Determining the pure component spectra of trace organometallic intermediates by combined application of in situ Raman spectroscopy and band-target entropy minimization analysis

Trace organometallic intermediates arising from complex organic syntheses are usually quite difficult to detect spectroscopically. In situ FTIR and in situ NMR are the only techniques that are used with any regularity for such studies. In this contribution, high-pressure in situ Raman spectroscopic measurements were performed for the rhodium catalyzed hydroformylation of 3,3-dimethylbut-1-ene using Rh₄(CO)₁₂ as catalyst precursor at 298 K – a reaction extensively studied previously by more sensitive in situ FTIR. The Raman spectroscopic measurements were analyzed using the band-target entropy minimization (BTEM) algorithm. As expected, the pure component spectra of dissolved CO, 3,3-dimethylbut-1-ene, and 4,4-dimethylpentanal were easily recovered. In addition, the pure component spectra of the precursor Rh₄(CO)₁₂ and the intermediate RCORh(CO)₄ (R = (CH₃)₃CCH₂CH₂) were successfully reconstructed – even though the mean concentrations of both species were on the order of 150 ppm. The BTEM estimate of the Raman spectrum of RCORh(CO)₄ is reported for the first time. This Raman spectrum is consistent with the DFT predicted spectrum. This study represents the first combined application of Raman spectroscopy and BTEM analysis to a homogeneously catalyzed metal-mediated reaction. The potential and limitations of this general approach are discussed.     

Multi‐component analysis: blind extraction of pure components mass spectra using sparse component analysis

The paper presents sparse component analysis (SCA)‐based blind decomposition of the mixtures of mass spectra into pure components, wherein the number of mixtures is less than number of pure components. Standard solutions of the related blind source separation (BSS) problem that are published in the open literature require the number of mixtures to be greater than or equal to the unknown number of pure components. Specifically, we have demonstrated experimentally the capability of the SCA to blindly extract five pure components mass spectra from two mixtures only. Two approaches to SCA are tested: the first one based on ?₁ norm minimization implemented through linear programming and the second one implemented through multilayer hierarchical alternating least square nonnegative matrix factorization with sparseness constraints imposed on pure components spectra. In contrast to many existing blind decomposition methods no a priori information about the number of pure components is required. It is estimated from the mixtures using robust data clustering algorithm together with pure components concentration matrix. Proposed methodology can be implemented as a part of software packages used for the analysis of mass spectra and identification of chemical compounds. Copyright © 2009 John Wiley & Sons, Ltd.     

Application of principal component analysis to the extraction of pure mass spectra in chemical analysis by gas chromatography/mass spectrometry

In this work, we investigated the possibility of the purification of mass spectra of coeluted substances containing at least one characteristic value of m/z using principal component analysis. Simulated and real gas chromatographic/mass spectrometric data were analyzed. For the simulated data, the resolution of the chromatographic peaks varied from 0.075 to 0.75, and the ratio of component concentrations ranged from 0.01 to 100. Noise-free simulated data and simulated data with randomly distributed noise were considered. It was shown that the method gave satisfactory results even when the chromatographic resolution (R _s ) was less than 0.05.     

A combination of spectral re-alignment and BTEM for the estimation of pure component NMR spectra from multi-component non-reactive and reactive systems

The deconvolution of multi-component mixtures in NMR spectroscopy is a challenging problem due to the spectral non-linearities. In the present contribution, two data sets were studied (A) 10 samples of a four-component non-reactive mixture measured with ¹H, ¹³C, ¹⁹F, ³¹P NMR and (B) a three-solute cyclo-addition reaction measured with ¹³C NMR. Both data sets were treated with a re-alignment procedure to correct for the non-stationary chemical shifts, followed by band-target entropy minimization (BTEM) analysis. For data set A, quite good spectral estimates of the two hydrogen-containing species, four carbon-containing species, two fluorine-containing species and two phosphorus-containing species were obtained from the multi-component data. For data set B quite good spectral estimates of all three carbon-containing reactants were obtained as well as their relative concentration profiles. The present contribution using model systems indicates the usefulness of re-alignment procedures for correcting non-stationary characteristics, prior to self-modeling curve resolution (SMCR), and the potential for investigating more complex problems.     

