Experimental and Theoretical Studies on the Rearrangement of 2‐Oxoazepane α,α‐Amino Acids into 2′‐Oxopiperidine β2,3,3‐Amino Acids: An Example of Intramolecular Catalysis

Enantiopure β‐amino acids represent interesting scaffolds for peptidomimetics, foldamers and bioactive compounds. However, the synthesis of highly substituted analogues is still a major challenge. Herein, we describe the spontaneous rearrangement of 4‐carboxy‐2‐oxoazepane α,α‐amino acids to lead to 2′‐oxopiperidine‐containing β^2,3,3‐amino acids, upon basic or acid hydrolysis of the 2‐oxoazepane α,α‐amino acid ester. Under acidic conditions, a totally stereoselective synthetic route has been developed. The reordering process involved the spontaneous breakdown of an amide bond, which typically requires strong conditions, and the formation of a new bond leading to the six‐membered heterocycle. A quantum mechanical study was carried out to obtain insight into the remarkable ease of this rearrangement, which occurs at room temperature, either in solution or upon storage of the 4‐carboxylic acid substituted 2‐oxoazepane derivatives. This theoretical study suggests that the rearrangement process occurs through a concerted mechanism, in which the energy of the transition states can be lowered by the participation of a catalytic water molecule. Interestingly, it also suggested a role for the carboxylic acid at position 4 of the 2‐oxoazepane ring, which facilitates this rearrangement, participating directly in the intramolecular catalysis.     

Gauge natural formulation of conformal gravity

We consider conformal gravity as a gauge natural theory. We study its conservation laws and superpotentials. We also consider the Mannheim and Kazanas spherically symmetric vacuum solution and discuss conserved quantities associated to conformal and diffeomorphism symmetries.     

Setting local rank constraints by orthogonal projections for image resolution analysis: Application to the determination of a low dose pharmaceutical compound

Raman chemical imaging provides chemical and spatial information about pharmaceutical drug product. By using resolution methods on acquired spectra, the objective is to calculate pure spectra and distribution maps of image compounds. With multivariate curve resolution-alternating least squares, constraints are used to improve the performance of the resolution and to decrease the ambiguity linked to the final solution. Non negativity and spatial local rank constraints have been identified as the most powerful constraints to be used.     

The Effect of the Spacer of Bis(biurea) Ligands on the Structure of A2L3‐type (A=anion) Phosphate Complexes

By tuning the length and rigidity of the spacer of bis(biurea) ligands L, three structural motifs of the A₂L₃ complexes (A represents anion, here orthophosphate PO₄^3?), namely helicate, mesocate, and mono‐bridged motif, have been assembled by coordination of the ligand to phosphate anion. Crystal structure analysis indicated that in the three complexes, each of the phosphate ions is coordinated by twelve hydrogen bonds from six surrounding urea groups. The anion coordination properties in solution have also been studied. The results further demonstrate the coordination behavior of phosphate ion, which shows strong tendency for coordination saturation and geometrical preference, thus allowing for the assembly of novel anion coordination‐based structures as in transition‐metal complexes.