In this paper we focus on the non-perturbative approximation scheme we have introduced in the Section 2.3. To this end we have implemented derived formulas within the SAPT suite of codes, 32 and used the molpro2012 package for evaluation of the molecular integrals and the cluster amplitudes T 1 and T 2 . The linear equation for σ 11 is solved iteratively: in case of the closed-shell systems or UHF orbitals it is possible to extract from the first term of the Eq. 53 the dominant part which is (in closed-shell case) simply the orbital energy difference