the results shows that the method can be considered as generating the SCF and correlation energies in the normal course.