Structures of the Reactive Intermediates in Organocatalysis with Diarylprolinol Ethers

Structures of the reactive intermediates (enamines and iminium ions) of organocatalysis with diarylprolinol derivatives have been determined. To this end, diarylprolinol methyl and silyl ethers, 1 , and aldehydes, Ph? CH₂? CHO, ^tBu? CH₂? CHO, Ph? CH=CH? CHO, are condensed to the corresponding enamines, A and 3 (Scheme 2), and cinnamoylidene iminium salts, B and 4 (Scheme 3). These are isolated and fully characterized by melting/decomposition points, [α]_D, elemental analysis, IR and NMR spectroscopy, and high‐resolution mass spectrometry (HR‐MS). Salts with BF₄, PF₆, SbF₆, and the weakly coordinating Al[OC(CF₃)₃]₄ anion were prepared. X‐Ray crystal structures of an enamine and of six iminium salts have been obtained and are described herein (Figs. 2 and 4–8, and Tables 2 and 7) and in a previous preliminary communication (Helv. Chim. Acta 2008 , 91, 1999). According to the NMR spectra (in CDCl₃, (D₆)DMSO, (D₆)acetone, or CD₃OD; Table 1), the major isomers 4 of the iminium salts have (E)‐configuration of the exocyclic N?C(1′) bond, but there are up to 11% of the (Z)‐isomer present in these solutions (Fig. 1). In all crystal structures, the iminium ions have (E)‐configuration, and the conformation around the exocyclic N‐C? C‐O bond is synclinal‐exo (cf. C and L ), with one of the phenyl groups over the pyrrolidine ring, and the RO group over the π‐system. One of the meta‐substituents (Me in 4b , CF₃ in 4c and 4e ) on a 3,5‐disubstituted phenyl group is also located in the space above the π‐system. DFT Calculations at various levels of theory (Tables 3–6) confirm that the experimentally determined structures (cf. Fig. 10) are by far (up to 8.3 kcal/mol) the most stable ones. Implications of the results with respect to the mechanism of organocatalysis by diarylprolinol derivatives are discussed.     

Oil whirl,oil whip and whirl/whip synchronization occurring in rotor systems with full-floating ring bearings

High-speed rotors are often supported in floating ring bearings because of their good damping behavior. In contrast to conventional hydrodynamic bearings with a single oil film, full-floating ring bearings consist of two oil films: An inner and an outer oil film. As single oil-film bearings, full-floating ring bearings also show the typical fluid-film-induced instabilities (self-excited vibrations). Both inner and outer oil films can become unstable and exhibit oil whirl/whip instabilities. The paper at hand considers a Laval (Jeffcott) rotor, which is symmetrically supported in full-floating ring bearings, and investigates the occurring oil whirl/whip effects by means of run-up simulations. It is shown that the inner oil film, which usually becomes unstable first, gives rise to a limit-cycle oscillation with an exactly circular rotor orbit, if gravity and imbalance are neglected. Interesting is the instability generated by the outer oil film. The calculations demonstrate that instability in the outer oil film does not lead to a simple circular limit-cycle orbit. Whirl/whip-induced limit-cycle oscillations generated by the outer oil film are more complex and entail a coupled circumferential and radial motion, although the mechanical problem is radially symmetric, if gravity and imbalance are neglected. Thus, whirl/whip instability in the outer fluid film may be interpreted as symmetry breaking. Finally, a further kind of bifurcation/instability occurring in rotors supported in full-floating ring bearings—called Total Instability in this paper—is analyzed. It is shown that Total Instability is caused by synchronization of two limit cycles, namely synchronization of the inner and outer oil whirl/whip. Total Instability is of practical interest and observed in real technical rotor systems, and frequently leads to complete rotor damage.     

