The electron propagator is calculated for a set of closed-shell atoms using GW-like self-energies that contain the coupling of single-particle degrees of freedom with excited states in the framework of the random phase approximation. The effect of including exchange diagrams is investigated. Calculations are performed in the Hartree-Fock (HF) basis of the neutral atom. The HF continuum is taken into account using a discretization procedure, and the basis set limit is estimated using a systematic increase of basis set size. We check the approximation of taking the self-energy diagonal in the HF basis, and to what extent the extended Koopman’s theorem is fulfilled using an approximate self-energy. Finally we try to model the information contained in the propagator in terms of a functional containing Hartree-Fock quantities and demonstrate the feasibility of simultaneously reproducing the correlation and ionization energy of an underlying ab initio model.