In the Dyson equation, the self-energy describes all relaxation and correlation corrections to Koopmans's theorem. Energy-independent contributions to the self-energy depend on the one-electron reduced density matrix of the reference state. Three formalisms for calculating these terms are considered: perturbation theory, coupled-cluster theory, and contour integral theory. In one method, combinations of coupled-cluster singles and doubles amplitudes are substituted for first-order double excitation coefficients and for second-order single excitation coefficients. Another approach generates a description of reference state correlation through the evaluation of approximate contour integral expressions. Calculations on electron binding energies of closed-shell molecules and anions reveal that the coupled-cluster results for the energy-independent self-energy terms are closer to the perturbative results than to the contour integral values. © 1993 John Wiley & Sons, Inc.