Some aspects of the scope and limitations of derivative spectroscopy

Synthesised spectra are used to illustrate discussion of some relationships between recorded absorption profiles and their second and fourth derivative spectra. Limitations arising from the fortuitous overlap of a derivative peak with a neighbouring wing, and the possibilities of resolving spectra into their overlapping bands are also considered. The combined use of second and fourth derivative spectra to ascertain the correct number of bands within an observed profile is described. It is suggested that the practice of computing a least-squares fit of overlapping bands to a spectral profile be changed, because the minimisation achieved often produces a result involving excessive or negative absorbances: the spectral profile should be regarded as a boundary limit and any unaccounted (positive) absorbance then assessed as possible evidence for an additional band. An example is given, concerning the resolution of the spectrum of a thin, single crystal of uranium(IV) oxide at 77 K superimposed on an absorption edge. A comparison of the difference between the observed spectrum and the sum of its resolution into twelve overlapping bands, plus a similar comparison of their fourth derivative spectra, reveals a thirteenth band.