Classical Correlation Model of Resonance Raman Spectroscopy

A classical correlation model (CCM), based on forces instead of potentials, is developed and applied to resonance Raman scattering to provide a foundation for further advances in understanding the effects of fields and vibronic perturbations on the optical properties of materials by a simple, yet versatile, description. The model consists of a charge connected by a classical spring to a surface and driven by an external electric field. The spring represents the charge cloud of the electrons and the transition strength, and the surface represents the nucleus or molecule. Molecular vibrations are assumed to be many-body effects that change the configuration and hence modify the spring constant directly, as opposed to all previous classical models of Raman scattering, and opposed to the anisotropic bond model (ABM) of nonlinear optics, by adding anharmonic terms to the potential. The resulting expression agrees exactly with quantum mechanical models of resonance Raman scattering in the limit of weak electron-phonon coupling, and it agrees well when the coupling becomes strong. The result is a classical derivation of Kramers-Heisenberg-Dirac scattering theory. We show that the difference between classical and quantum approaches lies only in the interpretation of the prefactor. In particular, the Raman excitation profile shows excellent agreement with all other methods of calculation. By comparing complementary classical and quantum solutions of the same complex system, understanding of both is enhanced.