  The dynamical properties of an extended Hubbard model, which is relevant to
quarter-filled layered organic molecular crystals, are analyzed. We have
computed the dynamical charge correlation function, spectral density, and
optical conductivity using Lanczos diagonalization and large-N techniques. As
the ratio of the nearest-neighbour Coulomb repulsion, V, to the hopping
integral, t, increases there is a transition from a metallic phase to a charge
ordered phase. Dynamical properties close to the ordering transition are found
to differ from the ones expected in a conventional metal. Large-N calculations
display an enhancement of spectral weight at low frequencies as the system is
driven closer to the charge ordering transition in agreement with Lanczos
calculations. As V is increased the charge correlation function displays a
plasmon-like mode which, for wavevectors close to (pi,pi), increases in
amplitude and softens as the charge ordering transition is approached. We
propose that inelastic X-ray scattering be used to detect this mode. Large-N
calculations predict superconductivity with dxy symmetry close to the ordering
transition. We find that this is consistent with Lanczos diagonalization
calculations, on lattices of 20 sites, which find that the binding energy of
two holes becomes negative close to the charge ordering transition.
