Quantum qualitative dynamics

We describe our work on qualitative methods for visualizing the quantum eigenstates of systems with nonlinear classical dynamics. For two-degree-of-freedom systems, our approach is based on the use of generalized coherent states, and allows systems with nonoscillator kinematics to be investigated. The general approach is illustrated with two examples involving vibration-rotation interaction in polyatomic molecules. We apply the coherent states of the Lie groupH ₄SU(2) to define quantum surfaces of section for a model involving centrifugal coupling of a harmonic bend with molecular rotation, andSU(2)SU(2) coherent states to study two harmonic normal modes coupled to overall molecular rotation through coriolis interaction. In both systems, quantum states are visualized on the rotational surface of section and compared with the corresponding classical phase space structure. Striking classical-quantum correspondence is observed. We then describe recent results on the quantum states of (N 3)-dimensional systems of coupled nonlinear oscillators, which reveal a quantum delocalization that is reminiscent of classical Arnold diffusion.     

Ionic Pd/NHC Catalytic System Enables Recoverable Homogeneous Catalysis: Mechanistic Study and Application in the Mizoroki–Heck Reaction

N-Heterocyclic carbene (NHC) ligands are ubiquitously utilized in catalysis. A common catalyst design model assumes strong M–NHC binding in this metal–ligand framework. In contrast to this common assumption, we demonstrate here that lability and controlled cleavage of the M−NHC bond (rather than its stabilization) could be more important for high-performance catalysis at low catalyst concentrations. The present study reveals a dynamic stabilization mechanism with labile metal–NHC binding and [PdX₃]⁻[NHC-R]⁺ ion pair formation. Access to reactive anionic palladium intermediates formed by dissociation of the NHC ligands and plausible stabilization of the molecular catalyst in solution by interaction with the [NHC-R]⁺ azolium ion is of particular importance for an efficient and recyclable catalyst. These ionic Pd/NHC complexes allowed for the first time the recycling of the complex in a well-defined form with isolation at each cycle. Computational investigation of the reaction mechanism confirms a facile formation of NHC-free anionic Pd in polar media through either Ph–NHC coupling or reversible H–NHC coupling. The present study formulates novel ideas for M/NHC catalyst design.     

THE FIRST SYNTHESIS OF A 2H-1,4-BENZOTHIAZINE-BASED PHOSPHINE OXIDE AND SULFIDE

Abstract

The synthesis of a cyclic α-amino phosphine oxide and sulfide with an incorporated benzo-thiazine moiety is described. The products can be regarded as analogues of the biologically active thiazolidinylphosphonates, in which several characteristic functional groups have been modified.     

A New Synthetic Route to Selected Indenones

Indenones are useful intermediates in the synthesis of several natural products, e.g. gibberellins (1) and steroid hormones with a C-nor-D-home system (2). Despite the nernerous methods for indenone synthesized, or the yields was much lower as mentioned in earlier reports (1)(4). One of the difficulties of the usual methods is the required electrophilic cyclization meta to a methoxyl substiruent. House (5) deals with these difficulties in more detail. In our method the synthesis of 6-methoxyinde-nones is effected by substitution dara to methoxyl function.     

Decarboxylation of α-Amino Acids Containing Two and Three Stereogenic Centers: A Simple One-Step Procedure to Prepare two Optically Active β-Amino Alcohols and a Bicyclic Pyrrolidine Derivative

The decarboxylation of L-threonine (2S,3R)-1, L-hydroxyproline (2S,4R)-2 and D-2-azabicyclo[3.3.0]octan-3-carboxylic acid (1R,3R,5R)-5 yield in a simple one-step procedure the corresponding optically active β-amino alcohols (R)-3 and (R)-4 and the bicyclic pyrrolidine derivative (1R,5R)-6 in 72–82% yield and >99% ee.     

Newton's method on Riemannian manifolds and a geometric model for the human spine

To study a geometric model of the human spine we are led tofinding a constrained minimum of a real valued function definedon a product of special orthogonal groups. To take advantgeof its Lie group structure we consider Newton's method on thismanifold. Comparisons between measured spines and computed spinesshow the pertinence of this approach.     

New supported beta-amino alcohols as efficient catalysts for the enantioselective addition of diethylzinc to benzaldehyde under flow conditions

[formula: see text] Polymeric monoliths 10 containing an amino alcohol moiety derived from an industrial waste material represent one of the best ligands for the enantioselective catalytic addition of ZnEt2 to benzaldehyde (99% ee), being recoverable and usable under flow conditions.     

On the geometry of master-slave synchronization

In 1990, Pecora and Carroll reported the observation that one can synchronize the orbits of two identical dynamical systems, which may be chaotic, by feeding state variables of one of them to the other one with no feedback, a phenomenon often called master-slave synchronization. We report here some results on the theory of master-slave synchronization for maps and flows, which are all inspired by a similar geometric and coordinate independent point of view to the one introduced in master-slave synchronization by Tresser, Worfolk, and Bass. Our results are variations on the theme that projection often can compensate for expansion.(c) 2002 American Institute of Physics.     

The Bell inequalities and the joint measurement of incompatible observables

A quantum-mechanical theory of joint nonideal measurement of incompatible polarization observables is applied to an EPR-like experiment. It is demonstrated that this experiment yields both information satisfying and information violating the Bell inequalities. The measurement is also discussed in the context of a local hidden-variables theory. It is argued that the violation of an additional assumption of reproducibility of the hidden variable rather than violation of locality may be responsible for the violation of the Bell inequalities.