Resolving factor analysis

A new strategy for the computer-assisted development of reversed-phase liquid chromatography separation methods of unknown sample mixtures

A new strategy for the computer-assisted methods development in the reversed-phase liquid chromatographic separations of unknown sample mixtures has been developed using the latent spectral information in chromatogram raw data files of appropriately designed experiments, rather than resorting to elemental information functions (e.g., the number of peaks in chromatograms or similar criteria). The strategy developed allows unification of the approach for samples of both known and unknown composition and, thus, provide a general strategy for computer-aided tools in the chromatography laboratory. The operation principle of this strategy departs from extracting the spectra of components in the mixture chromatograms by resorting to multivariate curve resolution-alternating least squares (MCR-ALS). This technique allows the estimation of the true spectra for the individual components except when they have identical spectra or are fully overlapped. Thus, a convenient experimental design will try to perform separations of the sample mixture having at least partial resolution of components in some runs. This will allow estimating the spectra of components and, then, assign these components to the peaks in each run chromatogram. In this way, a retention model can be built for each component so computerized optimization process can be developed to provide the chromatographer with the best possible separation programs. Following this approach, strategies for sample mixtures of known and unknown composition are only different in the need of an initial spectrum discovery process for unknown mixtures and therefore a real general approach for the computer-assisted LC methods development is now available for the first time.

Model-based analysis for kinetic complexation study of Pizda and Cu(II)

In the present work, the multivariate kinetic complexation of a new synthesized ligand, 1-(2''-hydroxyl cyclohexyl)-3'-[aminopropyl]-4-[3'-aminopropyl]piperazine (Pizda) and Cu(2+) in 50% ethanol-water solution is investigated using the UV-vis stopped-flow technique and state-of-the-art multi-wavelength numerical analysis. Model-based least squares fitting analysis or hard modeling is a specific part of chemometrics which is based on mathematical relationships for describing the measurements. Some recent developments include the incorporation of the effects of non-ideal experimental conditions into the fitting algorithm so it can substantially simplify experimental procedures. In this study no buffers are required because pH changes are taken into computations. Some 21 multi-wavelength kinetic measurements, taken at various initial concentrations of [H(+)] were analyzed globally, i.e. simultaneously applying an all inclusive reaction mechanism and a common set of species spectra. Using numerical analysis, the pH of the experimental solutions was allowed to vary as a consequence of the proceeding reactions. This enabled the complete kinetic analysis of the formation and dissociation of Cu(Pizda)(n+). Here protonation equilibria have been directly incorporated into the rate law, so thus variable pH values have been allowed during each measurement. Using the independently estimated stability constants (from spectrophotometric and potentiometric measurements) for the Cu(Pizda)(n+) complexes, a total of six rate constants and one protonation constant could be elucidated. The results of the analysis include the concentration distribution and spectra of all chemical species involved in the reaction. A low standard deviation and residual profiles obtained validate the results.

Multivariate curve resolution-alternating least squares (MCR-ALS) applied to spectroscopic data from monitoring chemical reactions processes

This paper overviews the application of multivariate curve resolution (optimized by alternating least squares) to spectroscopic data acquired by monitoring chemical reactions and other processes. The goals of the resolution methods and the principles for understanding their applications are described. Some of the problems arising from these evolving systems and the limitations of the multivariate curve resolution methods are also discussed. This article reviews most of the applications of multivariate curve resolution applied to reacting systems published between January 2000 and June 2007. Some basic papers dated before 2000 have also been included.

Factor analysis of hyphenated chromatographic data

Factor analysis (FA) is a family of widely used methods to obtain the underlying sources of variation of data tables. Typically, hyphenated chromatographic data provide data tables with one elution direction and another linked to the detector response. In this context, the factors are the eluting compounds and the profiles defining each factor are the elution profile and the pure response of the compound. This article describes the use of FA in chromatography through diverse tools and problems. Examples of determination of number of compounds, peak purity problems, resolution of overlapped compounds or extension to simultaneous analysis of multiple runs (higher-order data structures) to obtain qualitative and quantitative information are reviewed.

