Universal quadratures for boundary integral equations on two-dimensional domains with corners

We describe the construction of a collection of quadrature formulae suitable for the efficient discretization of certain boundary integral equations on a very general class of two-dimensional domains with corner points. The resulting quadrature rules allow for the rapid high-accuracy solution of Dirichlet boundary value problems for Laplace’s equation and the Helmholtz equation on such domains under a mild assumption on the boundary data. Our approach can be adapted to other boundary value problems and certain aspects of our scheme generalize to the case of surfaces with singularities in three dimensions. The performance of the quadrature rules is illustrated with several numerical examples.     

Highly enantioselective,catalytic conjugate addition of cyanide to alpha,beta-unsaturated imides

(Salen)Al-Cl complex 1a catalyzes the asymmetric conjugate addition of hydrogen cyanide to alpha,beta-unsaturated imides in high yields and enantioselectivities. The cyanide adducts can readily be converted into a variety of useful chiral building blocks, including alpha-substituted-beta-amino acids and beta-substituted-gamma-aminobutyric acids. Mechanistic data obtained thus far point to a cooperative bimetallic mechanism for nucleophile and electrophile activation.     

Copper‐Catalyzed Intermolecular Carboetherification of Unactivated Alkenes by Alkyl Nitriles and Alcohols

A three‐component carboetherification of unactivated alkenes has been developed allowing the rapid building of complexity from simple starting materials. A wide range of α‐substituted styrenes underwent smooth reactions with unactivated alkyl nitriles and alcohols to afford γ‐alkoxy alkyl nitriles with concomitant generation of a quaternary carbon center. A radical clock experiment provided clear‐cut evidence that the reaction proceeds through a tertiary alkyl radical intermediate.     

Photoinduced electron-transfer-promoted redox fragmentation of N-alkoxyphthalimides

A new photoinduced electron-transfer-promoted redox fragmentation of N-alkoxyphthalimides has been developed. Mechanistic experiments have established that this reaction proceeds through a unique concerted intramolecular fragmentation process. This distinctive mechanism imparts many synthetic advantages, which are highlighted in the redox fragmentation of various heterocyclic substrates.     

Cooperative dual catalysis: application to the highly enantioselective conjugate cyanation of unsaturated imides

Cooperative heterobimetallic catalysis was used as a design principle to achieve a highly reactive system for the enantioselective conjugate addition of cyanide to alpha,beta-unsaturated imides. A dual-catalyst pathway involving chiral (salen)Al complex 1b and chiral (pybox)Er complex 4b provides measurable improvements in rates and enantioselectivities relative to single-catalyst systems. Mechanistic studies point to a cooperative bimetallic mechanism involving activation of the imide by the Al complex and activation of cyanide by the Er complex.     

Fluorine transfer to alkyl radicals

The development of new synthetic technologies for the selective fluorination of organic compounds has increased with the escalating importance of fluorine-containing pharmaceuticals. Traditional methods potentially applicable to drug synthesis rely on the use of ionic forms of fluorine (F(-) or F(+)). Radical methods, while potentially attractive as a complementary approach, are hindered by a paucity of safe sources of atomic fluorine (F(?)). A new approach to alkyl fluorination has been developed that utilizes the reagent N-fluorobenzenesulfonimide as a fluorine transfer agent to alkyl radicals. This approach is successful for a broad range of alkyl radicals, including primary, secondary, tertiary, benzylic, and heteroatom-stabilized radicals. Furthermore, calculations reveal that fluorine-containing ionic reagents are likely candidates for further expansion of this approach to polar reaction media. The use of these reagents in alkyl radical fluorination has the potential to enable powerful new transformations that otherwise would take multiple synthetic steps.