  An approximate method based on adiabatic time dependent density functional
theory (TDDFT) is presented, that allows for the description of the electron
dynamics in nanoscale junctions under arbitrary time dependent external
potentials. In this scheme, the density matrix of the device region is
propagated according to the Liouville-von Neumann equation. The semi-infinite
leads give rise to dissipative terms in the equation of motion which are
calculated from first principles in the wide band limit. In contrast to earlier
{\em ab-initio} implementations of this formalism, the Hamiltonian is here
approximated by a density expansion in the spirit of the density functional
based tight-binding (DFTB) method without introducing empirical parameters.
Results are presented for two prototypical molecular devices and compared to
calculations at the full TDDFT level. The issue of non-existence of a steady
state under certain conditions is also briefly touched on.
