On the proton kinetic energy in H₂ O and in nanotube water

We calculated the kinetic energies of the H-atom in ice Ih between 5 and 269 K and in water in the range 293-673 K. To do so we used the literature optical vibration frequencies of ice and water of the different phases assuming the harmonic approximation and decoupling between the degrees of freedom of translation, rotation (libration), and internal vibrations. Apart for ice at 269 K, good agreement was obtained with published experimental values for both cases. Similar agreement with experiment was found for the case of water confined in 14 Å diameter carbon nanotubes at 268 K. However, serious deviations from measured values were found in nanotube water in the range 5-230 K. Possible reasons for those deviations are discussed.