Overtone resonance Raman scattering beyond the Condon approximation: Transform theory and vibronic properties

Abstract

The time correlator formalism is used to develop the expression for nth order (overtone) resonance Raman scattering (RRS) to include both Raman frequency shifts upon electronic excitation as well as non-Condon vibronic coupling. In particular the compact operator formalism recently introduced by Hizhnyakov and Tehver [J. Raman Spectrosc. 19, 383 (1988)] to obtain several RRS correlators (including overtone scattering with frequency shift, but in the Condon approximation) is used to extend the theory. At the same time a formal advantage is achieved by the limited introduction of the Born–Oppenheimer approximation. Also transform relationships including non-Condon effects are given that link the Raman excitation profile of nth order scattering to the absorption spectrum. Finally, it is emphasized how all three vibronic parameters—potential energy surface displacement, Raman mode frequency changes, and the linear non-Condon coupling parameter—can be quantitatively determined without the need for absolute Raman cross-section measurements. The relative scattering intensity of the fundamental and three (or more) overtones suffices to fix the three. By way of application, the vibronic parameters are determined from published single wavelength overtone RRS in six molecules.