A New Type of Valence Tautomerism in Cobalt Dioxolene Complexes - Temperature-Induced Transition from a Cobalt(III) Catecholate to a Low-Spin Cobalt(II) Semiquinonate State.

The synthesis and characterization of the monocationic cobalt(III) catecholate complex [Co(L-N4 t Bu2 )(Cl2 cat)]+ (L-N4 t Bu2 =N,N'-Di-tert.-butyl-2,11-diaza[3.3](2,6)pyridinophane, Cl2 cat2- =4,5-dichlorocatecholate) are presented. The complex exhibits valence tautomeric properties in solution; but, in contrast to the usually observed conversion from a cobalt(III) catecholate to a high-spin cobalt(II) semiquinonate state, valence tautomerism of [Co(L-N4 t Bu2 )(Cl2 cat)]+ leads to the formation of a low-spin cobalt(II) semiquinonate complex upon raising the temperature. This new type of valence tautomerism for a cobalt dioxolene complex has been unambiguously established by a detailed spectroscopic investigation using variable-temperature NMR, IR and UV-Vis-NIR spectroscopy. Determination of the enthalpies and entropies characterizing the valence tautomeric equilibria in various solutions shows that the influence of the solvent is almost exclusively entropic.

An active constraint approach to identify essential spectral information in noisy data.

Multivariate curve resolution (MCR) methods aim at extracting pure component profiles from mixed spectral data and can be applied to high-dimensional data, e.g., from process spectroscopy or hyperspectral imaging techniques. One often observes that some parts of this data, namely certain rows and columns of the data matrix, are considered essential for MCR outcomes, while other parts are of minor importance. Some methods for determining essential data are known, but all have different disadvantages concerning the application for noisy data. This work presents a new approach on how to detect the essential information for noisy, experimental spectral data. Active nonnegativity constraints in combination with duality arguments are the key ingredients for determining essential spectra and frequency channels. The new approach is conceptually simple, computationally cheap and stable with respect to noise. The algorithm is tested for noisy experimental Raman, UV-Vis and FTIR-SEC data.

Model-based signal tracking in the quantitative analysis of time series of NMR spectra.

Hard modeling of NMR spectra by Gauss-Lorentz peak models is an effective way for dimensionality reduction. In this manner high-dimensional measured data are reduced to low-dimensional information as peak centers, amplitudes or peak widths. For time series of spectra these parameters can be assumed to be smooth functions in time. We suggest to model these time-dependent parameter functions by cubic spline functions, which makes a stable quantitative analysis of NMR series possible even for crossing, highly overlapping peaks. Applications are presented for the batch distillation of methanol and diethylamine, and the reaction of acetic anhydride with 2-propanol.

A multi-method chemometric analysis in spectroelectrochemistry: Case study on molybdenum mono-dithiolene complexes.

Spectroelectrochemical (SEC) analyses combine spectroscopic measurements with electrochemical techniques and can provide deep insight into complex multi-component chemical reaction systems. SEC experiments typically produce large amounts of spectroscopic data. Chemometric techniques are required for the data analysis and aim at extracting the underlying pure component information. Here we analyze spectroelectrochemically gained UV-vis data from five molybdenum mono-dithiolene complexes with changing redox states. SEC enables an electrochemical control of the mixture composition which supports the application of chemometric curve resolution techniques. The factor ambiguity problem is addressed by a multi-method approach combining chemometric tools from the evolving factor analysis (EFA) and from the area of feasible solutions (AFS) methodology in combination with factor duality arguments. EFA enables a subsystem analysis. Two subsystems with three species each are identified, which belong to a reductive and to an oxidative region. A joint species is contained in both regions. A complete pure component decomposition becomes possible in a final step.

Reaction rate ambiguities for perturbed spectroscopic data: Theory and implementation.

