A time-dependent momentum-space density functional theoretical approach for electron transport dynamics in molecular devices

We propose a time-dependent density functional theoretical (TDDFT) approach in momentum $(\mathcal{P})$ space for the study of electron transport in molecular devices under arbitrary biases. The basic equation of motion, which is a time-dependent integrodifferential equation obtained by Fourier transform of the time-dependent Kohn-Sham equation in spatial coordinate $(\mathcal{R})$ space, is formally exact and includes all the effects and information of the electron transport in the molecular devices. The electron wave function is calculated by solving this equation in a finite $\mathcal{P} $-space volume. This approach is free of self-energy function and memory term related to the electrodes in the $\mathcal{R} $ space and beyond the wide-band limit (WBL). The feasibility and power of the approach are demonstrated by the calculation of current through one-dimensional systems