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Use of Entropy Minimization for the Preconditioning of Large Spectroscopic Data Arrays: Application to in Situ FT-IR Studies From the Unmodified Homogeneous Rhodium Catalyzed Hydroformylation Reaction
Volume 56, Number 11 (Nov. 2002) Page 1422-1428
Chen, Li; Garland, Marc
In situ spectroscopic measurements are fairly common in homogeneous catalysis. However, although it is easy to accumulate vast amounts of data, their appropriate analysis becomes a critical issue. Accordingly, we have developed a simple-to-implement but numerically sophisticated tool. Let A denote a matrix of absorbance data, n denote the number of preliminary spectra obtained from the stepwise addition of reagents, k denote the number of sequential reaction spectra, and ν the spectroscopic channels. Then the preconditioning problem can be stated as Aexp(n+k)×ν → Aprek×ν. A single experiment results in (1) a set of n "pure" component reference spectra and (2) a set of k preconditioned reaction spectra where the reagents have been optimally subtracted. Entropy minimization is examined as a means of achieving both objectives. The developed algorithm was applied to a set of FT-IR spectra obtained from a complex transition-metal homogeneous catalyzed organic synthesis. Excellent reference spectra and excellent preconditioned reaction spectra were readily obtained. In addition, the absorbance of the products in the preconditioned spectra was compared to the absorbance obtained after manual user-defined subtraction. Comparable results were obtained. The present approach is clearly useful for the automated numerical treatment of very large sequential spectroscopic data arrays arising from in situ kinetic studies. Extension to related types of problems in the chemical sciences and to other spectroscopic methods such as NMR are obvious.