We investigated the structural and dynamical properties of a tetrahedrally coordinated crystalline ice from first principles based on density functional theory within the generalized gradient approximation with the projected augmented wave method. First, we report the structural behaviour of ice at finite temperatures based on the analysis of radial distribution functions obtained by molecular dynamics simulations. The results show how the ordering of the hydrogen bonding breaks down in the tetrahedral network of ice with entropy increase in agreement with the neutron diffraction data. We also calculated the phonon spectra of ice in a 3x1x1 supercell by using the direct method. So far, due to the direct method used in this calculation, the phonon spectra is obtained without taking into account the effect of polarization arising from dipole-dipole interactions of water molecules which is expected to yield the splitting of longitudinal and transverse optic modes at the Gamma-point. The calculated longitudinal acoustic velocities from the initial slopes of the acoustic mode is in a reasonable agreement with the neutron scatering data. The analysis of the vibrational density of states shows the existence of a boson peak at low energy of translational region a characteristic common to amorphous systems.
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