Theoretical study of charge carrier transport in organic molecular crystals using the Nakajima-Zwanzig-Mori generalized master equation.

There has been a long history of applying the generalized master equation (GME) to study charge carrier and exciton transport in molecular systems. Yet exact memory kernels in the GME are generally difficult to obtain. In this work, exact memory kernels of the Nakajima-Zwanzig-Mori GME for a one dimensional Holstein type of model are calculated by employing the Dyson relation for the exact memory kernel, combined with the hierarchical equations of motion method. Characteristics of the exact memory kernels, as well as the transition rate constants within the Markovian approximation, are then analyzed for different sets of parameters ranging from the hopping to bandlike transport regimes. It is shown that, despite the memory effect of the exact kernels, the Markovian approximation to the exact GME can reproduce the diffusion constants accurately. We also investigate the validity of the second and fourth order perturbation theories with respect to the electronic coupling constant in calculating the rate constants and the diffusion constant. It is found that, due to the cancellation of errors, the second order diffusion constant gives a reasonable estimate of the exact one within a wide range of electronic coupling constants.