Quantum yield of the charge-separated state in $\mathrm{Zn}$-porphyrin derivatives excited into the $S_2$ state

To investigate the effect of dynamic characteristics of a solvent on the kinetics of charge separation from the second singlet excited state and following charge recombination into the first singlet excited and ground states of $\mathrm{Zn}$-porphyrin-amino naphthalene diimide dyad in toluene the set of numerical simulations in the framework of the generalized stochastic point-transition approach has been performed. The model incorporates four electronic states (the first and the second singlet excited, the charge separated, and the ground states) as well as their vibrational sublevels corresponding to the excitation of intramolecular high frequency vibrational modes. The solvent motion to its equilibrium is described in the terms of three relaxation modes. The model explicitly describes the hot transitions from the charge separated state into the first excited state occurring in the course of the nuclear relaxation. For description of the intramolecular reorganization a realistic model considering up to $10$ high-frequency modes is used. The model has allowed us to get an quantitative fitting to the kinetics of the charge-separated state population of $\mathrm{Zn}$-porphyrinamino naphthalene diimide dyad in toluene solvent. Calculated population kinetics of the chargeseparated state re produces the experimentally observed kinetics of the charge separated state population. The fitting predicts the quantum yield of the charge separated state to be as large as $20\%$. Such a good fitting can be obtained only if the energy reorganization of intramolecular low frequency modes is extremely large. Although the model involves too many parameters and the set of the best fit parameters is not unique, we expect that the predicted value of the charge separated state yield is rather reliably estimated because a variation of these parameters does not strongly change this estimation.