Non-Markovianity Measurement and Coherent Modified Redfield Theory in Simulating Dynamics of Excitation Energy Transfer

Excitation energy transfer (EET) is a crucial process in many natural and artificial light-harvesting systems. Such process may occur when the energies of two weakly coupled electronic excitations are matched, which is widely recognized as a Förster resonance energy transfer. However, EET can also occur through a relaxation process especially for the cases, where the interaction between the interested system and its external environment is weak. This process is called a Redfield energy transfer. A successful theoretical method to simulate EET dynamics strongly depends on how to solve the balance between the two limits. In this study, we first investigate the shortcoming of the Markovian Redfield theory, which is widely used in simulating energy relaxation in molecular systems. We show that for general initial conditions, Markovian Redfield theory almost always yields dynamics that violates the positivity requirement for density matrices particularly on strong electron-phonon coupling and high temperature, making the theory inadequate for simulating EET in molecular systems. It is evident that the non-Markovian effects cannot be ignored in most situations. We then adopt the positivity violation to establish a non-Markovianity measure to quantify non-Markovian effects. To remedy the Redfield approach, a coherent modified Redfield theory was recently developed. Compared to traditional Förster and Redfield theory, the CMRT has a wider range of applicability resulting from the smaller perturbation and inclusion of multiphonon relaxation. In addition, by using a secular approximation to retain the major pathways in dissipation process, the secular CMRT can not only reduce the computational cost, but also capture the important coherent dynamics. In this work, the accuracy of CMRT is comprehensively investigated in the comparisons with numerically exact path-integral method. The results reveal an important role of “dynamical localization” when the coherence effect is overestimated. Finally, we apply the CMRT to study non-Förster EET dynamics in a silylene-spaced copolymer system. We reproduce the absorption and fluorescence spectra of the systems and derive parameters from spectral fitting. The parameters are subsequently used to calculate the EET dynamics, which allows us to describe both Förster and non-Förster dynamics in the system. We also investigated the effects of static energetic disorder on EET dynamics, which shows several dynamical groups with different EET rates. The energetic disorder causes a distribution of delocalization lengths, where the longer delocalization lengths characterized by strongly coherent systems is accounted for the fast dynamics. In summary, we examine the applicability of Markovian Redfield theory and simulate the EET dynamics with newly developed CMRT.