Configuration interaction approach for the computation of the electronic self-energy

In order to properly understand the utility of many-body perturbation theory as applied to finite systems, we use the configuration interaction approach to compute the electronic self-energy. The validity of the commonly used GW approximation from many-body perturbation theory is tested by comparing the self-energy explicitly computed according to the diagrammatic expansions to that from the inversion of the Dyson equation. It is constructed as a functional of the interacting Green function G and screened Coulomb interaction W. W is explicitly computed through the diagonalization of the many-body Hamiltonian and, thus, takes polarization effects into account beyond the random phase approximation. The Na₉⁺ cluster and the dissociation of the C₂ molecule are discussed as examples. We find that the GW approximation yields accurate results for weakly correlated systems with a predominantly single-determinant ground state such as Na₉⁺ clusters. The C₂ molecule is a pathological system with multideterminantal ground state where the GW approach ceases to be valid.