Fourier transform Raman spectral measurements of powdered quaternary mixtures of organic compounds: Exceptional pure component spectral reconstruction using band-target entropy minimization (BTEM)

Fourier transform Raman spectra of eight mixtures of four organic solids, namely dicyandiamide, melamine, acetamide and urea were measured. Matrices formed from these spectra were first subjected to singular value decomposition to obtain the right singular vectors. The right singular vectors were then subjected to blind source separation using band-target entropy minimization (BTEM), thus no a priori information (i.e. involving the nature of the components present, their spectra, nor their concentrations) was included in the analysis. The recovered pure component spectra are of exceptionally high quality and are consistent with pure reference spectra. Various empirical and statistical tests, such as the Euclidean norm and target transform factor analysis, were employed to assess the quality of the recovered spectra. The present results indicate the applicability of combined Raman and BTEM analysis for solid mixtures.     

Empirical kernel map approach to nonlinear underdetermined blind separation of sparse nonnegative dependent sources: pure component extraction from nonlinear mixture mass spectra

Nonlinear underdetermined blind separation of nonnegative dependent sources consists in decomposing a set of observed nonlinearly mixed signals into a greater number of original nonnegative and dependent component (source) signals. This hard problem is practically relevant for contemporary metabolic profiling of biological samples, where sources (a.k.a. pure components or analytes) are aimed to be extracted from mass spectra of nonlinear multicomponent mixtures. This paper presents a method for nonlinear underdetermined blind separation of nonnegative dependent sources that comply with a sparse probabilistic model, that is, sources are constrained to be sparse in support and amplitude. This model is validated on experimental pure component mass spectra. Under a sparse prior, a nonlinear problem is converted into an equivalent linear one comprised of original sources and their higher‐order, mostly second‐order, monomials. The influence of these monomials, which stand for error terms, is reduced by preprocessing a matrix of mixtures by means of robust principal component analysis and hard, soft and trimmed thresholding. Preprocessed data matrices are mapped in high‐dimensional reproducible kernel Hilbert space (RKHS) of functions by means of an empirical kernel map. Sparseness‐constrained nonnegative matrix factorizations in RKHS yield sets of separated components. They are assigned to pure components from the library using a maximal correlation criterion. The methodology is exemplified on demanding numerical and experimental examples related respectively to extraction of eight dependent components from three nonlinear mixtures and to extraction of 25 dependent analytes from nine nonlinear mixture mass spectra recorded in nonlinear chemical reaction of peptide synthesis. Copyright © 2014 John Wiley & Sons, Ltd.     

Cluster configuration method: application to the spectra of π-electron systems

A simplified method to calculate the excitation spectra of π-electron systems is proposed. The method is based on the assumption that a “cluster” approximation can be applied to excited states. It is demonstrated that, for the low-lying triplet and optically allowed states of butadiene, hexatriene and benzene, the method yields good agreement with complete CI calculations in the Pariser–Pan–Pople approximation.     

Simulation of high- and low-resolution mass spectra for assessment of calibration methods

Calibrating mixtures of residual gases in quadrupole mass spectrometry (QMS) can be difficult since low m/z ratios of molecular ions and their fragments result in overlap of signals especially in the lower mass regions. This causes problems in univariate calibration methods and encourages use of full spectral multivariate methods. Experimental assessment of regression methods has limitations since experimental sources of error can only be minimised and not entirely eliminated. A method of simulating full spectra at low and high resolution to accurate masses is described and these are then used for a calibration study of some popular linear regression methods [classical least squares regression (CLS), partial least squares (PLS), principal component regression (PCR)].     

Explicit–implicit mapping approach to nonlinear blind separation of sparse nonnegative dependent sources from a single mixture: pure component extraction from nonlinear mixture mass spectra

The nonlinear, nonnegative single‐mixture blind source separation problem consists of decomposing observed nonlinearly mixed multicomponent signal into nonnegative dependent component (source) signals. The problem is difficult and is a special case of the underdetermined blind source separation problem. However, it is practically relevant for the contemporary metabolic profiling of biological samples when only one sample is available for acquiring mass spectra; afterwards, the pure components are extracted. Herein, we present a method for the blind separation of nonnegative dependent sources from a single, nonlinear mixture. First, an explicit feature map is used to map a single mixture into a pseudo multi‐mixture. Second, an empirical kernel map is used for implicit mapping of a pseudo multi‐mixture into a high‐dimensional reproducible kernel Hilbert space. Under sparse probabilistic conditions that were previously imposed on sources, the single‐mixture nonlinear problem is converted into an equivalent linear, multiple‐mixture problem that consists of the original sources and their higher‐order monomials. These monomials are suppressed by robust principal component analysis and hard, soft, and trimmed thresholding. Sparseness‐constrained nonnegative matrix factorizations in reproducible kernel Hilbert space yield sets of separated components. Afterwards, separated components are annotated with the pure components from the library using the maximal correlation criterion. The proposed method is depicted with a numerical example that is related to the extraction of eight dependent components from one nonlinear mixture. The method is further demonstrated on three nonlinear chemical reactions of peptide synthesis in which 25, 19, and 28 dependent analytes are extracted from one nonlinear mixture mass spectra. The goal application of the proposed method is, in combination with other separation techniques, mass spectrometry‐based non‐targeted metabolic profiling, such as biomarker identification studies. Copyright © 2015 John Wiley & Sons, Ltd.     

