Complete Lattice Vibration Dispersion Curves (36 Branches) for the Frozen (T=0K) Bernal-Fowler Hexagonal Close Packed Crystalline Ice with Four Water Molecules in One Primitive Unit Cell Containing 8 Protons and 4 Oxygen Nuclei*

In 1969, Faure computed the lowest 12 branches of dispersion curves of lattice vibrational modes for Ice Ih, assuming the water molecule H₂O in the crystalline ice as point mass (PM), in order to analyze the experimental infrared and Raman spectra of ice. In 1973, Bosi-Tubino-Zerbi removed the PM approximation of H₂O in the 1933 Bernal-Fowler Hexagonal Close Packed (HCP) Primitive Unit Cell (PUC) containing 4 H₂O (8 protons and 4 Oxygen nuclei) in order to account for the experimental spectra in the low vibrational frequency (LVF) range. During 1969-2019 (50 years) theoretical and experimental spectra of hexagonal Ice Ih are lacking in the high vibrational frequency (HVF) range. Our 2013 melted-ice model for pure liquid water, demonstrated the dominance of the HVF modes in accounting for the abnormally high mobilities of positive and negative ions in pure liquid water. This talk gives the computed 36 branches of dispersion curves of Ice Ih at 0K, using six prime force constants, four values of which from isolated water molecule, further proving the connection of water’s crystalline solid phase and single molecule gas phase, by our 2013 melted-ice lattice model for the liquid phase of water.