Fluorescence lifetimes of 9-(N-carbazolyl)-anthracene: Effects of intramolecular vibrational redistribution and electronic transitions in coupled bright and dark states

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Abstract
The fluorescence lifetimes of 9-(N-carbazolyl)-anthracene (C9A) in selected vibronic states |1̃ l〉 are calculated by means of a simple model. Specifically, the states |1̃ l〉 are excited to the bright electronic state S1 which is coupled to a dark state X, as well as to the l-th vibrational excitation of the torsional mode of C9A. The model takes into account the torsional moments of inertia of C9A, the empirical diabatic torsional potentials, the potential couplings, the dipole couplings, and the vibrational couplings between the torsion and the other vibrations of C9A. The corresponding model parameters are fit to the experimental spectra and fluorescence lifetimes of Monte et al. [J. Chem. Phys. 98, 2580 (1993)]. Three competing processes are described by the model, i.e.: (i) fluorescence from doublets of states |1̃ l,+〉 and |1̃ l,−〉 with + and − parity; (ii) intramolecular vibrational redistribution IVR from the torsion to the other vibrational modes; and (iii) the coupling between states S1 and X. The resulting fluorescence lifetimes decrease systematically from ca. 20 ns for |1̃ 0〉 to ca. 6 ns for |1̃ 50〉, with an exceptional decrease to ca. 7 ns for intermediate states such as |1̃ 24〉, with energies close to the crossings of the diabatic potentials of the bright and dark states S1 and X. These systematic and exceptional trends agree well with the experimental results of Monte et al., and they are explained and interpreted as consequences of the three processes (i)–(iii) within our model. Accordingly, the fluorescence lifetimes contain some information about the intramolecular dynamics, e.g., IVR from the torsion to the other vibrations should be faster in the dark state X than in the bright state S1, where it proceeds on the extraordinarily long time scale of several ns.