This paper describes an empirical model in which a derivative term is added to the usual sum Cauchy-Gauss function. The modified function introduces asymmetry into the band profile enabling it to fit bands to distorted infrared spectra, such as infrared attenuated total reflectance (ATR) spectra. The model uses 3M + 5 parameters (for M bands). Parameters for each band are height, position, and half-width, with additional parameters for the Cauchy proportion, derivative scaling, half-width scaling, and baseline. The model has been applied to the splitting of the ATR spectra of liquid benzene and appears to give a good fit to the experimental data.
L. J. Janik, "A Modified Sum Cauchy-Gauss Function to Fit Nonsymmetrical Bands to Infrared Internal-Reflectance Spectra," Appl. Spectrosc. 40, 661-667 (1986)