Pure component reconstructions using entropy minimizations and variance-weighted piecewise-continuous spectral regions. Application to the unstable experimental system Co-2(CO)(8)/Co-4(CO)(12)
The organometallic complex Co-2(CO)(8) is an air-, light-, heat- and moisture-sensitive species and rapidly decomposes in n-hexane solutions to give Co-4(CO)(12); Owing to the instability of Co-2(CO)(8), calibration is extremely difficult. Moreover, the published literature measurements of the mid-infrared spectrum of Co-2(CO)(8) are inconsistent. To solve this problem, a chemometric approach involving singular value decompositions and entropy minimizations was used. First, n-hexane solutions of mixtures of Co-2(CO)(8) and Co-4(CO)(12) were prepared and measured in the mid-infrared on the interval 1700-2200 cm(-1). After spectral subtractions of n-hexane and background gases, two absorbance matrices were constructed, namely the unweighted matrix A(8x2501) and the piecewise-continuous variance-weighted matrix A*(8x2501). The piecewise-continuous variance-weighted matrix possesses a discontinuity at 1925 cm(-1), between the region of strong terminal carbonyl vibrations and the region of weak bridging carbonyl vibrations, where both regions have strongly overlapping characteristics. The significant right singular vectors V-2x2501(T) and V-2x2501(T*) were then subjected to both second-derivative and fourth-derivative entropy minimizations. In addition, two numerical modifications were implemented, namely full-spectrum optimizations and half-spectrum optimizations. It was found that extremely good spectral estimates for Co-2(CO)(8) and Co-4(CO)(12) were obtained from (i) the global solutions for both the unweighted and variance-weighted second-derivative entropy minimizations when using the half-spectrum minimizations and (ii) the local solutions for both the unweighted and variance-weighted fourth-derivative entropy minimizations when using both the half-spectrum and full-spectrum minimizations. These results suggest that (a) half-spectrum optimizations and second-derivative entropy measures are potentially very useful for particular types of real strongly overlapping spectra, (b) the failure of the fourth-derivative entropy measures to produce the correct estimates is probably associated with the sensitivity to experimental noise and (c) although the variance-weighted approach did not help in the present case, variance-weighted analyses still hold potential for spectral analyses involving both strong and weak absorbance characteristics. Copyright (C) 2000 John Wiley & Sons, Ltd.
entropy minimizations co-2(co)(8) singular value decompositions exploratory chemometric studies pure component spectra