Band-Target Entropy Minimization (BTEM):  An Advanced Method for Recovering Unknown Pure Component Spectra. Application to the FTIR Spectra of Unstable Organometallic Mixtures

Abstract

A newly developed band-target entropy minimization (BTEM) algorithm was tested on experimental FTIR data of Rh 4 (CO) 12 /Rh 6 (CO) 16 mixtures in order to recover the pure component spectra of the constituent complexes. Bands in the nonoverlapping bridging carbonyl region as well as bands in the highly overlapping terminal carbonyl region were targeted for retention. The bands are identified in the vector-space decomposition of the observations, a crucial first step in untangling the superposition of the pure component spectra. In both cases, the targeted band was retained, and exceptionally accurate whole spectral estimates of Rh 4 (CO) 12 and Rh 6 (CO) 16 were obtained. Due to the constructs used in BTEM, enhanced signal-to-noise characteristics result, and spectral nonlinearities arising from changing band positions and changing band shapes are essentially eliminated. For the experimentalist, the utility of BTEM arises from its direct one-spectrum-at-a-time spectral reconstruction approachswhich is guided by the choice of the targeted region. As such, BTEM appears particularly applicable to spectroscopy possessing highly localized features: i.e., FTIR, Raman, etc. The BTEM algorithm is so useful that the spectral pattern from the minute presence of suspended particles of Rh 6 (CO) 16 could be reconstructed. Indeed, the integrated absorbance of Rh 4 (CO) 12 , Rh 6 (CO) 16 , and Rh 6 (CO) 16 solids account for only ca. 0.3, 0.09, and 0.04% of the experimental observations. The new BTEM algorithm was compared to other algorithms such as SIMPLISMA, IPCA, and OPA-ALS. The latter either fail with the present data set or are unable to produce reconstructed spectra of similar quality to BTEM. This new algorithm holds considerable promise for the analysis of in-situ spectroscopic reaction data such as those arising in complex organometallic and organic syntheses, where absolutely no a priori information about the constituents/intermediates is available.

Decomposition of in vivo spatially offset Raman spectroscopy data using multivariate analysis techniques

“…Singular value decomposition was performed on each large file and the relevant features targeted (plastic 1332-1342 cm À1 and in vivo 955-970 cm À1 ). [21,23] Five eigenvectors were used in the decompositions shown in Figs 2 and 4.…”

“…For these systems, more sophisticated methods, such as library-based fitting, need to be employed. [20] Another approach is to use multivariate analysis; band-target entropy minimization (BTEM), [21][22][23] coupled with SORS, has been used to measure the carbonate-to-phosphate ratio of rat tibia through 1 mm of skin (with an error of 2.3%), [12] of chicken tibia through 4 mm of skin/soft tissue (with an error of 8%) [12] and of porcine bone through~1 mm of soft tissue. [19] In the latter study, a second spectral decomposition method, parallel factor analysis (PARAFAC) [24] , was also used to retrieve the bone spectrum.…”

Measurement of abnormal bone composition in vivo using noninvasive Raman spectroscopy

“…10,11 The BTEM decomposition was repeated 15 times for the patient and 15 times for the control (that is, the whole-data set, with one spectrum left out in turn, was analysed for each individual); the algorithm was applied to sections of each spectrum (735-1384 cm À 1 ) and to the dominant phosphate band (955-970 cm À 1 ); fifteen eigenvectors were used. The 15 resultant spectra were averaged and s.d.…”

Estimating the number of pure chemical components in a mixture by maximum likelihood

“…SMCR does not require a priori knowledge of the pure component spectra, which is particularly useful in characterizing unknown chemical species [3,4]. In general, homogeneity, concentration, and the number of pure components within the chemical or biological system is seldom known in advance [5,6].…”