Accurate Perturbation-Variation Treatment of the Hydrogen Molecule

A Rayleigh-Schrödinger perturbation treatment of electron repulsion in the ground state of the hydrogen molecule is presented. The perturbation energies were accurately determined from Hylleraas-type variational principles using a 50-term basis. The perturbation series appears to converge rapidly at the equilibrium distance, in a similar fashion to the series for the united atom, helium, obtained by Scherr and Knight (1963). The electronic energy through fifth order is − 1.88872 hartree, which is comparable with the straight variational result of − 1.88876 obtained by Kolos and Wolniewicz (1964).