As shown by our (CRJ's) lab, this expansion can be inserted into the DFT total energy functional to arrive at a generalization of Eq. ( ). Such a density-based many-body expansion converges significantly faster than the corresponding energy-based many-body expansion, in particular if it is combined with frozen-density embedding for the fragment calculations. For water clusters as well as ion-water clusters , it provides chemical accuracy (compared to the supermolecular calculation) already for a two-body expansion.