Inclusion of exact exchange in the noniterative partial-differential-equation method of electron-molecule scattering: Application to e-N2.

Abstract

A method for including exchange exactly in the framework of the noniterative partial-differential-equation (PDE) approach [Phys. Rev. A 28, 621 (1983)] to electron-molecule scattering is presented. The method consists of breaking down the exchange equation into a set of inhomogeneous equations without integral terms. The difference form of the latter can then be solved by a straightforward generalization of the uncoupled noniterative PDE technique. Application is made to e-${\mathrm{N}}_{2}$ scattering in the fixed-nuclei approximation. The method is checked by comparing with other static- (exact) exchange calculations; agreement is found to be satisfactory particularly with new (unpublished) linear-algebraic results of Collins. A polarization potential, previously derived on the basis of a polarized-orbital treatment generalized to molecular targets, is then added; comparison is made with our previous results based on a Hara local exchange (HFEGE) approximation. The results show that HFEGE, as we had previously modified it, was less attractive than exact exchange. With exact exchange we are led alternatively to weaken the short-range part of the polarization potential with the consequence that agreement with other (exact) exchange-adiabatic calculations is excellent. The modified polarization potential is expected to be very useful in more elaborate scattering calculations.