Results of the Hartree-Fock-Wigner model for He, and LiH using an atomic and a molecular parameterization of the correlation kernel are presented and interpreted in terms of Wigner intracules. The purely atomic parameterization turns out to be insufficient for molecules and is replaced by a fit along the potential curve on a per-molecule basis. It is argued that the remaining shortcomings partly result from the restriction of the currently used correlation function to be symmetric in relative position and momentum. (c) 2005 Elsevier B.V. All rights reserved.