Forming Stereogenic Centers in Acyclic Systems from Alkynes

The combined carbometalation/zinc homologation followed by reactions with α‐heterosubstituted aldehydes and imines proceed through a chair‐like transition structure with the substituent of the incoming aldehyde residue preferentially occupying a pseudo‐axial position to avoid the two gauche interactions. The heteroatom in the axial position produces a chelated intermediate (and not a Cornforth–Evans transition structure for α‐chloro aldehydes and imines) leading to a face differentiation in the allylation reaction. This method provides access to functionalized products in which three new carbon–carbon bonds and two to three stereogenic centers, including a quaternary one, were created in acyclic systems in a single‐pot operation from simple alkynes.     

Selective Carbon–Carbon Bond Cleavage for the Stereoselective Synthesis of Acyclic Systems

Most of the efforts of organic chemists have been directed to the development of creative strategies to build carbon–carbon and carbon–heteroatom bonds in a predictable and efficient manner. In this Review, we show an alternative approach where challenging molecular skeletons could be prepared through selective cleavage of carbon–carbon bonds. We demonstrate that it has the potential to be a general principle in organic synthesis for the regio‐, diastereo‐, and even enantioselective preparation of adducts despite the fact that C? C single bonds are among the least reactive functional groups. The development of such strategies may have an impact on synthesis design and can ultimately lead to new selective and efficient processes for the utilization of simple hydrocarbons.     

Reliable parallel solution of bidiagonal systems

Summary. This paper presents a new efficient algorithm for solving bidiagonal systems of linear equations on massively parallel machines. We use a divide and conquer approach to compute a representative subset of the solution components after which we solve the complete system in parallel with no communication overhead. We address the numerical properties of the algorithm in two ways: we show how to verify the à posteriori backward stability at virtually no additional cost, and prove that the algorithm is à priori forward stable. We then show how we can use the algorithm in order to bound the possible perturbations in the solution components. Received March 13, 1998 / Revised version received December 21, 1999 / Published online June 20, 2001     

Coalescing times for IID random variables with applications to population biology

We consider a coalescing particle model where particles move in discrete time. At each time period, each remaining ball is independently put in one of n bins according to a probability distribution p = (p₁, …, p_n), and all balls put into the same bin merge into a single ball. Starting with k balls, we are interested in the properties of E[N( p , k)], the expected time until all balls merge into one. We derive both upper and lower bounds for E[N( p , k)], some asymptotic results, and show that P{N( p , k) > t}, and thus E[N( p , k)], is a Schur concave function of p . Applications to population biology are noted. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 155–166, 2003     

Rhodium‐Catalyzed Arylation of Cyclopropenes Based on Asymmetric Direct Functionalization of Three‐Membered Carbocycles

A variety of highly diastereo‐ and enantiomerically enriched arylcyclopropanes is obtained through the asymmetric rhodium‐catalyzed arylation reaction of achiral nonfunctionalized cyclopropene derivatives with commercially available aryl boronic acids in the presence of (R,S)‐Josiphos.     

Preparation and Reactivity of Acyclic Chiral Allylzinc Species by a Zinc‐Brook Rearrangement

The zinc‐Brook rearrangement of enantiomerically enriched α‐hydroxy allylsilane produces a chiral allylzinc intermediate, which reacts with retention of configuration in the presence of an electrophile. Two remarkable features of this transformation are the stereochemical outcome during the formation of the allylzinc species and the complete stereocontrol in the organized six‐membered transition state, which leads to an overall and complete transfer of chirality within the reaction sequence.     

Brook Rearrangement as a Trigger for the Ring Opening of Strained Carbocycles

The combined regio‐ and stereoselective carbometalation of cyclopropenyl amides, followed by the addition of an acyl silane, led to the formation of polysubstituted cyclopropyl derivatives as unique diastereoisomers. Upon warming of the reaction mixture to room temperature, a Brook rearrangement proceeded with inversion of configuration to provide ready access to δ‐ketoamides possessing a quaternary carbon center with high enantiomeric ratios through selective C? C bond cleavage of the ring.     

Stereoselective Formation of Fully Substituted Ketone Enolates

The application of stereochemically defined acyclic fully substituted enolates of ketones to the enantioselective synthesis of quaternary carbon stereocenters would be highly valuable. Herein, we describe an approach leading to the formation of several new stereogenic centers through a combined metalation–addition of a carbonyl–carbamoyl transfer to reveal in situ stereodefined α,α‐disubstituted enolates of ketone as a single stereoisomer. This approach could produce a series of aldol and Mannich products from enol carbamate with excellent diastereomeric ratios.     

A shift in retrosynthetic paradigm

The current state-of-the-art synthesis for the formation of enantiomerically enriched all-carbon quaternary stereocenters in acyclic system relies on the formation of a single carbon-carbon bond per chemical step by asymmetric catalysis. These extraordinary sophisticated methods were logically classified among the most powerful and innovative ones. In this concept article, we are proposing a new retrosynthetic paradigm to solve differently such challenging problems. These new synthetic pathways lead to the diastereo- and enantiomerically pure formation of three new carbon-carbon bonds in acyclic system, in a one-pot reaction, including the formation of all-carbon quaternary stereocenters by using classical reagents and experimental conditions and from common starting materials.