Stereoselective Rh-catalyzed hydrogenation of cyclobutyl chiral enamides: double stereodifferentiation vs catalyst-controlled diastereoselection

The hydrogenation reactions of several cyclobutyl enamides derived from (-)-alpha-pinene or (-)-verbenone have been investigated by using different catalysts. The chiralities of both the substrate and the catalyst as well as the Z/E stereochemistry of the double bond have been considered, and the observed diastereoselectivity has been rationalized. For enamides with the double bond separated from the cyclobutane by a methylene, the Wilkinson catalyst did not induce any diastereoselection, but excellent diastereoselectivity was observed when using Et-DuPHOS-Rh and ChiraPHOS-Rh. The configuration of the new stereogenic center was catalyst-dependent and can be rationalized according to the Halpern mechanism. For (Z)-enamides with the double bond directly linked to the cyclobutane ring, the chirality of the substrate governed the diastereoselection and the Halpern mechanism seemed not to be operative in the hydrogenation with ChiraPHOS, with the configuration of the new stereogenic center being determined by steric effects. On the contrary, the chirality of the catalyst was the factor determining the stereochemistry of the major products with alkyl-DuPHOS-Rh. Z/E stereochemistry influenced the stereodifferentiation, and a different behavior for each Z or E stereoisomer was found. For both (Z)- and (E)-enamides, some instances of match/mismatch between the chirality of the substrate and that of the catalyst were observed. As a result of all of these studies, a series of new cyclobutyl alpha-amino acids has been synthesized. These products are interesting to incorporate into conformationally constrained peptides.     

(+)- and (-)-2-aminocyclobutane-1-carboxylic acids and their incorporation into highly rigid beta-peptides: stereoselective synthesis and a structural study

[Chemical reaction: See text] Several derivatives of (+)- and (-)-2-aminocyclobutane-1-carboxylic acid, 1, have been prepared through enantiodivergent synthetic sequences. The stereoselective synthesis of free amino acid (+)-1 has been achieved, and this product has been fully characterized for the first time. Stereocontrolled alternative synthetic methodologies have been developed for the preparation of bis(cyclobutane) beta-dipeptides in high yields. Among them, enantio and diastereomers have been synthesized. beta,beta- and beta,delta-Dimers resulting from the coupling of a cyclobutane residue and a linear amino acid have also been prepared. The ability of the cyclobutane ring as a structure-promoting unit both in the monomers and in the dimers has been manifested. The NMR structural study and DFT theoretical calculations evidence the formation of strong intramolecular hydrogen bonds giving rise to cis-fused [4.2.0]octane structural units that confer high rigidity on these molecules both in solution and in the gas phase. The contribution of a cis-trans conformational equilibrium derived from the rotation around the carbamate N-C(O) bond has also been observed, the trans form being the major conformer. In the solid state, this equilibrium does not exist, and moreover, intermolecular hydrogen bonds are present.     

Stereoselective synthesis of novel types of cyclopropyl carbocyclic nucleosides containing quaternary stereogenic centers

Versatile and stereocontrolled synthetic entries to novel types of cyclopropyl carbocyclic nucleosides are described. The target products have been synthesized from suitable cyclopropane precursors obtained, in turn, from olefinic compounds derived from D-glyceraldehyde as a chiral precursor. Selective manipulation of the functional groups has allowed the preparation of enantiopure nucleosides, some of them displaying opposite chirality. All these molecules contain a quaternary stereogenic carbon at C-1 or C-3 of the cyclopropane ring and bear an amino, a hydroxymethyl, or a methyl group as an additional substituent. In one instance, thymine is directly linked to the cyclopropane. A methylene unit serves as the spacer in the other synthesized nucleosides.     

