Ab initio Force Constant Approach to Phonon Dispersion Relations of Diamond and Graphite

The phonon dispersion relations of diamond and graphite are calculated using an ab initio force constant method. The force constants are calculated via a self-consistent supercell approach in the local-density approximation in terms of the Hellmann-Feynman forces induced by the displacement of a single atom in the supercell. For diamond our ab initio results are in very good agreement with the neutron inelastic scattering and Raman data. For graphite we find good agreement with the neutron data for the low-energy modes as well as with the reflections electron energy loss spectroscopy (REELS) and optical data at higher energies. Significant differences to the predictions of semi-empirical models appear.