A general theory of inhomogeneous broadening for nonlinear   susceptibilities: the second hyperpolarizability
  A general theory of inhomogeneous broadening is rarely applied to nonlinear spectroscopy in lieu of either a simple Lorentzian or Gaussian model. In this work, we generalize all the important third-order nonlinear susceptibility expressions obtained with sum-over state quantum calculations to include Gaussian and stretched Gaussian distributions of Lorentzians. This theory gives a better fit to subtle spectral features - such as the shoulder of the electroabsorption peak, and is a more accurate tool for determining transition moments from spectroscopy experiments. 
Robert J. Kruhlak and Mark G. Kuzyk