Quantum master equation approach to singlet fission dynamics in pentacene ring-shaped aggregate models

Abstract

The quantum master equation approach is applied to the singlet fission (SF) dynamics of pentacene ring-shaped aggregate models to clarify the Frenkel excitonic (FE) coupling effects on the SF rate and correlated-triplet pair (TT) yield as well as their dependences on the aggregate structure and size. Interestingly, the smallest ring model, a ring-shaped trimer, is found to exhibit a significantly smaller SF rate and a slightly smaller TT yield than those of the dimer model with the same intermonomer interaction and to show remarkable variations in the SF dynamics with increasing the FE coupling. With increasing the size of the aggregates with FE coupling, it is found that the SF rate rapidly increases, attains the maximum at 17-mer (∼3 times enhancement compared to the non-FE-coupling case), and then decreases, approaching a stationary value around 25-mer, while the almost stationary TT yield at 25-mer remains 16% smaller than that in the non-FE-coupling case. These features are found to be in qualitative agreement with those in the corresponding linear aggregates, although the aggregate size gives a maximum SF rate, and the values of the maximum SF rate as well as of the converged TT yield are different between the ring-shaped and linear aggregates. These results are interpreted based on the relative relaxation factors between the adiabatic exciton states as well as on the vibronic coupling effects. The present results contribute to a deeper understanding of the aggregate structure and size dependences of SF dynamics and to constructing the design guidelines for highly efficient SF aggregates.