Application of non-linear optimization methods to the estimation of multivariate curve resolution solutions and of their feasible band boundaries in the investigation of two chemical and environmental simulated data sets

Although alternating least squares algorithms have revealed extremely useful and flexible to solve multivariate curve resolution problems, other approaches based on non-linear optimization algorithms using non-linear constraints are possible. Once the subspaces defined by PCA solutions are identified, appropriate rotation and perturbation of these solutions can produce solutions fulfilling the constraints obeyed by the physical nature of the investigated systems. In order to perform such a rotation, an optimization algorithm based in the fulfillment of constraints and some examples of application in chemistry and environmental chemistry are given. It is shown that the solutions obtained either by alternating least squares or by the new proposed algorithm are rather similar and that they are both within the boundaries of the band of feasible solutions obtained by an algorithm previously developed to estimate them.

Tautomerization equilibria in aqueous micellar solutions: a spectrophotometric and factor-analytical study

The keto-enol equilibria of benzoylacetone (BZA) as a model for 1,3-dicarbonyl compounds are studied in aqueous acid and cationic micellar solution. Evolving factor analysis (EFA), multivariate curve resolution-alternating least-squares (MCR-ALS), and rank annihilation factor analysis (RAFA) are used for complete resolving of measured spectrophotometric data. The acidity constants of the enolic, KaE, and ketonic, KaK, forms of BZA and also the tautomerization constant, Kt, and its related thermodynamic parameters have been determined by using EFA and MCR-ALS methods and spectral variation of BZA solutions in various pHs and temperatures. The concentration and spectral profiles of all species were calculated without any assumption about chemical models. The spectral variation of BZA solutions as a function of cationic micelle concentration sufficiently beyond its critical micelle concentration is analyzed according to the partition model for distribution between water and micellar pseudo-phase and RAFA. The outputs of using RAFA on measured rank deficient data are the spectrum of enolic form in the micellar pseudo-phase, free from contribution of the enolic form in the aqueous phase, the partition coefficient of enolic form, KdE, between the micelle and water phases, and the tautomerization constant in the micellar pseudo-phase, Ktm.

Photochemistry of the [Fe4(μ3-S)3(NO)7]− complex in the presence of S-nucleophiles: A spectroscopic study

Biological systems usually contain cysteine, glutathione or other sulfur-containing biomolecules. These S-nucleophiles were found to affect drastically the [Fe(4)(mu(3)-S)(3)(NO)(7)](-) photolysis pathway generating products completely different from that of the neat cluster, which produces Fe(II) and NO and S(2-). The effect is interpreted in terms of formation of a pseudo-cubane adduct, [Fe(4)(mu(3)-S)(3)(mu(3)-SR)(NO)(7)](2-), whose existence in equilibrium with the parent complex has no detectable influence on the spectral properties, whereas shifts the redox potential and induces photoconversion leading to the Fe(III) species and N(2)O. Characteristic bond lengths, bond angles and atomic Mulliken charges were calculated using semi-empirical quantum chemical methods for the RBS anion and a series of pseudo-cubane complexes with S-donor or N-donor ligands. The results justify the hypothesis of the adduct formation and show that only in case of S-ligands the higher contribution of the Fe(III)-NO(-) components in adduct than in RBS is observed, which on excitation can undergo heterolytic cleavage yielding Fe(III) and NO(-), converted rapidly into N(2)O. These results are crucial in understanding the physiological activity of RBS. Fe(III) formation can be detected only when the S-ligand enables formation of a stable Fe(III) compound; the effect was recorded in the presence of sulfide, thioglycolate, 2-mercaptopropionate, mercaptosuccinate, penicillamine, 2,3-dimercaptosuccinate, 2,3-dimercaptopropanol, and thiocyanate. For all these S-ligands the Fe(III) photoproducts were identified and characterised. In the case of other thiolates, their excess results in fast reduction of Fe(III) to Fe(II), whereas N(2)O can be still detected. Quantum yields of Fe(III) formation in the presence of the S-ligands are considerably higher than that of the Fe(II) photoproduction from neat [Fe(4)(mu(3)-S)(3)(NO)(7)](-).