The relationship between double excitation amplitudes and <i>Z</i> vector components in some post-Hartree-Fock correlation methods

The relationship between Z vector components and excitation amplitudes is analyzed for several post-Hartree-Fock correlation methods limited to double excitation amplitudes. An analytical formula approximating the Z vector for the coupled cluster doubles method is presented and shown to be quite accurate. This approximation is also used to determine the prefactor of the norm of doubly excited states in averaged coupled pair functional-type energy functionals self-consistently leading to better agreement with coupled cluster results.