Primary Amine–2-Aminopyrimidine Chiral Organocatalysts for the Enantioselective Conjugate Addition of Branched Aldehydes to Maleimides

Chiral primary amines containing the (R,R)- and (S,S)-trans-cyclohexane-1,2-diamine scaffold and a pyrimidin-2-yl unit are synthesized and used as general organocatalysts for the Michael reaction of α-branched aldehydes to maleimides. The reaction takes place with 10 mol% organocatalyst loading and hexanedioic acid as cocatalyst in aqueous N,N-dimethylformamide at 10 °C affording the corresponding succinimides in good yields and enantioselectivities. DFT calculations support the stereochemical results and the role played by the solvents.

Bifunctional primary amine 2-aminobenzimidazole organocatalyst anchored to trans-cyclohexane-1,2-diamine in enantioselective conjugate additions of aldehydes

Bifunctional chiral primary amine 8 containing an (S,S)-trans-cyclohexane-1,2-diamine scaffold and a 2-benzimidazole unit is used as a general organocatalyst for the Michael addition of α,α-branched aldehydes to nitroalkenes and maleimides. The reactions take place, with 20 mol % of catalyst in dichloromethane at rt for nitroalkenes and with 15 mol % catalyst loading in toluene at 10 °C for maleimides, in good yields and enantioselectivities. DFT calculations demonstrate the bifunctional character of this organocatalyst activating the aldehyde by enamine formation and the Michael acceptor by double hydrogen bonding.

Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

Enantioselective Michael addition of isobutyraldehyde to nitroalkenes organocatalyzed by chiral primary amine-guanidines

Primary amine-guanidines derived from trans-cyclohexane-1,2-diamines are used as organocatalysts for the enantioselective conjugate addition of isobutyraldehyde to arylated and heteroarylated nitroalkenes. The reaction was performed in the presence of imidazole as the additive in aqueous DMF as the solvent at 0 °C. The corresponding Michael adducts bearing a new stereocenter were obtained in high yields and with enantioselectivities of up to 80%. Theoretical calculations are used to justify the observed sense of the stereoinduction.

Enantioselective Michael addition of aldehydes to maleimides organocatalysed by chiral 1,2-diamines: an experimental and theoretical study

Simple and commercially available chiral 1,2-diamines were used as organocatalysts for the enantioselective conjugate addition of aldehydes, including α,α-disubstituted, to maleimides. The reaction was carried out in the presence of hexanedioic acid as an additive in aqueous solvents at room temperature. By employing (1S,2S)- and (1R,2R)-cyclohexane-1,2-diamine as organocatalysts, the corresponding Michael adducts bearing new stereocenters were obtained in high or quantitative yields with enantioselectivities of up to 92%, whereas the use of (1S,2S)-1,2-diphenylethane-1,2-diamine gave a much lower ee. Theoretical calculations were used to justify the observed sense of the stereoinduction.

Enantioselective Synthesis of Succinimides by Michael Addition of 1,3-Dicarbonyl Compounds to Maleimides Catalyzed by a Chiral Bis(2-aminobenzimidazole) Organocatalyst

A wide variety of chiral succinimides have been prepared in high yields and enantioselectivities by asymmetric conjugate addition of 1,3-dicarbonyl compounds to maleimides under very mild reaction conditions using a bifunctional benzimidazole-derived organocatalyst. Computational and NMR studies support the hydrogen-bonding activation role of the catalyst and the origin of the stereoselectivity of the process.

Disipation Functions of Flow Equations in Models of Complex Systems

In an open system, each disequilibrium causes a force. Each force causes a flow process, these being represented by a flow variable formally written as an equation called flow equation, and if each flow tends to equilibrate the system, these equations mathematically represent the tendency to that equilibrium. In this paper, the authors, based on the concepts of forces and conjugated fluxes and dissipation function developed by Onsager and Prigogine, they expose the following hypothesis: Is replaced in Prigogine’s Theorem the flow by its equation or by a flow orbital considering conjugate force as a gradient. This allows to obtain a dissipation function for each flow equation and a function of orbital dissipation.

Solvent-dependent enantioswitching in the Michael addition of α,α-disubstituted aldehydes to maleimides organocatalyzed by mono-N-Boc-protected cyclohexa-1,2-diamines

Enantiomerically pure mono-N-Boc-protected trans-cyclohexa-1,2-diamines are used as organocatalysts for the enantioselective conjugate addition of α,α-disubstituted aldehydes to maleimides. Using a single enantiomer of the organocatalyst, both enantiomeric forms of the resulting Michael adducts bearing a new quaternary stereocenter are obtained in high yields, by only changing the reaction solvent from chloroform (up to 86% ee) to aqueous DMF (up to 84% ee).

Solvent-Induced Reversal of Enantioselectivity in the Synthesis of Succinimides by the Addition of Aldehydes to Maleimides Catalysed by Carbamate-Monoprotected 1,2-Diamines

A simple change in the polarity of the solvent allows both enantiomers of substituted succinimides to be obtained in the enantioselective conjugate addition reaction of aldehydes, mainly α,α-disubstituted, to maleimides catalysed by chiral carbamate-monoprotected trans-cyclohexane-1,2-diamines. Using a single enantiomer of the organocatalyst, both enantiomers of the resulting Michael adducts are obtained in high yields by simply changing the reaction solvent from aqueous DMF (up to 84 % ee) to chloroform (up to 86 % ee). Theoretical calculations are used to explain this uncommon reversal of the enantioselectivity; two transition state orientations of different polarities are differently favoured in polar or nonpolar solvents.

An approximate Hahn–Banach theorem for positively homogeneous functions

This note provides an approximate version of the Hahn–Banach theorem for non-necessarily convex extended-real valued positively homogeneous functions of degree one. Given p : X → R∪{+∞} such a function defined on the real vector space X, and a linear function defined on a subspace V of X and dominated by p (i.e. (x) ≤ p(x) for all x ∈ V), we say that can approximately be p-extended to X, if is the pointwise limit of a net of linear functions on V, every one of which can be extended to a linear function defined on X and dominated by p. The main result of this note proves that can approximately be p-extended to X if and only if is dominated by p∗∗, the pointwise supremum over the family of all the linear functions on X which are dominated by p.