Atomic Z Expansions and Electronic Structure of Molecules: Second-Order One-Center Calculation of the Hydrogen-Molecule Ground State

Abstract

Double-perturbation theory is applied to calculate the ground state of the hydrogen molecule. In this treatment the unperturbed system is formed by the two noninteracting electrons moving in the field of a virtual nucleus of charge Z located halfway between the two hydrogen nuclei. The rest of the molecular Hamiltonian—electronic repulsion and the part of the electron—nuclear attraction—is treated as a perturbation. We determine the virtual charge Z from the variational principle for the total energy through first order. With this approach the total molecular energy of H2 can be built up from the energy Z expansion of (1s)2 1S, twice the exact electronic energy of 1sσ H2+, and correction terms of second and higher orders. Using the published results for (1s)2 1S and 1sσ H2+ we calculate the second-order corrections to get the equilibrium distance within 4% of the very accurate result obtained by Kol/os and Roothaan; our dissociation energy is 4.207 eV, 11% smaller than their value 4.747 eV.