Comparison between Gibbs free energy minimization and mass action law for a multitemperature plasma with application to nitrogen

This paper gives all the necessary physical equations to determine the composition and the thermodynamic properties in a multitemperature plasma utilizing two different methods: the first method is based on Gibbs free energy minimization and the second is based on the resolution of the mass action law. The lowering terms of the ionization potential and thermodynamic properties are given for a multitemperature plasma using the Debye-Hückel approximation. Numerical application is made to a nitrogen plasma.     

Extraction of multiple pure component H and C NMR spectra from two mixtures: Novel solution obtained by sparse component analysis-based blind decomposition

Sparse component analysis (SCA) is demonstrated for blind extraction of three pure component spectra from only two measured mixed spectra in ¹³C and ¹H nuclear magnetic resonance (NMR) spectroscopy. This appears to be the first time to report such results and that is the first novelty of the paper. Presented concept is general and directly applicable to experimental scenarios that possibly would require use of more than two mixtures. However, it is important to emphasize that number of required mixtures is always less than number of components present in these mixtures. The second novelty is formulation of blind NMR spectra decomposition exploiting sparseness of the pure components in the wavelet basis defined by either Morlet or Mexican hat wavelet. This enabled accurate estimation of the concentration matrix and number of pure components by means of data clustering algorithm and pure components spectra by means of linear programming with constraints from both ¹H and ¹³C NMR experimental data. The third novelty is capability of proposed method to estimate number of pure components in demanding underdetermined blind source separation (uBSS) scenario. This is in contrast to majority of the BSS algorithms that assume this information to be known in advance. Presented results are important for the NMR spectroscopy-associated data analysis in pharmaceutical industry, medicine diagnostics and natural products research.     

Automatic extraction of relevant peaks and reconstruction of mass spectra for low signal-to-noise GC-MS data

A method for the automatic extraction of spectra from GC-MS data is described. The program localizes chromatographic peaks and provides a reconstructed spectrum of each compound. It is particularly designed for low-sampling conditions frequently encountered with efficient GC columns, requiring threshold methods rather than methods based on peak shape; automatic threshold adjustments on the mass chromatograms are thus performed at different stages of the process. A test of the program on two sets of experimental data revealed better performances than manual data treatment, particularly in the case of low signal-to-noise ratios.     

Direct calculation of solid-vapor coexistence points by thermodynamic integration: application to single component and binary systems

We present a new thermodynamic integration method that directly connects the vapor and solid phases by a reversible path. The thermodynamic integration in the isothermal-isobaric ensemble yields the Gibbs free energy difference between the two phases, from which the sublimation temperature can be easily calculated. The method extends to the binary mixture without any modification to the integration path simply by employing the isothermal-isobaric semigrand ensemble. The thermodynamic integration, in this case, yields the chemical potential difference between the solid and vapor phases for one of the components, from which the binary sublimation temperature can be calculated. The coexistence temperatures predicted by our method agree well with those in the literature for single component and binary Lennard-Jones systems.     

Pure component spectral reconstruction from mixture data using SVD, global entropy minimization, and simulated annealing. Numerical investigations of admissible objective functions using a synthetic 7-species data set

A combination of singular value decomposition, entropy minimization, and simulated annealing was applied to a synthetic 7-species spectroscopic data set with added white noise. The pure spectra were highly overlapping. Global minima for selected objective functions were obtained for the transformation of the first seven right singular vectors. Simple Shannon type entropy functions were used in the objective functions and realistic physical constraints were imposed in the penalties. It was found that good first approximations for the pure component spectra could be obtained without the use of any a priori information. The present method out performed the two widely used routines, namely Simplisma and OPA-ALS, as well as IPCA. These results indicate that a combination of SVD, entropy minimization, and simulated annealing is a potentially powerful tool for spectral reconstructions from large real experimental systems.     

