Extraction of ionization energies from the ground-state two-particle reduced density matrix

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 |Ψg〉 and (ii) diagonalization of the Hamiltonian in the basis of two annihilation and one creation operators applied to the ground-state |Ψg〉. 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.