Charge Mobility Prediction in Organic Semiconductors: Comparison of Second-Order Cumulant Approximation and Transient Localization Theory

In the last years, several theoretical models for the simulation of charge transfer in organic semiconductors have been developed. Two particularly interesting approaches, because of their low computational cost and high accuracy, are the transient localization theory (TLT) and the second-order cumulant expansion of the density matrix (SOC). In this work, we apply these models for the evaluation of charge carrier mobility of four prototypical molecules, that is, tetracene, pentacene, picene, and rubrene. Their relative performances in reproducing experimental data are discussed, and their predictions are compared with the outcomes of semiclassical Marcus theory. We focus on a simplified framework for the SOC model, resorting to constant transfer integrals and time-averaged kinetic constants, showing that, despite the rather severe approximations introduced, the results are in good agreement with the TLT approach and experimental data. The temperature dependence of the mobility is also analyzed for pentacene and rubrene, showing that SOC and TLT models lead to very similar results in good agreement with experimental evidences, while the Marcus approach leads to incorrect trends.