A unique aspect of our model is its sole use of electron densities of the molecules of a system as if they are not interacting with each other in a, finite, sum obtained by means of consecutive applications of the Laplace operator to the densities. Using Hohenberg and Kohn's theorem, it is demonstrated that for non-degenerate cases mapping the non-interacting electron densities of the molecules to the energy of the interacting system is possible. This argument extends to systems with degenerate ground states in their non-interacting components through Levy's constrained search formulation. The main advantage of this approach is that besides requiring the usual molecular specification needed by any, full atom, force field model, e.g. Z-matrix, it only needs the partial charges, e.g. Mulliken, Löwdin charges, of every molecule in the system (when isolated) once a set of exchange and correlation coefficients are fitted against experimental or accurate ab initio reference data. However, these partial charges are treated as constants, which therefore makes our previous version of our model non-polarizable, and potentially too inaccurate for some systems.