Two methods for extracting ionization energies from the two-particle reduced density matrix (2-RDM) are explored: (i) diagonalization of the Hamiltonian in the basis of a single annihilation operator applied to the ground-state wave function |psi(g)> and (ii) diagonalization of the Hamiltonian in the basis of two annihilation and one creation operators applied to the ground-state |psi(g)>. While the second basis set is more accurate, its Hamiltonian matrix elements depend upon the 3- and 4-RDMs. Using cumulant theory, however, we can approximate the 3- and 4-RDMs as functionals of the 2-RDM. Both methods are illustrated with calculations on a series of atoms and molecules. (C) 2004 Elsevier B.V. All rights reserved.