Ice under pressure: Transition to symmetrical hydrogen bonds

We have examined at a rudimentary level the quantum-mechanical many-body problem for coupled proton motions along hydrogen bonds in compressed ices. Four cases are considered: ice Ic, ices VII and VIII, and the hypothetical planar "square ice". Soft mode calculations were carried out for each to help identify patterns of long-range proton order that contribute to the ground state. With a two-level description of each hydrogen bond, and the Hartree approximation, a phase transition in the ground state is predicted to occur when the oxygen neighbor spacing has been reduced sufficiently. This transition can be viewed as an "ionization catastrophe", and in fact such is expected to occur at all temperatures in the phase diagram of water at which ices VII and VIII experimentally are encountered.