  We identify peak and valley structures in the exact exchange-correlation
potential of time-dependent density functional theory that are crucial for
time-resolved electron scattering in a model one-dimensional system. These
structures are completely missed by adiabatic approximations which consequently
significantly underestimate the scattering probability. A recently-proposed
non-adiabatic approximation is shown to correctly capture the approach of the
electron to the target when the initial Kohn-Sham state is chosen judiciously,
and is more accurate than standard adiabatic functionals, but it ultimately
fails to accurately capture reflection. These results may explain the
underestimate of scattering probabilities in some recent studies on molecules
and surfaces.
