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Some molecules of chemical and biological significance possess vibrations with significant Herzberg-Teller (HT) couplings, which render the Franck-Condon (FC) approximation inadequate and cause the breakdown of the well-known mirror-image symmetry between linear absorption and emission spectra. Using a model two-state system with displaced harmonic potential surfaces, we show analytically that the FC-HT interference gives rise to asymmetric intensity modification, which has the same sign for all transitions on one side of the 0-0 absorption line and the opposite sign in the equivalent fluorescence transitions, while the trend is exactly reversed for all transitions on the other side the 0-0 line. We examine the dependence of the absorption-emission asymmetry on the mode frequency, Huang-Rhys factor, and dipole moment parameters to show the recovery of symmetry with particular combinations of parameters and a crossover from fluorescence to absorption dominance. We illustrate the analytical predictions through numerically exact calculations in models of one and two discrete vibrational modes and in the presence of a harmonic dissipative bath. In addition to homogeneous broadening effects, we identify large asymmetric shifts of absorption and emission band maxima, which can produce the illusion of unequal frequencies in the ground and excited potential surfaces as well as a nontrivial modulation of spectral asymmetry by temperature, which results from the enhancement of transitions on one side of the 0-0 line. These findings will aid the interpretation of experimental spectra in HT-active molecular systems.
Kundu et al. (Thu,) studied this question.