Pauling’s successful estimation of the residual entropy of hydrogen-disordered ice was based on the homogeneity of the binding energy of individual water molecules in ice. However, it has not been explained why the binding energies are homogeneous although the pair interaction energy of hydrogen-bonded dimers distributes widely. Here, we provide a rationale for this phenomenon. The topological constraints imposed by the ice rules, in which water molecules form directed cyclic paths of hydrogen bonds, cancel out the variability of local interactions. We also show that the cancellation mechanism does not work due to some imperfect cyclic paths on the surface of ice. Such water molecules do not enjoy homogeneity in the bulk state and suffer from a wide spectrum in the binding energy.
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