Direct diagrammatic construction scheme for the inelastic propagator between simply excited states

We develop a direct diagrammatic construction scheme for the inelastic propagator, which describes inelastic scattering processes. Starting from the previously presented "direct approach" to the inelastic propagator, which involves a higher-order elastic Green's function, we show how one can obtain the inelastic propagator for simple excitations without actually evaluating all the diagrams for the higher-order Green's function. The three cases where either the target molecule itself or its cation or anion is a closed-shell system are discussed. A generalization of the method to obtaining inelastic propagators between higher excitations is briefly addressed.