thus, all we are left to do is to show that ρ A and ρ B can be mapped to E AB . Estimating ρ AB by simply knowing ρ A and ρ B is likely to be problematic in many cases, especially in ones where two atoms of different molecules are placed at short distances. Since the HK theorem tells us that the external potentials of ψ A and ψ B are functionals of ρ A and ρ B respectively, it is possible to map the two electron densities to a set with the cartesian coordinates and atomic numbers of the atoms of both molecules, which is all information required to fully describe the Hamilton operator ĤAB of two molecules interacting with each other (Equation ).