Coupled perturbation theory within the antisymmetrized product of separated geminals (APSG) framework

A coupled perturbation theory for the antisymmetrized product of separated geminals (APSG ) approximation is derived. The variational principle for the APSG wave function in an external oscillating field is employed and a set of equations of the form analogous to the normal RPA is obtained. At this level the reduced resolvent in the form of a spectral expansion is written and it is used for the evaluation of the second-order properties.