Phonon Frequencies of the Hexagonal Metals Be, Mg, and Zn

The phonon frequencies of hexagonal metals Be, Mg, and Zn are computed using the single-orthogonalized-plane-wave electron-ion matrix element and the dielectric function due to Singwi et al. The bare-ion potential is obtained by a modified Hartree-Fock-Slater scheme. The exchange potential is determined by the Kohn-Sham approach, and the correlation corrections are included according to the prescription of Robinson et al. The calculated phonon frequencies of these metals are in good agreement with the neutron spectrometric measurements, except for Zn in the [$01\overline{1}0$] direction. The phonon frequencies for these metals are also calculated for different $\frac{c}{a}$ ratios.