Hole Hopping Rates in Organic Semiconductors: A Second-Order Cumulant Approach

Second-order cumulant expansion of the time dependent reduced density matrix has been employed to evaluate hole hopping rates in pentacene, tetracene, picene, and rubrene homodimers. The cumulant expansion is a full quantum mechanical approach, which enables the use of the whole set of nuclear coordinates in computations and the inclusion of both the effects of the equilibrium position displacements and of normal mode mixing upon hole transfer. The time dependent populations predicted by cumulant approach are in good agreement with those obtained by numerical solution of time dependent Schrödinger equation, even for ultrafast processes, where the Fermi Golden Rule fails.