Transient vibrational dynamics unveils the intricate mechanism of ultrafast photorelaxation in a molecular rotor

We investigate the excited-state vibrational dynamics of the second-generation molecular rotor 9-(2-methyl-2,3-dihydro-1H-cyclopenta[a]naphthalen-1-ylidene)-9H-fluorene using an integrated theoretical-computational approach. Our methodology combines ab initio molecular dynamics with time-dependent density functional theory and a polarizable continuum model to characterize the ground- and excited-state potential energy surfaces of the rotor in cyclohexane. Time-resolved vibrational analysis based on wavelet transform enables the decomposition of the nuclear motion into time-frequency components. This approach allows us to follow the evolution of vibrational dynamics and their role in key relaxation pathways and spectroscopic signals. We propose that, although not directly observable, complex vibrational dynamics influence the emission by modulating both the transition energy and the emission dipole moment. These include C=C stretching, out-of-plane motions at the axle carbon, and rotor-stator torsional modes. For the first time, we assign and interpret low-frequency modes observed experimentally at ∼180 cm-1 in time-resolved fluorescence. We reproduce the extent and the dynamics of the pronounced red shift of the C=C stretching mode upon excitation, as observed in the femtosecond stimulated Raman spectrum (1585 cm-1 in the ground state vs 1350-1440 cm-1 in the excited state). Regarding the photoisomerization, we identify a clear correlated steric-relief mechanism of the two main relaxation coordinates: torsion about the C=C axle and pyramidalization at the stator-bridge carbon. This study demonstrates the power of transient vibrational analysis in unraveling complex photorelaxation mechanisms by establishing a direct link between experimental data and excited-state molecular dynamics simulations.