The analysis of reaction systems and their kinetic modeling is important for both exploratory research and process design. Multivariate curve resolution (MCR) methods are state-of-the-art tools for the analysis of spectral series, but are also affected by an unavoidable solution ambiguity that impacts the obtained concentration profiles, spectra and model parameters. These uncertainties depend on the underlying model and the magnitude of the measurement perturbations. We present a general theoretical approach together with a computational method for the analysis of the solution ambiguity underlying arbitrary kinetic models. The main idea is to determine all those model parameters for which the corresponding pure component factorizations satisfy all given constraints within small error tolerances. This makes it possible to determine bands of concentration profiles and spectra that reflect the underlying ambiguity and circumscribes the potential reliability of MCR solutions. False conclusions on the uniqueness of a solution can be prevented. The procedure can be applied as a post-processing step to MCR methods as MCR-ALS, ReactLab or others. The Matlab program code is freely accessible and includes not only the proposed ambiguity analysis but also an MCR hard-modeling approach. Application studies are presented for two experimental data sets, namely for UV/Vis spectra on the relaxation of a photoexcited state of benzophenone and for Raman spectra on an aldehyde formation process.

On the analysis of chromatographic biopharmaceutical data by curve resolution techniques in the framework of the area of feasible solutions.

Monitoring preparative protein chromatographic steps by in-line spectroscopic tools or fraction analytics results in medium or large sized data matrices. Multivariate Curve Resolution (MCR) serve to compute or to estimate the concentration values of the pure components only from these data matrices. However, MCR methods often suffer from an inherent solution ambiguity which underlies the factorization problem. The typical unimodality of the chromatographic profiles of pure components can support the chemometric analysis. Here we present the pure components estimation process within the framework of the area of feasible solutions, which is a systematic approach to represent the range of all possible solutions. The unimodality constraint in combination with Pareto optimization is shown to be an effective method for the pure component calculation. Applications are presented for chromatograms on a model protein mixture containing ribonuclease A, cytochrome c and lysozyme and on a two-dimensional chromatographic separation of a monoclonal antibody from its aggregate species. The root mean squared errors of the first case study are 0.0373, 0.0529 and 0.0380 g/L compared to traditional off-line analytics. The second case study illustrates the potential of recovering hidden components with MCR from off-line reference analytics.

Unraveling VEALYL Amyloid Formation Using Advanced Vibrational Spectroscopy and Microscopy.

Intermediate species are hypothesized to play an important role in the toxicity of amyloid formation, a process associated with many diseases. This process can be monitored with conventional and two-dimensional infrared spectroscopy, vibrational circular dichroism, and optical and electron microscopy. Here, we present how combining these techniques provides insight into the aggregation of the hexapeptide VEALYL (Val-Glu-Ala-Leu-Tyr-Leu), the B-chain residue 12-17 segment of insulin that forms amyloid fibrils (intermolecularly hydrogen-bonded ß-sheets) when the pH is lowered below 4. Under such circumstances, the aggregation commences after approximately an hour and continues to develop over a period of weeks. Singular value decompositions of one-dimensional and two-dimensional infrared spectroscopy spectra indicate that intermediate species are formed during the aggregation process. Multivariate curve resolution analyses of the one and two-dimensional infrared spectroscopy data show that the intermediates are more fibrillar and deprotonated than the monomers, whereas they are less ordered than the final fibrillar structure that is slowly formed from the intermediates. A comparison between the vibrational circular dichroism spectra and the scanning transmission electron microscopy and optical microscope images shows that the formation of mature fibrils of VEALYL correlates with the appearance of spherulites that are on the order of several micrometers, which give rise to a "giant" vibrational circular dichroism effect.

Application of a new method for simultaneous phase and baseline correction of NMR signals (SINC).

Recently, we presented a new approach for simultaneous phase and baseline correction of nuclear magnetic resonance (NMR) signals (SINC) that is based on multiobjective optimization. The algorithm can automatically correct large sets of NMR spectra, which are commonly acquired when reactions and processes are monitored with NMR spectroscopy. The aim of the algorithm is to provide spectra that can be evaluated quantitatively, for example, to calculate the composition of a mixture or the extent of reaction. In this work, the SINC algorithm is tested in three different studies. In an in-house comparison study, spectra of different mixtures were corrected both with the SINC method and manually by different experienced users. The study shows that the results of the different users vary significantly and that their average uncertainty of the composition measurement is larger than the uncertainty obtained when the spectra are corrected with the SINC method. By means of a dilution study, we demonstrate that the SINC method is also applicable for the correction of spectra with low signal-to-noise ratio. Furthermore, a large set of NMR spectra that was acquired to follow a reaction was corrected with the SINC method. Even in this system, where the areas of the peaks and their chemical shifts changed during the course of reaction, the SINC method corrected the spectra robustly. The results show that this method is especially suited to correct large sets of NMR spectra and it is thus an important contribution for the automation of the evaluation of NMR spectra.

