  We present a new class of non-adiabatic approximations in time-dependent
density functional theory derived from an exact expression for the
time-dependent exchange-correlation potential. The approximations reproduce
dynamical step and peak features in the exact potential that are missing in
adiabatic approximations. Central to this approach is an approximation for the
one-body reduced density-matrix as a functional of the Kohn-Sham
density-matrix, and we demonstrate two such examples.
