  By introducing the self-energy density functionals for the dissipative
interactions between the reduced system and its environment, we develop a
time-dependent density-functional theory formalism based on an equation of
motion for the Kohn-Sham reduced single-electron density matrix of the reduced
system. Two approximate schemes are proposed for the self-energy density
functionals, the complete second order approximation and the wide-band limit
approximation. A numerical method based on the wide-band limit approximation is
subsequently developed and implemented to simulate the steady and transient
current through various realistic molecular devices. Simulation results are
presented and discussed.
