Theory of resonance Raman scattering and fluorescence from strongly vibronically coupled excited states of polyatomic molecules

A theoretical description of secondary emission from complex absorption bands of isolated polyatomic molecules is developed. The strong non-Born-Oppenheimer coupling associated with conical intersections of the multidimensional excited-state potential-energy surfaces is included in a fully microscopic manner by solving the time-dependent Schrödinger equation for appropriate model systems incorporating the most relevant electronic states and vibrational modes. The effect of the large number of remaining vibrational modes and of the weaker coupling with additional electronic states is modeled by phenomenological relaxation terms (lifetime broadening and pure dephasing) in the framework of the density-matrix formalism. Explicit eigenstate-free expressions for absorption, resonance Raman, and fluorescence spectra are derived via density-matrix perturbation theory. The computational feasibility of the resulting mixed microscopic/phenomenological theory is demonstrated for a simple three-mode model of the vibronic coupling of the S₁ (nπ*) and S₂ (ππ*) states of pyrazine. The effect of excited-state vibronic coupling and ultrafast S₂→ S₁, internal conversion on resonance Raman and fluorescence spectra is analyzed on the basis of these model calculations.