Exchange perturbation theory. IV. Calculations on H2+

Abstract

We have applied the two localized-wave-function (LW) exchange- perturbation-theories (EPT) which we have proposed, to the 1sσg and 2pσu states of H2+ with the objective of verifying the insights gained from these EPT’s and of testing their accuracy. The one LW EPT determines a primitive wave function identical to that of the Eisenschitz–London EPT through first order, but which differs from it in all higher orders. The other determines a function identical to that of the Hirschfelder–Silbey EPT through first order and through infinite order, but which differs from it through all intermediate orders. We find that in terms of the perturbation expansion of the interaction energy through third order, our EPT’s are as accurate as the original EPT’s to which they are related. The LW EPT’s have the conceptual asset that their primitive wave functions are least distorted from the zero order wave function in a precisely defined sense. We have also calculated interaction energies using the integrals which define the interaction energies in terms of LW’s, and substituting the LW’s approximated by sums through first, second, and third order. The energies generally increase in accuracy as the LW is summed to higher orders. When each order contribution to the LW is multiplied by a weight which is determined to minimize the interaction energy, and the LW is summed through third order, the interaction energy is in error by 0.07% or less for nuclear separations ranging from 1.0 to 10.0 bohr. An examination of the LW’s shows how the optimization procedure works. Other quantities are calculated which show that the LW EPT’s are systematically refinable methods for the calculation of LW’s as well as for the calculation of interaction energies. This is important because LW’S may be used to calculate distinct ’’physical’’ contributions to interaction energies.