While it can be proved that there exists a functional that maps the non-interacting neutral ground states eigendensity of all the atoms in a polyatomic system to its interacting, not necessarily neutral, ground states eigendensity can be done using the modified Hohenberg-Kohn theorem, it does not provide an explicit formula for the map. As an ansatz, we model U AB as being a functional whose mathematical expression is identical to our exchange and correlation corrected interaction energy (Equation ), and whose polarization coefficients minimize it, akin to a self-energy minimization. However, the physical interpretation of this functional is dubious, thus, a set of different exchange and correlation coefficients are used to model the Mulliken charges. This separate set of exchange and correlation coefficients are obtained from least squares minimization against the Mulliken charges of the same dataset used to calibrate the interaction energy model.