Coherent state-based generating function approach for Franck–Condon transitions and beyond

One-photon and multi-photon absorption, spontaneous and stimulated photon emission, resonance Raman scattering and electron transfer are important molecular processes that commonly involve combined vibrational-electronic (vibronic) transitions. The corresponding vibronic transition profiles in the energy domain are usually determined by Franck-Condon factors (FCFs), the squared norm of overlap integrals between vibrational wavefunctions of different electronic states. FC profiles are typically highly congested for large molecular systems and the spectra usually become not well-resolvable at elevated temperatures. The (theoretical) analyses of such spectra are even more difficult when vibrational mode mixing (Duschinsky) effects are significant, because contributions from different modes are in general not separable, even within the harmonic approximation. A few decades ago Doktorov, Malkin and Man'ko [1979 J. Mol. Spectrosc. 77, 178] developed a coherent state-based generating function approach and exploited the dynamical symmetry of vibrational Hamiltonians for the Duschinsky relation to describe FC transitions at zero Kelvin. Recently, the present authors extended the method to incorporate thermal, single vibronic level, non-Condon and multi-photon effects in energy, time and probability density domains for the efficient calculation and interpretation of vibronic spectra. Herein, recent developments and corresponding generating functions are presented for single vibronic levels related to fluorescence, resonance Raman scattering and anharmonic transition.