Bridging steady-state and time-domain descriptions of molecular electron transport

Electron transmission from an input electrode, through a molecular system, to an output electrode has been widely studied using the steady-state non-equilibrium Green's function (NEGF) method. Recently, the wave packet method, which provides access to the transient dynamics of electrons as well as internal molecular degrees of freedom, has been employed to investigate enantiospecific electron transport through chiral molecules. In this work, we derive the quantitative relation between the transmission of a finite-size wave packet and the energy-resolved NEGF transmission, showing that the former corresponds to a spectral average of the latter weighted by the wave packet energy distribution. Exploiting this correspondence, we construct non-Gaussian auxiliary wave packets whose spectral weight encodes the Landauer energy-window, allowing current-voltage characteristics to be obtained directly from time propagation. We further show that the correspondence extends to spin-resolved transport in a spin-phonon model of chirality-induced spin selectivity.