Multi-objective optimization for an automated and simultaneous phase and baseline correction of NMR spectral data.

Spectral data preprocessing is an integral and sometimes inevitable part of chemometric analyses. For Nuclear Magnetic Resonance (NMR) spectra a possible first preprocessing step is a phase correction which is applied to the Fourier transformed free induction decay (FID) signal. This preprocessing step can be followed by a separate baseline correction step. Especially if series of high-resolution spectra are considered, then automated and computationally fast preprocessing routines are desirable. A new method is suggested that applies the phase and the baseline corrections simultaneously in an automated form without manual input, which distinguishes this work from other approaches. The underlying multi-objective optimization or Pareto optimization provides improved results compared to consecutively applied correction steps. The optimization process uses an objective function which applies strong penalty constraints and weaker regularization conditions. The new method includes an approach for the detection of zero baseline regions. The baseline correction uses a modified Whittaker smoother. The functionality of the new method is demonstrated for experimental NMR spectra. The results are verified against gravimetric data. The method is compared to alternative preprocessing tools. Additionally, the simultaneous correction method is compared to a consecutive application of the two correction steps.

A chemometric study in the area of feasible solution of an acid-base titration of N-methyl-6-oxyquinolone.

Multivariate curve resolution methods aim at recovering the underlying chemical components from spectroscopic data on chemical reaction systems. In most cases the spectra and concentration profiles of the pure components cannot be uniquely determined from the given spectral data. Instead continua of possible factors exist. This fact is known as rotational ambiguity. The sets of all possible pure component factors can be represented in the so-called area of feasible solutions (AFS). This paper presents an AFS study of the pure component reconstruction problem for a series of UV/Vis spectra taken from an acid-base titration of N-methyl-6-oxyquinolone. Additional information on the equilibrium concentration profiles for a varying acid concentration is taken from fluorescence measurements. On this basis chemometric duality arguments lead to the construction of a unique final solution.

A ray casting method for the computation of the area of feasible solutions for multicomponent systems: Theory, applications and FACPACK-implementation.

Multivariate curve resolution methods suffer from the non-uniqueness of the solutions. The set of possible nonnegative solutions can be represented by the so-called Area of Feasible Solutions (AFS). The AFS for an s-component system is a bounded (s-1)-dimensional set. The numerical computation and the geometric construction of the AFS is well understood for two- and three-component systems but gets much more complicated for systems with four or even more components. This work introduces a new and robust ray casting method for the computation of the AFS for general s-component systems. The algorithm shoots rays from the origin and records the intersections of these rays with the AFS. The ray casting method is computationally fast, stable with respect to noise and is able to detect the various possible shapes of the AFS sets. The easily implementable algorithm is tested for various three- and four-component data sets.

On the ambiguity of the reaction rate constants in multivariate curve resolution for reversible first-order reaction systems.

If for a chemical reaction with a known reaction mechanism the concentration profiles are accessible only for certain species, e.g. only for the main product, then often the reaction rate constants cannot uniquely be determined from the concentration data. This is a well-known fact which includes the so-called slow-fast ambiguity. This work combines the question of unique or non-unique reaction rate constants with factor analytic methods of chemometrics. The idea is to reduce the rotational ambiguity of pure component factorizations by considering only those concentration factors which are possible solutions of the kinetic equations for a properly adapted set of reaction rate constants. The resulting set of reaction rate constants corresponds to those solutions of the rate equations which appear as feasible factors in a pure component factorization. The new analysis of the ambiguity of reaction rate constants extends recent research activities on the Area of Feasible Solutions (AFS). The consistency with a given chemical reaction scheme is shown to be a valuable tool in order to reduce the AFS. The new methods are applied to model and experimental data.

A review of recent methods for the determination of ranges of feasible solutions resulting from soft modelling analyses of multivariate data.

Soft modelling or multivariate curve resolution (MCR) are well-known methodologies for the analysis of multivariate data in many different application fields. Results obtained by soft modelling methods are very likely impaired by rotational and scaling ambiguities, i.e. a full range of feasible solutions can describe the data equally well while fulfilling the constraints of the system. These issues are severely limiting the applicability of these methods and therefore, they can be considered as the most challenging ones. The purpose of the current review is to describe and critically compare the available methods that attempt at determining the range of ambiguity for the case of 3-component systems. Theoretical and practical aspects are discussed, based on a collection of simulated examples containing noise-free and noisy data sets as well as an experimental example.

