  We review calculations and measurements of the phonon-dispersion relation of
graphite. First-principles calculations using density-functional theory are
generally in good agreement with the experimental data since the long-range
character of the dynamical matrix is properly taken into account. Calculations
with a plane-wave basis demonstrate that for the in-plane optical modes, the
generalized-gradient approximation (GGA) yields frequencies lower by 2% than
the local-density approximation (LDA) and is thus in better agreement with
experiment. The long-range character of the dynamical matrix limits the
validity of force-constant approaches that take only interaction with few
neighboring atoms into account. However, by fitting the force-constants to the
ab-initio dispersion relation, we show that the popular 4th-nearest-neighbor
force-constant approach yields an excellent fit for the low frequency modes and
a moderately good fit (with a maximum deviation of 6%) for the high-frequency
modes. If, in addition, the non-diagonal force-constant for the second-nearest
neighbor interaction is taken into account, all the qualitative features of the
high-frequency dispersion can be reproduced and the maximum deviation reduces
to 4%. We present the new parameters as a reliable basis for empirical model
calculations of phonons in graphitic nanostructures, in particular carbon
nanotubes.
