Theoretical study of exciton-exciton annihilation dynamics in the approximation of weak coupling

Dynamics of exciton-exciton annihilation (EEA) in molecular aggregates is closely related to its luminescence characteristics and energy transfer. It is meaningful to uncover energy and charge transfer process in molecular systems. Therefore, studying the dynamics of exciton is important for simulating photosynthesis in nature and analyzing the transport process of photocarriers. In this paper the weak coupling approximation is adopted to obtain the rate equation in the framework of density matrix theory. The relation among the intermolecular distance, exciton state density, excited state dipole moment and exciton-exciton annihilation dynamics is studied by the rate equations. It is found that the decrease of intermolecular distance leads the generation rate of higher-order excited states to increase, resulting in the obvious S-shaped decay characteristics. Moreover, the dipole moment of the higher-order excited state is the key factor of the exciton fusion process, and the greater the exciton density, the more easily the exciton fusion process occurs. Therefore, the reduction of intermolecular distance and the increase of the dipole moment of the higher-order excited state make the nearest neighbor molecules have a strong coupling, resulting in a high generation rate of the higher-order excited state. It is found that the evolution processes of the first excited state in different exciton densities are consistent with the experimental results of the excitation of OPPV7 monomer (PPV oligomers of 7) at a low excitation energy, and the excitation of OPPV7 aggregates at different excitation energy levels. It can be observed that the exciton decay rate is faster under the excitation of the strong external field. Using the quantum wave packet under optical excitation as the initial state, the excited state dynamics is simulated at different exciton energy levels. It is found that the exciton state can maintain good locality within a few hundreds of femtoseconds, which shows that the exciton state is a coherent superposition state, and its local characteristics are related to the excitation energy level. These conclusions are applicable to the aggregations whose single molecule has an energy level of \begin{document}${E_{mf}} \approx 2{E_{me}}$\end{document}, and also provide a reasonable reference for the exciton-exciton annihilation process under optical excitation.