Charge carrier dynamics in phonon-induced fluctuation systems from time-dependent wavepacket diffusion approach.

A time-dependent wavepacket diffusion method is proposed to deal with charge transport in organic crystals. The electron-phonon interactions in both site energies and electronic couplings are incorporated by the time-dependent fluctuations which are generated from the corresponding spectral density functions. The numerical demonstrations reveal that the present approach predicts the consistent charge carrier dynamics with the rigorous quantum approaches. In addition, the diffusion coefficients obtained from the Marcus formula are well reproduced at the weak electronic coupling and high temperature limits. It is also found that the charge mobility feature of the crossover from the band-like to the hopping-type cannot be predicted from the fluctuations induced by the linear electron-phonon interactions with an Ohmic spectral density; however, it indeed appears as the electronic coupling fluctuation exponentially depends on the nuclear coordinates. Finally, it should be noted that although the present approach neglects the imaginary fluctuation, it essentially incorporates the coherent motion of the charge carrier and quantum effect of the phonon motion with a broad regime of the fluctuations for symmetric systems. Besides, the approach can easily be applied to systems having thousands of sites, which allows one to investigate charge transport in nanoscale organic crystals.