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The OH stretching vibrational spectrum of water was measured in a wide range of temperatures across the triple point, 269 K <T < 296 K, using Inelastic Neutron Scattering (INS). The hydrogen projected density of states and the proton mean kinetic energy, <EK>OH, were determined for the first time within the framework of a harmonic description of the proton dynamics. We found that in the liquid the value of <EK>OH is nearly constant as a function of T, indicating that quantum effects on the OH stretching frequency are weakly dependent on temperature. In the case of ice, ab initio electronic structure calculations, using non-local van der Waals functionals, provided <EK>OH values in agreement with INS experiments. We also found that the ratio of the stretching (<EK>OH) to the total (<EK>exp) kinetic energy, obtained from the present measurements, increases in going from ice, where hydrogen bonding is the strongest, to the liquid at ambient conditions and then to the vapour phase, where hydrogen bonding is the weakest. The same ratio was also derived from the combination of previous deep inelastic neutron scattering data, which does not rely upon the harmonic approximation, and the present measurements. We found that the ratio of stretching to the total kinetic energy shows a minimum in the metastable liquid phase. This finding suggests that the strength of intermolecular interactions increases in the supercooled phase, with respect to that in ice, contrary to the accepted view that supercooled water exhibits weaker hydrogen bonding than ice.

The quantum nature of the OH stretching mode in ice and water probed by neutron scattering experiments