The multicomponent factorization of multivariate data often results in nonunique solutions. The so‐called rotational ambiguity paraphrases the existence of multiple solutions that can be represented by the area of feasible solutions (AFS). The AFS is a bounded set that may consist of isolated subsets. The numerical computation of the AFS is well understood for two‐component systems and is an expensive numerical process for three‐component systems. In this paper, a new fast and accurate algorithm is suggested that is based on the inflation of polygons. Starting with an initial triangle located in a topologically connected subset of the AFS, an automatic extrusion algorithm is used to form a sequence of growing polygons that approximate the AFS from the interior. The polygon inflation algorithm can be generalized to systems with more than three components. The efficiency of this algorithm is demonstrated for a model problem including noise and a multicomponent chemical reaction system. Further, the method is compared with the recent triangle‐boundary‐enclosing scheme of Golshan, Abdollahi, and Maeder (Anal. Chem. 2011, 83, 836–841). Copyright © 2013 John Wiley & Sons, Ltd.

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.

Herein we report the evaluation of the frequently employed tetrabutyl ammonium and phosphonium halides as well as their bifunctional analogs as catalysts in cyclic carbonate synthesis under benchmarked conditions. The kinetic data of all catalysts were evaluated and the rate constants determined. Moreover, a systematic infrared spectroscopic study of the interactions between cation and anion of the catalysts as well as the interactions between the catalysts and the substrate were conducted. These experimental results were additionally supported by DFT calculations. The observed trends in the interaction between the onium cation and the anion are correlated to their catalytic activity. Moreover, these investigations revealed the mode of the substrate activation for the monofunctional and the bifunctional catalysts. Furthermore, the kinetic studies and in situ infrared experiments revealed a product inhibition of the bifunctional catalysts via the unexpected formation of catalyst−carbonate adducts. The interaction between the catalysts and the product was further studied by infrared spectroscopy. Finally, the rate and the equilibrium constants for the binfunctional catalysts were determined by a Michaelis− Menten model considering a reversible product inhibition.

Dedicated to Paul Kamer, a great scientist and inspiring person. A series of hydroxy-functionalized phosphonium salts were studied as bifunctional catalysts for the conversion of CO 2 with epoxides under mild and solvent-free conditions. The reaction in the presence of a phenol-based phosphonium iodide proceeded via a first order rection kinetic with respect to the substrate. Notably, in contrast to the aliphatic analogue, the phenol-based catalyst showed no product inhibition. The temperature dependence of the reaction rate was investigated, and the activation energy for the model reaction was determined from an Arrhenius-plot (E a = 39.6 kJ mol À 1). The substrate scope was also evaluated. Under the optimized reaction conditions, 20 terminal epoxides were converted at room temperature to the corresponding cyclic carbonates, which were isolated in yields up to 99 %. The reaction is easily scalable and was performed on a scale up to 50 g substrate. Moreover, this method was applied in the synthesis of the antitussive agent dropropizine starting from epichlorohydrin and phenylpiperazine. Furthermore, DFT calculations were performed to rationalize the mechanism and the high efficiency of the phenol-based phosphonium iodide catalyst. The calculation confirmed the activation of the epoxide via hydrogen bonding for the iodide salt, which facilitates the ring-opening step. Notably, the effective Gibbs energy barrier regarding this step is 97 kJ mol À 1 for the bromide and 72 kJ mol À 1 for the iodide salt, which explains the difference in activity.

A new rhodium catalyst is described that gives 99% regioselectivity in linear aldehyde in the hydroformylation of internal and terminal olefins. High-pressure NMR spectroscopic data verify an energetically preferred bis-equatorial mode of coordination for the bidentate phosphite ligand in the hydride resting state of the catalyst. Experimental FTIR spectra are compared with the individual spectra of the e,e and e,a isomers of [HRh(CO)2(P∩P)] calculated from density functional theory.

The rhodium‐catalyzed phosphite‐modified hydroformylation of 3,3‐dimethyl‐1‐butene is comparatively studied for a bidentate and a monodentate phosphite using in situ high‐pressure (HP) FTIR spectroscopy and GC analysis. With the bidentate ligand at 70 °C, a pseudo‐first‐order reaction with respect to the olefin takes place, with the pentacoordinate hydrido complex being the only detectable intermediate during the reaction. In contrast, for the monodentate ligand, a zeroth‐ to pseudo‐first‐order shift is characteristic with the major intermediate for this system subsequently changing from the coordinatively saturated acyl complex to the respective hydrido complex already at low conversions. Application of the PCD (pure component decomposition) algorithm to the reaction spectra affords the concentration versus time profiles of these intermediates, providing proof that the reaction rate remains controlled by rhodium acyl hydrogenolysis even at medium to high olefin conversions when the corresponding hydrido complex is the major organometallic component. If the reaction is carried out at a temperature of 30 °C in neat olefin, results from both GC and HP‐FTIR verify an intermediate regime of saturation kinetics and also the presence of an acyl complex at low olefin conversions for the diphosphite. Initial turnover frequencies of 237 h−1 and 1040 h−1 are obtained for the mono‐ and the diphosphite, respectively, at 30 °C, which implies an intrinsically faster hydrogenolysis of the diphosphite‐derived acyl rhodium complex at this low temperature.

A detailed quantitative study of phosphine-modified hydrido iridium complexes relevant for the hydroformylation reaction has been performed using HP-FTIR and HP-NMR spectroscopy. The equilibrium composition under typical reaction conditions has been characterized. Investigation of the temperature dependency allowed even for a distinction between both configurational isomers of [HIr(CO)2(PPh3)2]. The trihydride complex [H3Ir(CO)(PPh3)2] is part of the investigated equilibrium depending on the ratio of p(H2)/p(CO). Single rate constants for the sequence of corresponding equilibrium reactions have been estimated from stopped-flow experiments and conventional measurements, monitoring the concentrations after changing reactant concentrations.

A selective ruthenium-catalyzed water–gas shift/hydroformylation of internal olefins and olefin mixtures is reported. This novel domino reaction takes place through a catalytic water–gas shift reaction, subsequent olefin isomerization, followed by hydroformylation and reductive amination. Key to the success for the efficient one-pot process is the use of a specific 2-phosphino-substituted imidazole ligand and triruthenium dodecacarbonyl as precatalyst. Industrially important internal olefins react with various amines to give the corresponding tertiary amines generally in good yield and selectivity. This reaction sequence constitutes an economically attractive and environmentally favorable process for the synthesis of linear amines.