  We investigate the influence of diffraction on the statistics of energy
levels in quantum systems with a chaotic classical limit. By applying the
geometrical theory of diffraction we show that diffraction on singularities of
the potential can lead to modifications in semiclassical approximations for
spectral statistics that persist in the semiclassical limit $\hbar \to 0$. This
result is obtained by deriving a classical sum rule for trajectories that
connect two points in coordinate space.
