  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.
