where χ s is the irreducible response kernel for the non-interacting system. We proved in our work that Dyson's equation is equivalent to the atom-condensed Kohn-Sham approximated to second order (ACKS2) method. In the ACKS2-type model, atomic property 1 P i was used to predict η e and the symmetrized pairwise interaction 1 I ij was used to predict χ s .