An evaluation of mathematical functions to fit infrared band envelopes

Simulated infrared absorption bands of condensed phase systems have been fitted with simple analytical functions by least-squares procedures. The bands were of Cauchy (Lorentz) contour and were modified to conform with the finite spectral slit distortion of the spectrophotometer. Cauchy, Cauchy–Gauss product, and Cauchy–Gauss sum functions were used in the fitting procedures using transmittance ordinates. The fits achieved were compared and the dependence of the optimized indices on the band distortion and data range were analyzed. Some preference for the Cauchy–Gauss sum function is indicated.