Improved Curve Resolution of Highly Overlapping Bands by Comparison of Fourth-Derivative Curves

Abstract

Curve fitting of highly overlapping bands can be improved by comparison of the fourth derivative of the experimental composite band profile with that of the sum of the curve-fitted component bands. Optimization is achieved with fixed values of one band parameter, aiming thereby for optimal correspondence between the fourth-derivative curves. FT-IR spectra of nitrate's v1 band region in ≈1 M glassy Ca(NO3)2 solution, and of its v2 band region in 10 M LiNO3 solution, in ≈0.5 M glassy Mg(NO3)2 solution and in 5 M Ca(NO3)2 solution, all with D2O as solvent, were used. As a general rule, reliable curve fitting of two overlapping bands of unknown band shape is possible only when separation of their peak maxima is larger than their average full width at half-height (FWHH). We show here that by comparison of fourth-derivative curves many more overlapped composite bands can be reliably resolved into their component bands, and, for the favorable case of 10 M LiNO3 solution, separation of two bands by only about a third of their average FWHH is sufficient for reliable curve fitting. This method requires data with very high signal-to-noise ratios. Improved curve fitting of highly overlapping bands is demonstrated for both a sum and a product of Gaussian and Lorentzian peak shapes, and a sort of recipe is given for both types of curve fitting. Synthetic spectra of two overlapping bands, where the degree of overlap and their relative intensity were varied in a systematic way, are given together with their fourth-derivative curves. This information will be of help for interpreting fourth-derivative curves of experimental highly overlapping two-band systems.