Semiclassical Approach to Photophysics Beyond Kasha’s Rule and Vibronic Spectroscopy Beyond the Condon Approximation. The Case of Azulene

Azulene is a prototypical molecule with ananomalousfluorescence from the second excited electronic state,thus violating Kasha’s rule, and with an emission spectrum thatcannot be understood within the Condon approximation. To betterunderstand the photophysics and spectroscopy of azulene andother nonconventional molecules, we developed a systematic,general, and efficient computational approach combining thesemiclassical dynamics of nuclei withab initioelectronic structure.First, to analyze the nonadiabatic effects, we complement thestandard population dynamics by a rigorous measure ofadiabaticity, estimated with the multiple-surface dephasing representation. Second, we propose a new semiclassical method forsimulating non-Condon spectra, which combines the extended thawed Gaussian approximation with the efficient single-Hessianapproach. S1←S0and S2←S0absorption and S2→S0emission spectra of azulene, recorded in a new set of experiments, agree verywell with our calculations. Wefind that accuracy of the evaluated spectra requires the treatment of anharmonicity, Herzberg−Teller,and mode-mixing effects.