Density-matrix coupled time-dependent exchange-correlation functional approximations

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.