Lewis Acids as Activators in CBS‐Catalysed Diels–Alder Reactions: Distortion Induced Lewis Acidity Enhancement of SnCl4

The effect of several Lewis acids on the CBS catalyst (named after Corey, Bakshi and Shibata) was investigated in this study. While ²H NMR spectroscopic measurements served as gauge for the activation capability of the Lewis acids, in situ FT‐IR spectroscopy was employed to assess the catalytic activity of the Lewis acid oxazaborolidine complexes. A correlation was found between the Δδ(²H) values and rate constants k_DA, which indicates a direct translation of Lewis acidity into reactivity of the Lewis acid–CBS complexes. Unexpectedly, a significant deviation was found for SnCl₄ as Lewis acid. The SnCl₄–CBS adduct was much more reactive than the Δδ(²H) values predicted and gave similar reaction rates to those observed for the prominent AlBr₃–CBS adduct. To rationalize these results, quantum mechanical calculations were performed. The frontier molecular orbital approach was applied and a good correlation between the LUMO energies of the Lewis acid–CBS–naphthoquinone adducts and k_DA could be found. For the SnCl₄–CBS–naphthoquinone adduct an unusual distortion was observed leading to an enhanced Lewis acidity. Energy decomposition analysis with natural orbitals for chemical valence (EDA‐NOCV) calculations revealed the relevant interactions and activation mode of SnCl₄ as Lewis acid in Diels–Alder reactions.     

Symmetry justification of Lorenz’ maximum simplification

In 1960 Edward Lorenz (1917–2008) published a pioneering work on the ‘maximum simplification’ of the barotropic vorticity equation. He derived a coupled three-mode system and interpreted it as the minimum core of large-scale fluid mechanics on a ‘finite but unbounded’ domain. The model was obtained in a heuristic way, without giving a rigorous justification for the chosen selection of modes. In this paper, it is shown that one can legitimate Lorenz’ choice by using symmetry transformations of the spectral form of the vorticity equation. The Lorenz three-mode model arises as the final step in a hierarchy of models constructed via the component reduction by means of symmetries. In this sense, the Lorenz model is indeed the ‘maximum simplification’ of the vorticity equation.     

On the model of non-holonomic billiard

In this paper we develop a new model of non-holonomic billiard that accounts for the intrinsic rotation of the billiard ball. This model is a limit case of the problem of rolling without slipping of a ball without slipping over a quadric surface. The billiards between two parallel walls and inside a circle are studied in detail. Using the three-dimensional-point-map technique, the non-integrability of the non-holonomic billiard within an ellipse is shown.     

Nonlinear normal modes and band zones in granular chains with no pre-compression

We study standing waves (nonlinear normal modes—NNMs) and band zones in finite granular chains composed of spherical granular beads in Hertzian contact, with fixed boundary conditions. Although these are homogeneous dynamical systems in the notation of Rosenberg (Adv. Appl. Mech. 9:155–242, 1966), we show that the discontinuous nature of the dynamics leads to interesting effects such as separation between beads, NNMs that appear as traveling waves (these are characterized as pseudo-waves), and localization phenomena. In the limit of infinite extent, we study band zones, i.e., pass and stop bands in the frequency–energy plane of these dynamical systems, and classify the essentially nonlinear responses that occur in these bands. Moreover, we show how the topologies of these bands significantly affect the forced dynamics of these granular media subject to narrowband excitations. This work provides a classification of the coherent (regular) intrinsic dynamics of one-dimensional homogeneous granular chains with no pre-compression, and provides a rigorous theoretical foundation for further systematic study of the dynamics of granular systems, e.g., the effects of disorders or clearances, discrete breathers, nonlinear localized modes, and high-frequency scattering by local disorders. Moreover, it contributes toward the design of granular media as shock protectors, and in the passive mitigation of transmission of unwanted disturbances.     

Diastereoselective Coupling of Chiral Acetonide Trisubstituted Radicals with Alkenes

The stereochemical outcome of reactions of chiral nucleophilic trisubstituted acetonide radicals with electron‐deficient alkenes is dictated by a delicate balance between destabilizing non‐bonding interactions and stabilizing hydrogen‐bonding between substituents on the α and β carbons.