Model of mixed Frenkel and charge-transfer excitons in donor–acceptor molecular crystals: investigation of vibronic spectra

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The mixing of Frenkel excitons (FEs) and charge-transfer excitons (CTEs) in a molecular stack of regularly arranged donor (D) and acceptor (A) molecules is considered a model case and its vibronic line shapes have been calculated for several parameter sets. The two types of excitons (FE and CTE) are coupled linearly and quadratically with one vibrational mode of the D molecule (or of the A molecule). Using the methods of canonical transformation and of Green's functions (at T=0), as well as the vibronic approach which is applicable in the case of a narrow exciton band, the linear optical susceptibility is calculated for the three spectral regions: (a) excitonic, (b) one-phonon vibronics, and (c) two-phonon vibronics. As the study is directed to centrosymmetrical stacks, the cases of mixing of gerade excitons and of ungerade excitons have been treated separately in the calculation of the linear absorption coefficients. Because until now experimental observations of FE–CTE mixing in DA charge-transfer systems are absent, the numerical calculations have been performed for hypothetical sets of parameters which include: the parameters of CTEs in DA stacks (like anthracene–PMDA) and the parameters of FE–CTE mixing in a one-component stack (like that of PTCDA). The simulations establish the main features of the excitonic and vibronic spectra in the case of FE–CTE mixing, namely (i) the mutual influence on the positions and on the absorption intensities of all terms of the vibronic progressions stemming from FE and CTE levels; (ii) in the case of vibration of an A molecule (if the FE is assumed to be an excited electronic state of the D molecule), only one vibronic progression is manifest and the vibronic levels closer to the FE will be most enhanced; (iii) the redistribution of the absorption intensities depends on the sign of the mixing constant and may be so strong that the terms of the two vibronic progressions could have comparable absorption; (iv) spectral lines of different shape correspond to the bound and unbound exciton–phonon states; and (v) in the case of mixing of gerade excitons its possible impact on the absorption of the ungerade CTE-combination connected with the noncentral part k≠0 of the Brillouin zone was established. The simulation of the FE–CTE mixing can be useful in the assignment of the linear absorption spectra and in the description of the FE–CTE–vibration coupling.