A Theoretical Study of Absorption–Emission Asymmetry from Franck–Condon–Herzberg–Teller Interference and Duschinsky Mixing

Abstract Herzberg–Teller (HT) coupling beyond the Franck–Condon (FC) approximation can break the mirror-image relation between absorption and emission vibronic spectra through interference between the FC and HT transition amplitudes. Here, we analyze the geometry dependence of this FC–HT interference using a displaced harmonic-oscillator model and extend the treatment perturbatively to Duschinsky rotation. In the separable equal-frequency limit, the FC and HT vibrational integrals are strictly proportional, reducing the asymmetry to a single variable κ that separates into an electronic ratio of HT and shifted FC prefactors and a nuclear ratio of vibrational spacing to signed displacement. For HT-active totally symmetric modes, reversing the displacement reverses the interference direction, identifying signed displacement, rather than the Huang–Rhys factor, as the governing nuclear variable. For nondegenerate, nontotally symmetric modes, interference emerges under symmetry-breaking displacement, with its direction fixed by the vibrational quantum change alone. The normalized asymmetry depends only on vibrational spacing, allowing an observed progression to probe the same universal dependence at fixed geometry. Applied to experimental phenanthrene spectra, this progression-based analysis recovers strikingly similar first-order HT information from the absorption–emission asymmetry. Finally, the leading Duschinsky correction decomposes into geometric and electronic pathways built from the same one-mode quantities as the separable limit, showing that mode mixing redistributes FC and HT character between coordinates rather than introducing a new electronic quantity.