Note that with these definitions, V CS + V WW = V . Furthermore, note that due to the E(nH 2 O) term in V CS , the complex-shell energy excludes many-body effects on the interaction energy among the waters alone, e.g. polarization of water by water itself, but includes them in between the complex and the solvent. Such many-body effects are not included in the MM model. Figure shows that, for both models, V starts out more negative in the HS state than in the LS state, but as n increases, the total difference in interaction energies of the two states decreases. Interestingly, the difference in B3LYP-D3(BJ) complex-shell interaction energies, V CS (red line), are indiscernible within chemical accuracy between the two states, meaning that if only the direct interactions between solute and solvent existed, there should be no change in the solvation shell structure. The water-water interaction energies, V WW , are more stable in the HS states, however, although this difference is reduced with increasing numbers of water in the shell. This reduction is consistent with the aforementioned finding that the waters would need to rearrange themselves less for larger shells.