Charge transport in organic semiconductors: assessment of the mean field theory in the hopping regime.

The performance of the mean field theory to account for charge transfer rate in molecular dimers and charge transport mobility in molecular stacks with small intermolecular electronic coupling and large local electron-phonon coupling (i.e., in the hopping regime) is carefully investigated against various other approaches. Using Marcus formula as a reference, it is found that mean field theory with system-bath interaction and surface hopping approaches yield fully consistent charge transfer rates in dimers. However, in contrast to the dimer case, incorporating system-bath interaction in the mean field approach results in a completely wrong temperature dependence of charge carrier mobility in larger aggregates. Although the mean field simulation starting from the relaxed geometry of a charged molecule and neglecting system-bath interaction can reproduce thermally activated transport, it is not able to characterize properly the role of additional nonlocal electron-phonon couplings. Our study reveals that the mean field theory must be used with caution when studying charge transport in the hopping regime of organic semiconductors, where the surface hopping approach is generally superior.