Pure component reconstructions using entropy minimizations­and 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 8 × 2501 and the piecewise‐continuous variance‐weighted matrix ${\bf A}_{8\times 2501}^{*}$ . 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 ${\bf V}_{2\times 2501}^{\rm T}$ and ${\bf V}_{2\times 2501}^{{\rm T}*}$ 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 © 2000 John Wiley & Sons, Ltd.