Quantum Master Equation Approach to Singlet Fission Dynamics in Pentacene Linear Aggregate Models: Size Dependences of Excitonic Coupling Effects.

The singlet fission (SF) dynamics of pentacene linear aggregate models are investigated using the quantum master equation method by focusing on the Frenkel excitonic (FE) coupling effects on the SF rate and double triplet (TT) yield as well as on their aggregate size dependences. It is found that for the dimer model, unrealistically large FE couplings are needed to provide significant effects on the SF dynamics, while for the larger aggregate models a realistic FE coupling causes significant variations in the SF dynamics: as increasing the aggregate size, the SF rate rapidly increases, attains the maximum at 8-mer (~3 times enhancement as compared to the non-FE-coupling case) and then decreases, approaching a stationary value after 12-mer, although the stationary TT yield at 20-mer remains slightly smaller than that in the non-FE-coupling case. These features are explained based on the relative relaxation factors between the adiabatic exciton states. The present results contribute to constructing the design guidelines for highly efficient SF aggregates.