No abstract

A formal [3 + 3] cyclization reaction of diaziridines and quinones has been developed offering 1,3,4-oxadiazinanes in generally high yields (up to 96%). The reaction was catalyzed by Sc­(OTf)3 with a large substrate scope for both diaziridines and quinones. The synergistic activation of 1,3-dipolar diaziridines and the dipolar quinones was found to be essential to enable this reaction.

A three-component cascade reaction comprising cyclic ketones, arylamines, and benzoylmethylene malonates has been developed to access 4,5,6,7-tetrahydro-1H-indoles. The reaction was achieved through cooperative enamine-Brønsted catalysis in high yields with wide substrate scopes. Mechanistic studies identified the role of the Brønsted acid catalyst and revealed the formation of an imine intermediate, which was confirmed by X-ray crystallography.

The method of upper and lower solutions guarantees the interval of existence of nonlinear differential equations with initial conditions. To compute the solution on this interval, we need coupled lower and upper solutions on the interval of existence. We provide both theoretical as well as numerical methods to compute coupled lower and upper solutions by using a superlinear convergence method. Further, we develop monotone sequences which converge uniformly and monotonically, and with superlinear convergence, to the unique solution of the nonlinear problem on this interval. We accelerate the superlinear convergence by means of the Gauss-Seidel method. Numerical examples are developed for the logistic equation. Our method is applicable to more general nonlinear differential equations, including Riccati type differential equations.

The formation of enamine from primary arylamines was detected and confirmed by nuclear magnetic resonance spectroscopy. The presence of a radical quencher, e.g., (2,2,6,6-tetramethylpiperidin-1-yl)­oxidanyl, was found to be essential for the detection of enamine formation. A direct synthesis of α-enaminones from primary arylamines and ketones was also developed. Mechanistic investigation of α-enaminone formation suggests that an amine radical cation generated through O2 singlet energy transfer was involved in initiating α-enaminone formation. The reactivity and utility of α-enaminones were explored with a [3+3] cycloaddition reaction of enones affording dihydropyridines in good yields (58–85%). α-Enaminones displayed a set of reactivities that is different from that of enamines. The knowledge gained in this work advances our basic understanding of organic chemistry, providing insights and new opportunities in enamine catalysis.