Molecular Dynamics Simulations for Ice Modifications II and IX

Molecular vibrations of water (H2O and D2O) in crystals of ice II and ice IX are studied by molecular dynamics in a rigid bond approximation with a fixed bond angle. Using an atom-atomic potential PM for describing the interactions between water molecules in ice II (N = 576 molecules) and ice IX (N = 768) in an NVE ensemble leads to reproduction of the structure of both types of ice. For all water molecules and separately for each system of crystallographically equivalent water molecules in ice crystals, we defined the time dependence of the mean-square displacement of the center of mass of the molecule, the autocorrelation function of velocity for the center of mass, and the autocorrelation function of velocity for hydrogen (deuterium) atoms. The densities of vibrational states are calculated as Fourier integrals of the corresponding autocorrelation functions. In the case of ice II, the densities of states agree well with the experimental incoherent inelastic neutron scattering spectra. In the case of ice IX, agreement is worse. For both polymorphs, the mean-square displacement and the densities of vibrational states of the center of mass of the molecule and the hydrogen (deuterium) atom differ slightly between molecules belonging to different systems of crystallographic positions. This is explained by the difference in their environments.