An order analysis of the particle–hole propagator

The particle–hole propagator is examined in terms of orders in electron repulsion. The order analysis is accomplished by expressing the equation of motion for the particle–hole Green’s function in the superoperator formalism and by using the inner projection technique to represent the superoperator resolvent. A particular choice of the projection manifold leads to a propagator which is consistent through third order in electron repulsion and in addition contains terms which are important for the description of the collective motions in medium size systems. Our decoupling approach is compared with a diagrammatic perturbation expansion, and with the higher random-phase approximation, and the self-consistent polarization propagator approximation. The latter two approximations, with two-particle, two-hole corrections, are shown to be consistent through second order in electron repulsion. Finally, we demonstrate that approximate propagator methods give a more balanced description of an excitation process than approximate configuration interaction calculations.