Time-dependent density functional theory with ultrasoft pseudopotentials: Real-time electron propagation across a molecular junction

A practical computational scheme based on time-dependent density functional theory (TDDFT) and ultrasoft pseudopotentials (USPP) is developed to study electron dynamics in real time. A modified Crank-Nicolson time-stepping algorithm is adopted, under plane-wave basis. The scheme is validated by calculating the optical absorption spectra for a sodium dimer and a benzene molecule. As an application of this USPP-TDDFT formalism, we compute the time evolution of a test electron packet at the Fermi energy of the left metallic lead crossing a benzene-(1,4)-dithiolate junction. A transmission probability of 5-7%, corresponding to a conductance of 4.0-5.6 mu S, is obtained. These results are consistent with complex band structure estimates and Green's function calculation results at small bias voltages.