Theory of inhomogeneous environmental gaussian broadening of resonance Raman excitation profiles for polyatomic molecules in solution

The effect of static inhomogeneous environmental broadening of Raman excitation profiles and Raman peak intensity distribution of solute molecules was investigated. Homogeneous bradening is represented by Lorentzians and inhomogeneous broadening by Gaussians, where the latter reflect distributions in the purely electronic transition. The Raman scattering cross‐section is calculated analytically, and by means of recent optical bandshape theory for Voigt profiles it can be recast into rapidly converging and easily tractable series expansions well suited for numerical data fitting. The profile expressions also apply to arbitrary values of the broadening parameters and in these respects improve on several previous approaches to inhomogeneous broadening. Notable outcomes are that the excitation profile takes the from of a series of Franck–Condon modulated Voigt profiles when the broadening parameters are small compared with the vibrational frequencies of the Raman‐active modes. In this limit only diagonal terms in the sum over vibrational quantum numbers contribute. When the broadening parameters are not small, non‐diagonal terms are important and lead to additional broadening, profile maximum shifts and bandshape distortion.