  The Born effective charges of component atoms and phonon spectra of a
tetrahedrally coordinated crystalline ice are calculated from the first
principles method based on density functional theory within the generalized
gradient approximation with the projected augmented wave method. Phonon
dispersion relations in a 3x1x1 supercell were evaluated from Hellmann-Feynman
forces with the direct method. This calculation is an additional work to the
direct method in calculating the phonon spectra which does not take into
account the polarization charges arising from dipole interaction of molecules
of water in ice. The calculated Born effective polarization charges from linear
response theory are supplied as the correction terms to the dynamical matrix in
order to further investigate the LO-TO splitting of the polar modes of ice
crystal at k=0 which has long been speculated for this system especially in the
region between 28 and 37 meV both in the theoretical and experimental studies.
Our results clearly show the evidence of splitting of longitudinal and
transverse optic modes at the k=0-point in agreement with some experimental
findings.
