Computer aided chemistry—III. Spectral envelope deconvolution based on a simplex optimization procedure

Abstract

Abstract A Simplex optimization technique has been applied to the problem of fitting complicated absorption and magnetic circular dichroism (MCD) spectra that comprise many overlapping, Gaussian bands. Both a weighted centroid Simplex routine and a non-linear least-squares routine have been incorporated into a FORTRAN 77 program to carry out the fitting of electronic spectra. The performance of these two procedures was compared by fitting synthetic spectra to which varying degrees of noise had been added, and were judged according to the ability of each routine to reproduce the original band shape parameters that were used to construct the synthetic spectral envelopes. Only the Simplex procedure was successful at fitting the MCD data. Both the non-linear least-squares and Simplex routines performed adequately in tests using the synthetic absorption spectral data. However, the least-squares optimization routine was considerably faster than the Simplex routine at finding a solution when significant noise was present in the test absorption spectra. The presence of significant levels of electronic noise in a spectrum can reduce the precision and accuracy of the deconvolution results and many cause the deconvolution procedure to degenerate to a false minimum. Degeneracy of the fitting procedures at local minima, which corresponded to sets of band shape parameters that provided a good fit to either the absorption or MCD spectrum of a chemical species, but not both spectra, was overcome by fitting each absorption and MCD spectrum of a pair of spectra from the same chemical species, successively, until a set of band shape parameters was found that provided reasonable fits of both spectra. This deconvolution procedure, which successively optimizes a pair of absorption and MCD spectra, has been very valuable in fitting complex spectra of zinc phthalocyanine π-cation radical complexes.