Kinetic study of the solution polymerization of methacrylamide initiated with potassium persulfate using in situ Raman spectroscopy and band‐target entropy minimization

In this paper, the use of in situ Raman spectroscopy together with a novel multivariate data analysis method, band‐target entropy minimization (BTEM), is discussed to monitor the solution polymerization of methacrylamide in aqueous medium. Although FTIR spectroscopy is a more popular spectroscopic technique for polymer characterization and in situ polymerization monitoring, Raman spectroscopy is selected over FTIR in the current study. This is because water has very strong and broad infrared absorption bands and thus masks most of the other infrared signals contributed from monomer and polymer. On the contrary, water has very weak Raman scattering and thus it does not interfere the other Raman signals. The polymerization was initiated with potassium persulfate (KPS). A series of experiments were carried out varying initial monomer concentration, initial KPS concentration, and polymerization temperature. In situ Raman spectroscopy was used to monitor the polymerizing mixture and measure the compositions. The collected reaction spectra were subjected to BTEM to elucidate the pure component spectra, and then determine the conversion of monomer. The conversion data was then used to obtain kinetic parameters for the polymerization. The rate of consumption of monomers was found to follow the expression R = k_eff [I]^0.55[M]^1.41. The activation energy of the system was estimated at 121 kJ/mol. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5697–5704, 2007     

Validation using sensitivity and target transform factor analyses of neural network models for classifying bacteria from mass spectra

Temperature constrained cascade correlation networks (TCCCNs) are computational neural networks that configure their own architecture, train rapidly, and give reproducible prediction results. TCCCN classification models were built using the Latin-partition method for five classes of pathogenic bacteria. Neural networks are problematic in that the relationships among the inputs (i.e., mass spectra) and the outputs (i.e., the bacterial identities) are not apparent. In this study, neural network models were constructed that successfully classified the targeted bacteria and the classification model was validated using sensitivity and target transformation factor analysis (TTFA). Without validation of the classification model, it is impossible to ascertain whether the bacteria are classified by peaks in the mass spectrum that have no causal relationships with the bacteria, but instead randomly correlate with the bacterial classes. Multiple single output network models did not offer any benefits when compared to single network models that had multiple outputs. A multiple output TCCCN model achieved classification accuracies of 96 +/- 2% and exhibited improved performance over multiple single output TCCCN models. Chemical ionization mass spectra were obtained from in situ thermal hydrolysis methylation of freeze-dried bacteria. Mass spectral peaks that pertain to the neural network classification model of the pathogenic bacterial classes were obtained by sensitivity analysis. A significant number of mass spectral peaks that had high sensitivity corresponded to known biomarkers, which is the first time that the significant peaks used by a neural network model to classify mass spectra have been divulged. Furthermore, TTFA furnishes a useful visual target as to which peaks in the mass spectrum correlate with the bacterial identities.     

A simple and accurate technique to obtain pure component parameters for three-parameter equations of state

A generalized technique is presented for the calculation of the pure component parameters for the three-parameter equation of state. For illustration, the Usdin-McAuliffe form of cubic equation of state is evaluated.The method requires as input data the vapor pressure and saturated liquid volume of a component at a given temperature. This method may be considered as an extension of Panagiotopoulos-Kumar's method.     

Interpretation of butyltin mass spectra using isotope pattern reconstruction for the accurate measurement of isotope ratios from molecular clusters

The fragmentation patterns of butyltin compounds (mono-, di-, and tributyltin) in an electron impact ion source were studied using an isotope pattern reconstruction algorithm with emphasis on isotope ratio measurements from molecular clusters. For this purpose, standards of natural tin isotope abundance and a (119)Sn-enriched mixture of the three compounds were both ethylated and propylated using sodium tetraalkylborates. The corresponding mass spectra of the various tetraalkyltin compounds prepared were obtained by GC/MS after their extraction with hexane.The results showed that pure interference-free molecular clusters were obtained only for certain R(3)Sn(+) ions where no isobaric overlap with R(2)SnH(+) ions occurred (e.g. BuEt(2)Sn(+) overlaps with Bu(2)SnH(+)). These ions are ideal candidates for accurate Sn isotope ratio measurements, while isotope pattern perturbing interferences are observed for other molecular fragments down to Sn(.)(+). Isotope pattern reconstruction algorithm thus can be used as an analytical tool to ensure the absence of molecular interferences--a requirement for accurate isotope ratio measurements from molecular clusters. The relevance of these studies for the determination of butyltin compounds in environmental samples by isotope dilution GC/MS is also discussed.