Theory of resonant Raman scattering in the strong vibronic coupling limit--a Green's function approach

A Green's function approach for resonant Raman scattering is proposed here, which is suitable for both weak and strong vibronic couplings. The formalism is based on the solution of the exact Green's function in the Longuet--Higgins representation, using the solutions to the static equations in ordinary molecular quantum mechanics as the basis set. The physical meaning of various interaction schemes becomes clear in this representation. In particular, the vibronic coupling is based on the interactions between individual zero-order vibronic levels and is carried through to infinite order, whereas the traditional first-order results only account for the emission of one single vibrational quantum. Nonadiabatic contributions are also contained in the formulation. The method is applied to the following cases: (1) the change in nuclear equilibrium position due to electronic excitation, (2) vibronic coupling involving two excited states, and (3) the change in nuclear potential (force constants) due to electronic excitation. Numerical results show that the convergence is excellent even for large vibronic coupling and in exact resonance region. Furthermore, all the physical quantities of interest, such as Raman cross sections of fundamentals and overtones, absorption profiles, Franck--Condon factors, quantum yields can be obtained at the same time in this unified approach