Contribution of correlation and relaxation to generalized overlaps for outer-valence ionization

Abstract

In the generalized overlap approximation (GOA) and under appropriate experimental conditions, the electron momentum spectroscopy (EMS) triple differential cross section is proportional to the spherically averaged momentum distribution (MD) of the generalized overlap (GO) of the electronic wavefunctions of a parent molecule and its daughter cation. The GO is usually further approximated by the target Hartree-Fock approximation (THFA) which treats the parent wavefunction as uncorrelated. Improvements in EMS resolution have made it increasingly desirable to go beyond the THFA. This necessarily means taking parent correlation into account, but the relative importance of relaxation and ion correlation is not immediately obvious. In the present paper, finite-order nondegenerate perturbation theory (FOND PT) is used to derive explicit correction terms for the THFA. Although our result is equivalent to the previous formula of Pickup and Goscinski, our formulation is an improvement because it is easily interpreted in terms of wavefunctions. This makes the correction terms for the frozen orbital and target Hartree-Fock approximations particularly obvious. These correction terms are used to examine the relative importance of relaxation and ion correlation for outer valence ionization for a certain class of ion states which we call lone symmetry states. This symmetry restriction allows us to simplify our calculations of generalized overlaps (GOs) by ignoring second-order FOND PT contributions to the ion wavefunction. Although we find ion correlation to be of negligible importance when calculating GOs to second order in FOND PT for ionization out of the 1b 1, and 1b 2 orbitals of water and out of the π bonds of acetylene and ethylene, we find that these are isolated cases. In general, both relaxation and ion correlation are found to be significant for the calculation of GOs. Our work should make it quite clear that GOs are really neither purely an “initial-state” nor purely a “final-state” phenomenon, but rather involve contributions from both states. This bodes ill for the success of initial-state approximations for calculating GOs unless these approximations can in some way account for both relaxation and final-state correlation.