Stereoselective preparation of chiral compounds in Mannich-type reactions of a bicyclic imine and phenols or indole

Mannich-type reactions of a chiral bicyclic imine and various nucleophiles yield the corresponding adducts with good to high diastereoselectivity. The influence of the reaction conditions on the yield and stereochemical outcome is investigated. The configuration of the products is established by ¹H NMR spectroscopy, and the major isomers of two adducts are characterized by X-ray crystallography.     

Generalized charge sensitivity analysis

Charge sensitivity analysis was originally introduced in the trivial-atom resolution. Here, we extend this resolution into force-field atoms. The AMBERff99 force-field resolution was employed. The effective electronegativities and hardnesses were derived for five different population analyses (Mulliken, Hirschfeld, AIM, NPA and Voronoi charges) by applying evolutionary algorithms.     

Dynamical Trajectories of Simple Mechanical Systems as Geodesics in Space with an Extra Dimension

We show the advantages of representing thedynamics of simple mechanical systems described by anatural Lagrangian, in terms of geodesics of aRiemannian (or pseudo-Riemannian) space with anadditional dimension. We demonstrate how generaltrajectories of simple mechanical systems can be putinto one-toone correspondence with the geodesics of asuitable manifold. Two different ways in which thegeometry of the configuration space can be obtained froma higher dimensional model are presented and compared:(1) by a straightforward projection, and (2) as a spacegeometry of a quotient space obtained by the action of the timelike Killing vectorgenerating a stationary symmetry of a background spacegeometry with an additional dimension. The second modelis more informative and coincides with the so-called optical model of the line-of-sight geometry. Onthe base of this model we study the behavior of nearbygeodesics to detect their sensitive dependence oninitial conditions — the key ingredient ofdeterministic chaos. The advantage of such a formulation isits invariant character.