  We review our previous work on the dynamic structure factor S(k,omega) of
liquid Ge (l-Ge) at temperature T = 1250 K, and of amorphous Ge (a-Ge) at T =
300 K, using ab initio molecular dynamics [Phys. Rev. B67, 104205 (2003)]. The
electronic energy is computed using density-functional theory, primarily in the
generalized gradient approximation, together with a plane wave representation
of the wave functions and ultra-soft pseudopotentials. We use a 64-atom cell
with periodic boundary conditions, and calculate averages over runs of up to 16
ps. The calculated liquid S(k,omega) agrees qualitatively with that obtained by
Hosokawa et al, using inelastic X-ray scattering. In a-Ge, we find that the
calculated S(k,omega) is in qualitative agreement with that obtained
experimentally by Maley et al. Our results suggest that the ab initio approach
is sufficient to allow approximate calculations of S(k,omega) in both liquid
and amorphous materials.
