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We present a theoretical study on exciton–exciton annihilation (EEA) in a molecular dimer. This process is monitored using a fifth-order coherent two-dimensional (2D) spectroscopy as was recently proposed by Dostál et al. [Nat. Commun. 9, 2466 (2018)]. Using an electronic three-level system for each monomer, we analyze the different paths which contribute to the 2D spectrum. The spectrum is determined by two entangled relaxation processes, namely, the EEA and the direct relaxation of higher lying excited states. It is shown that the change of the spectrum as a function of a pulse delay can be linked directly to the presence of the EEA process.
This work focuses on theoretical approaches for predicting the valence and core excited states of aggregate systems. For the valence excitations, TD-HF and TD-DFT with different functionals have been tested at the Perylene bisimide (PBI) system. A simple character analysis method based on the calculated transition dipole moments is proposed. However, this method does not work for excited states without any transition dipole moment. Thus, we proposed a more general and more valid method based on a calculated CIS type wavefunction for the character analysis. Furthermore, a model Hamiltonian method is derived from a localized picture. The energies of the diabatic states and the corresponding coupling parameters were also determined on the basis of ab initio calculations. For the core excitation, three different methods were validated for C 1s-excited and ionized states if several small molecules. Also we tested the basis sets dependence of these core excited states. Based on those results, we chose the frozen core approximation method to evaluate the core excited states of NTCDA molecules. In order to explain the findings in the experiments, we developed an algorithm to evaluate the exciton coupling parameter where non-orthogonal MOs are used.