An Examination of the Uniqueness of Gaussian and Lorentzian Profiles

Abstract

The conditions under which Gaussian and Lorentzian peaks may meaningfully be fitted in terms of two subcomponent bands have been examined. It is shown that good fits are possible for a wide range of relative intensities and half-widths, given that the separation of the two component peaks is limited. In the case of the Lorentzian profile, of particular interest because infrared and Raman bands approximate to this shape, fits significantly better than the limit imposed by experimental errors are obtained for separation less than about 40% of the half-width. The practical implications of these results for the curve fitting of overlapping peaks are considered; in most practical situations Gaussian and Lorentzian profiles are unique and curve fitting may be undertaken.