Exchange energy of H2 calculated by the surface integral method in zeroth order approximation

Abstract

The surface integral method of Holstein and Herring is applied to the calculation of the exchange energy of the H2 molecule. This theory provides a means for calculating the exchange energy by taking into account the physical exchange of the two electrons with respect to the nuclei. Problems associated with symmetrization of the polarized wave functions which have encumbered previous attempts at developing a perturbation theory of the chemical bond are circumvented. Whereas the previous calculations using this method by Gor’kov and Pitaevski and Herring and Flicker were restricted to the asymptotic (R→∞) limit, in the present calculation we have used an extended formula to examine the validity also for the short range region down to R=0.5 a.u. In order to compare with the results of Heitler–London theory we have used the undisturbed zeroth order wave function of the H atoms in the calculations. An analytic expression is obtained for the exchange energy and the numerical results are found to be in good agreement with the exact calculations of Kolos and Wolnicwicz with an error of less than 20% for R≤8 a.u., where the zeroth order approximation is best justified. The agreement with the exact results is comparable to that of the original Heitler–London theory. The good agreement indicates that the basic assumption of the theory that electrons exchange places with respect to the nuclei is on a good physical basis and refutes previous textbook wisdom that the exchange energy cannot be given a simple physical interpretation.