A multiresolution approach for the convergence acceleration of multivariate curve resolution methods.

Modern computerized spectroscopic instrumentation can result in high volumes of spectroscopic data. Such accurate measurements rise special computational challenges for multivariate curve resolution techniques since pure component factorizations are often solved via constrained minimization problems. The computational costs for these calculations rapidly grow with an increased time or frequency resolution of the spectral measurements. The key idea of this paper is to define for the given high-dimensional spectroscopic data a sequence of coarsened subproblems with reduced resolutions. The multiresolution algorithm first computes a pure component factorization for the coarsest problem with the lowest resolution. Then the factorization results are used as initial values for the next problem with a higher resolution. Good initial values result in a fast solution on the next refined level. This procedure is repeated and finally a factorization is determined for the highest level of resolution. The described multiresolution approach allows a considerable convergence acceleration. The computational procedure is analyzed and is tested for experimental spectroscopic data from the rhodium-catalyzed hydroformylation together with various soft and hard models.

An operando FTIR spectroscopic and kinetic study of carbon monoxide pressure influence on rhodium-catalyzed olefin hydroformylation.

The influence of carbon monoxide concentration on the kinetics of the hydroformylation of 3,3-dimethyl-1-butene with a phosphite-modified rhodium catalyst has been studied for the pressure range p(CO)=0.20-3.83 MPa. Highly resolved time-dependent concentration profiles of the organometallic intermediates were derived from IR spectroscopic data collected in situ for the entire olefin-conversion range. The dynamics of the catalyst and organic components are described by enzyme-type kinetics with competitive and uncompetitive inhibition reactions involving carbon monoxide taken into account. Saturation of the alkyl-rhodium intermediates with carbon monoxide as a cosubstrate occurs between 1.5 and 2 MPa of carbon monoxide pressure, which brings about a convergence of aldehyde regioselectivity. Hydrogenolysis of the acyl intermediate is fast at 30 °C and low pressure of p(CO)=0.2 MPa, but is of minus first order with respect to the solution concentration of carbon monoxide. Resting 18-electron hydrido and acyl complexes that correspond to early and late rate-determining states, respectively, coexist as long as the conversion of the substrate is not complete.

On the area of feasible solutions and its reduction by the complementarity theorem.

Multivariate curve resolution techniques in chemometrics allow to uncover the pure component information of mixed spectroscopic data. However, the so-called rotational ambiguity is a difficult hurdle in solving this factorization problem. The aim of this paper is to combine two powerful methodological approaches in order to solve the factorization problem successfully. The first approach is the simultaneous representation of all feasible nonnegative solutions in the area of feasible solutions (AFS) and the second approach is the complementarity theorem. This theorem allows to formulate serious restrictions on the factors under partial knowledge of certain pure component spectra or pure component concentration profiles. In this paper the mathematical background of the AFS and of the complementarity theorem is introduced, their mathematical connection is analyzed and the results are applied to spectroscopic data. We consider a three-component reaction subsystem of the Rhodium-catalyzed hydroformylation process and a four-component model problem.

Exploring between the extremes: conversion-dependent kinetics of phosphite-modified hydroformylation catalysis.

The kinetics of the hydroformylation of 3,3-dimethyl-1-butene with a rhodium monophosphite catalyst has been studied in detail. Time-dependent concentration profiles covering the entire olefin conversion range were derived from in situ high-pressure FTIR spectroscopic data for both, pure organic components and catalytic intermediates. These profiles fit to Michaelis-Menten-type kinetics with competitive and uncompetitive side reactions involved. The characteristics found for the influence of the hydrogen concentration verify that the pre-equilibrium towards the catalyst substrate complex is not established. It has been proven experimentally that the hydrogenolysis of the intermediate acyl complex remains rate limiting even at high conversions when the rhodium hydride is the predominant resting state and the reaction is nearly of first order with respect to the olefin. Results from in situ FTIR and high-pressure (HP) NMR spectroscopy and from DFT calculations support the coordination of only one phosphite ligand in the dominating intermediates and a preferred axial position of the phosphite in the electronically saturated, trigonal bipyramidal (tbp)-structured acyl rhodium complex.