We derive a result from the polarizability theory of Raman scattering that unifies existing rules for preresonance and resonance Raman scattering. It states that for resonance Raman scattering the 0→n Raman amplitude is the average of the nth derivative of the polarizability contributed by the resonant excited electronic state over the ground vibrational state probability. By assuming a large energy denominator in the polarizability, it leads to the sum rule obtained by Harris, Mathies and Myers (1983) for preresonance Raman scattering. It is also shown that by a series expansion of the potential energy surfaces about the ground state equilibrium geometry, it leads to the simple sum rules for fundamental and overtone intensities derived by Heller, Sundberg and Tannor (1982). © 1988.
Lee, S. Y., & Mathies, R. A. (1988). Polarizability theory and sum rules. Chemical Physics Letters, 151(1–2), 9–15. https://doi.org/10.1016/0009-2614(88)80059-9