Abstract
The Born effective charges of component atoms and phonon spectra of tetrahedrally coordinated crystalline ice are calculated using the first principles method based on density functional theory within the generalized gradient approximation with the projected augmented wave method. The phonon dispersion relations in a 3× 1× 1 supercell were evaluated from Hellmann–Feynman forces with the direct method. This calculation is in addition to the direct method of calculating the phonon spectra, which does not take into account the polarization charges arising from the dipole interaction of molecules of water in the ice. The calculated Born effective polarization charges from linear response theory are supplied as correction terms to the dynamical matrix in order to further investigate the LO–TO splitting of the polar modes of ice crystals at k=0, which has long been speculated for this system, especially in the region between 28 and 37 meV, both in theoretical and experimental studies. Our results clearly show evidence of splitting of longitudinal and transverse optic modes at the k=0 point, in agreement with experimental findings.
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