Exchange and Coulomb Energy of H2 Determined by Various Perturbation Methods

Four different types of perturbation theories for the exchange forces between two atoms are applied to the ground and first excited state of the hydrogen molecule at internuclear separations R = 4,6,8a0. The energy through second order and the expectation value of the Hamiltonian using the wavefunction accurate through first order are calculated to compare the theories. The results for the Hirschfelder–Silbey procedure are satisfactory. The Murrell–Shaw or Musher–Amos results are equally good with the exception of the Hamiltonian expectation values for both states at R = 6 and 8a0, which are bad. The Eisenschitz–London, van der Avoird, or Hirschfelder (HAV) results are good at small separations but at large separations they give a second-order energy which appears to be about one-half the correct dispersion energy. The Rayleigh–Schrödinger treatment using a Sternheimer type of zeroth-order Hamiltonian gave the best energy for the ground state but not very good energy for the excited state. At the separations considered, deviations from the virial theorem are unimportant.