Optimal Groomings with Grooming Ratios Six and Seven

Grooming uniform all‐to‐all traffic in optical (SONET) rings with grooming ratio C requires the determination of a decomposition of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The determination of optimal C‐groomings has been considered for , and completely solved for . For , it has been shown that the lower bound for the drop cost of an optimal C‐grooming can be attained for almost all orders with 5 exceptions and 308 possible exceptions. For , there are infinitely many unsettled orders; especially the case is far from complete. In this paper, we show that the lower bound for the drop cost of a 6‐grooming can be attained for almost all orders by reducing the 308 possible exceptions to 3, and that the lower bound for the drop cost of a 7‐grooming can be attained for almost all orders with seven exceptions and 16 possible exceptions. Moreover, for the unsettled orders, we give upper bounds for the minimum drop costs.     

Rational Perturbation of the Fluorescence Quantum Yield in Emission‐Tunable and Predictable Fluorophores (Seoul‐Fluors) by a Facile Synthetic Method Involving C?H Activation

Fluorescence imaging enables the uniquely sensitive observation of functional‐ and molecular‐recognition events in living cells. However, only a limited range of biological processes have been subjected to imaging because of the lack of a design strategy and difficulties in the synthesis of biosensors. Herein, we report a facile synthesis of emission‐tunable and predictable Seoul‐Fluors, 9‐aryl‐1,2‐dihydrolopyrrolo[3,4‐b]indolizin‐3‐ones, with various R¹ and R² substituents by coinage‐metal‐catalyzed intramolecular 1,3‐dipolar cycloaddition and subsequent palladium‐mediated C H activation. We also showed that the quantum yields of Seoul‐Fluors are controlled by the electronic nature of the substituents, which influences the extent of photoinduced electron transfer. On the basis of this understanding, we demonstrated our design strategy by the development of a Seoul‐Fluor‐based chemosensor 20 for reactive oxygen species that was not accessible by a previous synthetic route.     

Polymerization of Ethylene by Silica‐Supported Dinuclear CrIII Sites through an Initiation Step Involving C?H Bond Activation

The insertion of an olefin into a preformed metal–carbon bond is a common mechanism for transition‐metal‐catalyzed olefin polymerization. However, in one important industrial catalyst, the Phillips catalyst, a metal–carbon bond is not present in the precatalyst. The Phillips catalyst, CrO₃ dispersed on silica, polymerizes ethylene without an activator. Despite 60 years of intensive research, the active sites and the way the first Cr C bond is formed remain unknown. We synthesized well‐defined dinuclear Cr^II and Cr^III sites on silica. Whereas the Cr^II material was a poor polymerization catalyst, the Cr^III material was active. Poisoning studies showed that about 65 % of the Cr^III sites were active, a far higher proportion than typically observed for the Phillips catalyst. Examination of the spent catalyst and isotope labeling experiments showed the formation of a Si–(μ‐OH)–Cr^III species, consistent with an initiation mechanism involving the heterolytic activation of ethylene at Cr^III O bonds.     

C?H Functionalization/Asymmetric Michael Addition Cascade Enabled by Relay Catalysis: Metal Carbenoid Used for C?C Bond Formation

A combination of either ruthenium(II) or rhodium(II) complexes and quinine‐derived squaramide enables 3‐diazooxindoles, indoles, and nitroalkenes to undergo highly efficient asymmetric three‐component reactions, thus affording optically active 3,3′‐bis(indole)s through a consecutive C C bond‐forming sequence, which turned out to be applicable to the facile total synthesis of (−)‐folicanthine.     

Direct Synthesis of 1,4‐Diols from Alkenes by Iron‐Catalyzed Aerobic Hydration and C?H Hydroxylation

Various 1,4‐diols are easily accessible from alkenes through iron‐catalyzed aerobic hydration. The reaction system consists of a user‐friendly iron phthalocyanine complex, sodium borohydride, and molecular oxygen. Furthermore, the effect of additional ligands on the iron complex was examined for a model reaction. The second hydroxy group is installed by direct C(sp³) H oxygenation, which is based on a [1,5] hydrogen shift process of a transient alkoxy radical that is formed by formal hydration of the olefin.     

Aldehyde‐Assisted Ruthenium(II)‐Catalyzed C?H Oxygenations

Versatile ruthenium(II) complexes allow for site‐selective C H oxygenations with weakly‐coordinating aldehydes. The challenging C H functionalizations proceed with high chemoselectivity by rate‐determining C H metalation. The new method features an ample substrate scope, which sets the stage for the step‐economical preparation of various bioactive heterocycles.     

One‐Pot Synthesis of Highly Substituted Polyheteroaromatic Compounds by Rhodium(III)‐Catalyzed Multiple C?H Activation and Annulation

A new method for the synthesis of highly substituted naphthyridine‐based polyheteroaromatic compounds in high yields proceeds through rhodium(III)‐catalyzed multiple C H bond cleavage and C C and C N bond formation in a one‐pot process. Such highly substituted polyheteroaromatic compounds have attracted much attention because of their unique π‐conjugation, which make them suitable materials for organic semiconductors and luminescent materials. Furthermore, a possible mechanism, which involves multiple chelation‐assisted ortho C H activation, alkyne insertion, and reductive elimination, is proposed for this transformation.