Addition of Organometallic Reagents to Chiral N‐Methoxylactams: Enantioselective Syntheses of Pyrrolidines and Piperidines

Enantioselective iridium‐catalyzed allylic substitutions were used to prepare N‐allyl hydroxamic acid derivatives that were suitable for ring‐closing metathesis, giving N‐methoxylactams. Reactions of these derivatives with Grignard or organolithium compounds gave hemiaminals, which could be reduced diastereoselectively via acyliminium intermediates to give cis‐piperidines or cis‐pyrrolidines with substituents in the 2,6‐ or 2,5‐positions, respectively. In addition, compounds with a quaternary carbon center could be synthesized by corresponding reactions with potassium cyanide/AcOH. The procedures were applied in the syntheses of alkaloids (?)‐209D and (+)‐prosophylline.     

Iridium‐Catalyzed Allylic Substitutions with Cyclometalated Phosphoramidite Complexes Bearing a Dibenzocyclooctatetraene Ligand: Preparation of (π‐Allyl)Ir Complexes and Computational and NMR Spectroscopic Studies

(π‐Allyl)Ir complexes derived from dibenzocyclooctatetraene and phosphoramidites by cyclometalation are effective catalysts for allylic substitution reactions of linear monosubstituted allylic carbonates. These catalysts provide exceptionally high degrees of regioselectivity and allow the reactions to be run under aerobic conditions. A series of (π‐allyl)Ir complexes were prepared and characterized by X‐ray crystal structure analyses. An allylic amination with aniline displayed different resting states depending on the presence of a strong base. DFT calculations were carried out on the mechanistic aspects of these reactions. The results suggest that for the (π‐allyl)Ir complexes, the formation and reactions with nucleophiles proceed with comparable rates.     

Enantioselective iridium-catalyzed allylic substitutions with hydroxamic acid derivatives as N-nucleophiles

Enantioselective Ir-catalyzed allylic aminations with hydroxamic acid derivatives are described. Catalysts were prepared in situ from [Ir(cod)Cl](2) or [Ir(dbcot)Cl](2), a phosphoramidite and base. In addition, pure (π-allyl)Ir complexes containing cod or dbcot as auxiliary ligands were used. Very high degrees of regio- and enantioselectivity were achieved. The reaction products were transformed into piperidine derivatives suited as precursors for aza-sugars.     

Singular values of the Rogers-Ramanujan continued fraction

Let z∊ C be imaginary quadratic in the upper half plane. Then the Rogers-Ramanujan continued fraction evaluated at q = e ^{2π iz} is contained in a class field of Q(z). Ramanujan showed that for certain values of z, one can write these continued fractions as nested radicals. We use the Shimura reciprocity law to obtain such nested radicals whenever z is imaginary quadratic. 2000 Mathematics Subject Classification Primary—11Y65; Secondary—11Y40