TiCl3‐Mediated Synthesis of 2,3,3‐Trisubstituted Indolenines: Total Synthesis of (+)‐1,2‐Dehydroaspidospermidine, (+)‐Condyfoline,and (−)‐Tubifoline

2,3,3‐Trisubstituted indolenine constitutes an integral part of many biologically important monoterpene indole alkaloids. We report herein an unprecedented access to this skeleton by a TiCl₃‐mediated reductive cyclization of tetrasubstituted alkenes bearing a 2‐nitrophenyl substituent. The proof of concept is demonstrated firstly by accomplishing a concise total synthesis of (+)‐1,2‐dehydroaspidospermidine featuring a late‐stage application of this key transformation. A sequence of reduction of nitroarene to nitrosoarene followed by 6π‐electron‐5‐atom electrocyclization and a 1,2‐alkyl shift of the resulting nitrone intermediate was proposed to account for the reaction outcome. A subsequent total synthesis of (+)‐condyfoline not only illustrates the generality of the reaction, but also provides a mechanistic insight into the nature of the 1,2‐alkyl shift. The exclusive formation of (+)‐condyfoline indicates that the 1,2‐alkyl migration follows a concerted Wagner–Meerwein pathway, rather than a stepwise retro‐Mannich/Mannich reaction sequence. Conditions for almost quantitative conversion of (+)‐condyfoline to (?)‐tubifoline by way of a retro‐Mannich/1,3‐prototropy/transannular cyclization cascade are also documented.     

Automated synthesis of lipomannan backbone alpha(1-6) oligomannoside via glycosyl phosphates: glycosyl tricyclic orthoesters revisited

Glycosyl tricyclic orthoesters provide a versatile basis for the efficient generation of glycosyl phosphates, which are used in the automated synthesis of lipomannan backbone alpha(1-6) hexa-mannoside.     

A modified approach to the phomoidrides: synthesis of a late-stage intermediate containing a key carbon quaternary stereocenter

A previously developed approach to the synthesis of the phomoidrides has been modified to incorporate all necessary carbon atoms prior to the key tandem carbonylation/Cope rearrangement reaction. This modification necessitated the synthesis of a challenging all-carbon quaternary stereocenter, which in turn rendered ineffective several reactions from the original synthesis. An oxidative radical cleavage of a spirocyclopropane ring system was developed that accomplishes the synthesis of the quaternary center, and a regioselective double hydroboration reaction was devised that provides an alternate approach to a key sequence of functional group interconversions, where the originally developed route was found to be ineffective.     

Qualitative counting closed geodesics

Geometriae Dedicata - We investigate the geometry of word metrics on fundamental groups of manifolds associated with the generating sets consisting of elements represented by closed geodesics. We...     

A projection method for the spectral solution of non‐homogeneous and incompressible Navier–Stokes equations

This paper is devoted to the development of a parallel, spectral and second‐order time‐accurate method for solving the incompressible and variable density Navier–Stokes equations. The method is well suited for finite thickness density layers and is very efficient, especially for three‐dimensional computations. It is based on an exact projection technique. To enforce incompressibility, for a non‐homogeneous fluid, the pressure is computed using an iterative algorithm. A complete study of the convergence properties of this algorithm is done for different density variations. Numerical simulations showing, qualitatively, the capabilities of the developed Navier–Stokes solver for many realistic problems are presented. The numerical procedure is also validated quantitatively by reproducing growth rates from the linear instability theory in a three‐dimensional direct numerical simulation of an unstable, non‐homogeneous, flow configuration. It is also shown that, even in a turbulent flow, the spectral accuracy is recovered. Copyright © 2012 John Wiley & Sons, Ltd.