General many-body theory of resonance Raman scattering including simultaneous mode mixing and non-Condon coupling

A consistent non-perturbative theory is obtained for treating resonance Raman (RR) scattering and the optical absorption of complex multimode systems having simultaneous linear plus quadratic electron-phonon (el.-ph.) coupling and linear plus non-Condon coupling. Through the development of suitably extended phonon many-body diagrammatic techniques within the framework of the time-correlator theory, exact finite analytic model expressions for first-order RR excitation profiles and the optical absorption are derived for nonzero temperature systems in the general case when quadratic plus linear non-Condon coupling (vibrational dependence of the electronic transition dipole matrix elements) and quadratic plus linear el.-ph. coupling (mode mixing, frequency shifts, and equilibrium position shifts upon electronic excitation) are present. By means of analytical and numerical discussions using these expressions, it is shown that the simultaneous inclusion of non-Condon coupling and quadratic el.-ph. coupling gives rise to important interference effects in the spectra. Numerical model calculations are given to demonstrate that the new theory provides a convenient and efficient finite-temperature modeling procedure for the first-order RR profiles and the optical absorption of multimode systems having complicated quadratic el.-ph. coupling and non-Condon coupling. Particularly, the new theory can be combined with the results of quantum ab initio calculations of multimode model parameters to allow the first truly ab initio calculation of the spectra for direct comparison with experiment.;Mode mixing effects are studied within the concept of practically important renormalization theories for the optical absorption, emission and RR profiles, and this study includes the derivation of new analytic model expressions for the emission and second-order RR profiles of systems having mode mixing. New analytic model expressions for second-order RR profiles are also derived for systems having linear el.-ph. and linear non-Condon coupling. Predictions for the second-order profiles involving the two modes of the azulene molecule are given, and these show that the measurement of these profiles will discriminate between a non-Condon model and a mode mixing model, both of which give equally successful explanations to this molecule's measured first-order profiles and the optical absorption. (Abstract shortened with permission of author.)...