Divergent Coupling of Benzocyclobutenones with Indoles via C−H and C−C Activations

Highly selective divergent coupling reactions of benzocyclobutenones and indoles, in which the chemoselectivity is controlled by catalysts, are reported herein. The substrates undergo C2(indole)–C8(benzocyclobutenone) coupling to produce benzylated indoles and benzo[b]carbazoles in the Ni- and Ru-catalyzed reactions. A completely different selectivity pattern C2(indole)–C2(benzocyclobutenone) coupling to form arylated indoles is observed in the Rh-catalyzed reaction. Preliminary mechanistic studies suggest C−H and C−C activations in the reaction pathway. Synthetic utility of this protocol is demonstrated by the selective synthesis of three different types of carbazoles from the representative products.     

A Divergent Enantioselective Total Synthesis of Post-Iboga Indole Alkaloids

Divergent enantioselective total syntheses of five naturally occurring post-iboga indole alkaloids, dippinine B and C, 10,11-demethoxychippiine, 3-O-methyl-10,11-demethoxychippiine, and 3-hydroxy-3,4-secocoronaridine, as well as the two analogues 11-demethoxydippinine A and D, are presented for the first time. The enantioenriched aza[3.3.1]-bridged cycle, a common core intermediate to the target molecules, was constructed through an asymmetric phase-transfer-catalyzed Michael/aldol cascade reaction. The challenging azepane ring fused around the indole ring and the [3.3.1]-bridged cycle were installed through an intramolecular S_N2′-type reaction. These cyclization strategies enabled rapid construction of the [6.5.6.6.7]-pentacyclic core at an early stage. Highlights of the late-stage synthetic steps include a Pd-catalyzed Stille coupling and a highly stereoselective catalyst-controlled hydrogenation to incorporate the side chain at C₂₀ with both R and S configurations in the natural products.     

Divergent Instability Domains of a Fluid-Conveying Cantilevered Pipe with a Combined Support

The divergent instability of a fluid-conveying pipe is analyzed numerically. The pipe is modeled by a cantilevered beam restrained at the left end and supported by a special device (a rotational elastic restraint plus a Q-apparatus) at the right end. Divergent instability domains of the pipe are obtained by varying the rotational elastic constant of the right restraint     

Stereoselective [3+2] Carbocyclization of Indole‐Derived Imines and Electron‐Rich Alkenes: A Divergent Synthesis of Cyclopenta[b]indole or Tetrahydroquinoline Derivatives

An unprecedented stereoselective [3+2] carbocyclization reaction of indole‐2‐carboxaldehydes, anilines, and electron‐rich alkenes to obtain cyclopenta[b]indoles is disclosed. This pathway is different from the well‐established Povarov reaction: the formal [4+2] cycloaddition involving the same components, which affords tetrahydroquinolines. Moreover, by simply changing the Brønsted acid catalyst, this multicomponent coupling process could be divergently directed towards the conventional Povarov pathway to produce tetrahydroquinolines or to the new pathway (anti‐Povarov) to generate cyclopenta[b]indoles. Supported by computational studies, a stepwise Mannich/Friedel–Crafts cascade is proposed for the new anti‐Povarov reaction, whereas a concerted [4+2] cycloaddition mechanism is proposed for the Povarov reaction.     

Divergent Bifurcations of a Double Pendulum under the Action of an Asymmetric Follower Force

The paper studies the influence of the orientation parameter of the follower force on the behavior of the pendulum with a simple zero eigenvalue in the linearization matrix     

Unsteady Self-Similar Flow of a Viscous Incompressible Fluid in a Plane Divergent Channel

The problem of two-dimensional unsteady flow of a viscous incompressible fluid in a sector-like domain is considered. Initially a strictly radial flow is imposed, which makes it possible to seek solutions within the class of self-similar flows. A numerical method based on mixed finite-difference and spectral spatial discretization is developed, making it possible to find the self-similar solution efficiently. The process of development and establishment of the steady Hamel-Jeffery and Moffatt flows is modeled mathematically.     

Flame balls dynamics in divergent channel

A three-dimensional reaction-diffusion model for lean low-Lewis-number premixed flames with radiative heat losses propagating in divergent channel is studied numerically. Effects of inlet gas velocity and heat-loss intensity on flame structure at low Lewis numbers are investigated. It is found that continuous flame front exists at small heat losses and the separate flame balls settled within restricted domain inside the divergent channel at large heat losses. It is shown that the time averaged flame balls coordinate may be considered as important characteristic analogous to coordinate of continuous flame stabilized in divergent channel.     

Divergent Coordination Chemistry: Parallel Synthesis of [2×2] Iron(II) Grid‐Complex Tauto‐Conformers

The coordination of iron(II) ions by a homoditopic ligand L with two tridentate chelates leads to the tautomerism‐driven emergence of complexity, with isomeric tetramers and trimers as the coordination products. The structures of the two dominant [Fe^II₄ L ₄]⁸⁺ complexes were determined by X‐ray diffraction, and the distinctness of the products was confirmed by ion‐mobility mass spectrometry. Moreover, these two isomers display contrasting magnetic properties (Fe^II spin crossover vs. a blocked Fe^II high‐spin state). These results demonstrate how the coordination of a metal ion to a ligand that can undergo tautomerization can increase, at a higher hierarchical level, complexity, here expressed by the formation of isomeric molecular assemblies with distinct physical properties. Such results are of importance for improving our understanding of the emergence of complexity in chemistry and biology.