Shared values of meromorphic functions on compact Riemann surfaces

Let S be a compact Riemann surface of genus g and gonality d. We derive upper bounds (in terms of g and/or d) for the number of values that two non-constant meromorphic functions on S can share. The case d = 2 (i.e., the surface is hyperelliptic or elliptic) is studied in more detail.Received: 14 April 2004     

Experimental and Theoretical Conformational Analysis of 5‐Benzylimidazolidin‐4‐one Derivatives – a ‘Playground’ for Studying Dispersion Interactions and a ‘Windshield‐Wiper’ Effect in Organocatalysis

The PF₆ salts of 5‐benzyl‐1‐isopropylidene‐ and 5‐benzyl‐1‐cinnamylidene‐3‐methylimidazolidin‐4‐ones 1 (Scheme) with various substituents in the 2‐position have been prepared, and single crystals suitable for X‐ray structure determination have been obtained of 14 such compounds, i.e., 2 – 10 and 12 – 16 (Figs. 2–5). In nine of the structures, the Ph ring of the benzyl group resides above the heterocycle, in contact with the cis‐substituent at C(2) (staggered conformation A ; Figs. 1–3); in three structures, the Ph ring lies above the iminium π‐plane (staggered conformation B ; Figs. 1 and 4); in two structures, the benzylic C? C bond has an eclipsing conformation ( C ; Figs. 1 and 5) which places the Ph ring simultaneously at a maximum distance with its neighbors, the CO group, the N?C‐π‐system, and the cis‐substituent at C(2) of the heterocycle. It is suggested by a qualitative conformational analysis (Fig. 6) that the three staggered conformations of the benzylic C? C bond are all subject to unfavorable steric interactions, so that the eclipsing conformation may be a kind of ‘escape’. State‐of‐the‐art quantum‐chemical methods, with large AO basic sets (near the limit) for the single‐point calculations, were used to compute the structures of seven of the 14 iminium ions, i.e., 3, 4 / 12, 5 – 7, 13 , and 16 (Table) in the two staggered conformations, A and B , with the benzylic Ph group above the ring and above the iminium π‐system, respectively. In all cases, the more stable computed conformer (‘isolated‐molecule’ structure) corresponds to the one present in the crystal (overlay in Fig. 7). The energy differences are small (≤2 kcal/mol) which, together with the result of a potential‐curve calculation for the rotation around the benzylic C? C bond of one of the structures, 16 (Fig. 8), suggests that the benzyl group is more or less freely rotating at ambident temperatures. The importance of intramolecular London dispersion (benzene ring in ‘contact’ with the cis‐substituent in conformation A ) for DFT and other quantum‐chemical computations is demonstrated; the benzyl‐imidazolidinones 1 appear to be ideal systems for detecting dispersion contributions between a benzene ring and alkyl or aryl CH groups. Enylidene ions of the type studied herein are the reactive intermediates of enantioselective organocatalytic conjugate additions, Diels–Alder reactions, and many other transformations involving α,β‐unsaturated carbonyl compounds. Our experimental and theoretical results are discussed in view of the performance of 5‐benzyl‐imidazolidinones as enantioselective catalysts.     

Probability distributions with given margins: Note on a paper by Finch and Groblicki

Recently, P. D. Finch and R. Groblicki determined all bivariate probability densities with specified margins. We point out that their result follows immediately from the complete solution to the problem of determining all n-dimensional cumulative probability distribution functions with specified one-dimensional margins, which was solved by one of us in 1959.     

Untersuchung von Eiern

Ohne Zusammenfassung     

Aromatic Interactions in Organocatalyst Design: Augmenting Selectivity Reversal in Iminium Ion Activation

Substituting N‐methylpyrrole for N‐methyindole in secondary‐amine‐catalysed Friedel–Crafts reactions leads to a curious erosion of enantioselectivity. In extreme cases, this substrate dependence can lead to an inversion in the sense of enantioinduction. Indeed, these closely similar transformations require two structurally distinct catalysts to obtain comparable selectivities. Herein a focussed molecular editing study is disclosed to illuminate the structural features responsible for this disparity, and thus identify lead catalyst structures to further exploit this selectivity reversal. Key to effective catalyst re‐engineering was delineating the non‐covalent interactions that manifest themselves in conformation. Herein we disclose preliminary validation that intermolecular aromatic (CH–π and cation–π) interactions between the incipient iminium cation and the indole ring system is key to rationalising selectivity reversal. This is absent in the N‐methylpyrrole alkylation, thus forming the basis of two competing enantio‐induction pathways. A simple L ‐valine catalyst has been developed that significantly augments this interaction.