Theoretical Study of Non-Markov Effects on Singlet Fission Dynamics of Model Pentacene Dimers Using the Second-Order Time-Convolutionless Quantum Master Equation Method

Abstract

Non-Markov effects on singlet fission (SF) dynamics of model pentacene dimers are investigated using the second-order time-convolutionless quantum master equation method with the state-independent (SI)/dependent (SD) spectral density of vibronic coupling for each diabatic exciton state. It is found on the early time scale (∼80 fs) that, as compared to Markov dynamics, non-Markov dynamics using the SD spectral density causes a significant increase of the double-triplet (TT) population by 15%, though the SI one just causes a negligible variation (∼3%) of the TT population. The difference in the non-Markov effects between the cases of using SI and SD spectral densities is found to be related to the frequency giving the peak of spectral density for the charge-transfer (CT) state (which is concerned with amplification of the non-Markov population relaxation) and the amplitude of the spectral density for the TT state at the energy gap between high-lying CT-like (CT′) and TT-like (TT′) adiabatic states (which is concerned with acceleration of the non-Markov population relaxation from the initial (Frenkel exciton (FE)-like; FE′) to the final (TT′) adiabatic states). We also examine the dependence of non-Markov effects on the energy gap between FE′ and TT′ states using SD spectral densities. It turns out (i) that non-Markov effects depend on the relationship between the SF time scale and the detuning degree between the peak frequency of the primary contributing spectral density and the energy gap between the related adiabatic exciton states, and (ii) that they appear more significantly in the case of the detuning degree closer to the SF time scale. The obtained results reveal the conditions for inducing the non-Markov effects in realistic SF materials and thereby pave the way toward constructing design guidelines for highly efficient SF systems based on non-Markov dynamics.