Critical test of equation-of-motion–Green’s function methods. II. Comparison with configuration interaction results

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Abstract
A detailed comparison is presented between calculated equation-of-motion (EOM) ionization potentials and electron affinities and highly converged configuration interaction (Cl) results for a variety of atomic and molecular systems. Since an exact EOM calculation and a full Cl calculation within the same orbital basis set must yield identical results, this type of study allows for the separation of errors due to the approximations employed in solving the EOM equations from those errors arising from the use of an incomplete orbital basis set. The convergence of the EOM calculations at different levels of approximation is also investigated for these same systems. Important EOM basis operators, involving ionization and excitation (shakeup operators) or ionization and de-excitation, are numerically identified by configuration selection routines and are diagonalized rather than treated perturbatively. Terms involving second order couplings (arising from ground state correlation) between these shakeup states are calculated, as are the lowest order contributions from ionization and double excitation and from ionization and double de-excitation operators. These terms, which are normally neglected in EOM calculations, are found to be significant in certain cases. The agreement between the most sophisticated EOM and CI results is excellent for the molecular systems studied. The results justify the need for retention of higher order couplings, addition of double shakeup operators, and the adoption of a nonperturbative approach as described in paper I. The agreement is not as good for the atomic systems and possible reasons for these discrepancies are discussed.