  A decomposition of the exact exchange-correlation potential of time-dependent
density functional theory into an interaction component and a kinetic component
offers a new starting point for non- adiabatic approximations. The components
are expressed in terms of the exchange-correlation hole and the difference
between the one-body density matrix of the interacting and Kohn-Sham systems,
which must be approximated in terms of quantities accessible from the Kohn-Sham
evolution. We explore several preliminary approximations, evaluate their
fulfillment of known exact conditions, and test their performance on simple
model systems for which available exact solutions indicate the significance of
going beyond the adiabatic approximation.
