The Second-Order Polarization Propagator Approximation is a generalization of the SCF linear response function [49,50,51]. In SOPPA, the SCF reference wave function in the linear response function or polarization propagator is replaced by a Møller-Plesset wave function and all matrix elements in the response function are then evaluted through second order in the fluctuation potential. This implies that electronic excitation energies and oscillator strenghts as well as linear response functions are correct through second order. Although it is a second-order method like MP2, the SOPPA equations differ significantly from the expressions for second derivatives of an MP2 energy.
In the Second Order Polarization Propgator Approximation with Coupled Cluster Singles and Doubles Amplitudes [SOPPA(CCSD)], the Møller-Plesset correlation coefficients are replaced by the corresponding coupled cluster singles and doubles amplitudes [53,52,63,60]. SOPPA(CCSD) is not a coupled cluster linear response function as they are implemented in the CC modules of Dalton program. However, the equations are essentially the same as for SOPPA.