On the Theory of Raman Intensities

The Herzberg-Teller development for vibronic transition moments is introduced into the Kramers-Heisenberg dispersion equation. It is shown how ``forbidden'' character (vibrationally induced intensity) in allowed electronic transitions is responsible for the Raman intensities of fundamentals. This suggests a direct link between certain vibronic spectroscopic observations and Raman intensities. The development is carried to the first order in nuclear displacements only—the higher terms give rise to Raman intensities of combinations and overtones. An equation for the polarizability components is obtained which leads directly to the Raman selection rules and in addition provides interesting predictions concerning the Raman and the resonance Raman effect in relation to excited electronic states. Rules are worked out governing the participation of excited electronic states in the Raman effect and these are employed to demonstrate a separability of σ and π contributions to the scattering of totally symmetric modes. The polarizability expression obtained here is compared with that of the semiclassical theory of Shorygin and an interesting resemblance is found. Finally it is shown how, depending on details of the electronic structure, the predicted form of the frequency dependence of scattered intensity ranges between the two expressions that have been commonly used to interpret observations.