Labile Base-Stabilized Silyliumylidene Ions. Non-Metallic Species Capable of Activating Multiple Small Molecules

Several base-stabilized silyliumylidene ions ( 2 and 3 ) with different ligands were synthesized. Their behaviour appeared strongly dependent on the nature of ligand. Indeed, in contrast to the poorly reactive silyliumylidene ions 3 c,d stabilized by strongly donating ligands (DMAP, NHC), the silylene- and sulfide-supported one ( 2-H and 3 a ) exhibits higher reactivity toward various small molecules. Furthermore, their capability to successively activate multiple small molecules was clearly demonstrated by processes involving successive reactions with silane/formamide, CO₂ and H₂. Moreover, HBPin adduct of 3 a ( 8-C ) catalyzes the hydroboration of pyridine. Of particular interest, silylene-supported silyliumylidene complex 2-H is one of the rare species able to activate two H₂ molecules.     

Catalytic Effect of Electric Fields on the Kemp Elimination Reactions with Neutral Bases

The effect of solvent reaction fields and oriented electric fields on the Kemp elimination reaction between methylamine or imidazole and 5-nitrobenzisoxazole has been theoretically studied. The Kemp reaction is the most widely used for the design of new enzymes. Our results, using the SMD continuous model for solvents, are in quite good agreement with the experimental fact that the rate of the analogous reaction with butylamine is one order of magnitude smaller in water than in acetonitrile. In the case of external electric fields, our results show that they can increase or decrease the energy barrier depending on the magnitude and orientation of the field. A duly oriented electric field may have a notable catalytic effect on the reaction. So, external electric fields and reaction fields due to the medium can contribute to the design of new enzymes. Several factors that must be taken into account to increase the catalytic effect are discussed.     

Variational Approach to Fourth-Order Impulsive Differential Equations with Two Control Parameters

In this paper, we are concerned with the multiplicity of solutions for a fourth-order impulsive differential equation with Dirichlet boundary conditions and two control parameters. Using variational methods and a three critical points theorem, we give some new criteria to guarantee that the impulsive problem has at least three classical solutions. We also provide an example in order to illustrate the main abstract results of this paper.     

Bifurcation near infinity for the Neumann problem with concave–convex nonlinearities

In this Note, we study a class of Neumann parametric elliptic equations driven by a nonhomogeneous differential operator and with a reaction that exhibits competing terms (concave–convex nonlinearities). Using the Ambrosetti–Rabinowitz condition and related topological and variational arguments, we prove a bifurcation result for large values of the parameter.     

Nonhomogeneous multiparameter problems in Orlicz–Sobolev spaces

This paper is concerned with the existence and multiplicity of solutions for a class of problems involving the Φ-Laplacian operator with general assumptions on the nonlinearities, which include both semipositone cases and critical concave convex problems. The research is based on the subsupersolution technique combined with a truncation argument and an application of the Mountain Pass Theorem. The results in this paper improve and complement some recent contributions to this field.     

Mathematical modelling and the learning trajectory: tools to support the teaching of linear algebra

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and span. The objective is to evaluate this didactic proposal by determining the level of match between the hypothetical learning trajectory (HLT) designed in this study with the actual learning trajectory in the second experimental cycle of an investigation design-based research more extensive. The results show a high level of match between the trajectories in more than half of the conjectures, which gives evidence that the HLT has supported, in many cases, the achievement of the learning objective, and that additionally mathematical modelling contributes to the construction of these linear algebra concepts.     

Nonhomogeneous Hemivariational Inequalities with Indefinite Potential and Robin Boundary Condition

We consider a nonlinear, nonhomogeneous Robin problem with an indefinite potential and a nonsmooth primitive in the reaction term. In fact, the right-hand side of the problem (reaction term) is the Clarke subdifferential of a locally Lipschitz integrand. We assume that asymptotically this term is resonant with respect the principal eigenvalue (from the left). We prove the existence of three nontrivial smooth solutions, two of constant sign and the third nodal. We also show the existence of extremal constant sign solutions. The tools come from nonsmooth critical point theory and from global optimization (direct method).