Proton dynamics in hydrogen-bonded systems

ABSTRACT: The proton mean kinetic energy Ke(H) in various systems was calculated between 5 and 320 K using a semi-empirical (SE) approach. The SE calculation relies on the harmonic approximation and decoupling between the various modes, where the input data of the internal and external frequencies were taken from inelastic neutron scattering (INS) and IR/Raman experiments. The studied systems included ordinary H₂O phases, water of crystallisation in sulphate salts, adsorbed water and water confined in various samples of pore dimensions less than 20 Å. These included some zeolites, periodic mesoporous organosilicas (PMOs), beryl, Bikitaite and single- and double-wall carbon nanotubes. All SE calculated Ke(H) values were close to that of pure ice/liquid water, for which a good agreement was found with the deep inelastic neutron scattering (DINS) measurements. However, for water in Beryl at 5 K and ice in carbon nanotubes, at 170 K, large deviations from DINS results were found. Some insight into this problem may be gained by comparing those deviations with recently studied anharmonic systems involving proton double well potentials: Rb₃H(SO₄)₂ and KH₂PO₄, where an excellent agreement was obtained between SE calculations and DINS measurements.