  While the vast majority of calculations reported on molecular conductance
have been based on the static non-equilibrium Green's function formalism
combined with density functional theory, in recent years a few time-depedent
approaches to transport have started to emerge. Among these, the driven
Liouville-von Neumann equation (J. Chem. Phys. 124, 214708 (2006)) is a simple
and appealing route relying on a tunable rate parameter, which has been
explored in the context of semi-empirical methods. In the present study, we
adapt this formulation to a density functional theory framework and analyze its
performance. In particular, it is implemented in an efficient all-electron DFT
code with Gaussian basis functions, suitable for quantum-dynamics simulations
of large molecular systems. At variance with the case of the tight-binding
calculations reported in the literature, we find that now the initial
perturbation to drive the system out of equilibrium plays a fundamental role in
the stability of the electron dynamics, and that the equation of motion used in
previous tight-binding implementations has to be modified to conserve the total
number of particles during time propagation. Moreover, we propose a procedure
to get rid of the dependence of the current-voltage curves on the rate
parameter. This method is employed to obtain the current-voltage characteristic
of saturated and unsaturated hydrocarbons of different lenghts, with very
promising prospects.
