Analysis of the vibronic fine structure in circularly polarized emission spectra from chiral molecular aggregates

Using a Frenkel-exciton model, the degree of circular polarization of the luminescence ${\mathrm{(g}}_{\mathrm{lum}})$ from one-dimensional, helical aggregates of chromophoric molecules is investigated theoretically. The coupling between the electronic excitation and a local, intramolecular vibrational mode is taken into account. Analytical expressions for the fluorescence band shape and $g_{\mathrm{lum}}$ are presented for the case of strong and weak electronic coupling between the chromophoric units. Results are compared to those from numerical calculations obtained using the three particle approximation. $g_{\mathrm{lum}}$ for the 0-0 vibronic band is found to be independent of the relative strength of electronic coupling between chromophores and excitation-vibration coupling. It depends solely on the number of coherently coupled molecules. In contrast, for the higher vibronic transitions ${\mathrm{|g}}_{\mathrm{lum}}|$ decreases with decreasing strength of the electronic coupling. In the limit of strong electronic coupling, ${\mathrm{|g}}_{\mathrm{lum}}|$ is almost constant throughout the series of vibronic transitions but for weak coupling ${\mathrm{|g}}_{\mathrm{lum}}|$ becomes vanishingly small for all vibronic transitions except for the 0-0 transition. The results are interpreted in terms of dynamic localization of the excitation during the zero point vibrational motion in the excited state of the aggregate. It is concluded that circular polarization measurements provide an independent way to determine the coherence size and bandwidth of the lowest exciton state for chiral aggregates.