While we have shown that it is possible to map the two non-interacting electron densities to the energy of the interacting system (Equation ), the same cannot be stated for mapping the non-interacting electronic density to the electronic density of the interacting system, that is, the map (ρ A , ρ B ) → ρ AB will normally not exist since there exist instances with more than one ground state of the interacting system (AB) in case of degeneracies. Furthermore, using the same argument but for the separated molecules instead it also follows that (globally) mapping the electronic density of the interacting system ρ AB to the electronic densities of the separated molecules ρ A and ρ B (or in other words ρ AB → (ρ A , ρ B )) is normally not possible either since one or both of the separated molecules may also have degenerate ground states.