Engineering a Small HOMO–LUMO Gap and Intramolecular C−H Borylation by Diborene/Anthracene Orbital Intercalation

The diborene 1 was synthesized by reduction of a mixture of 1,2-di-9-anthryl-1,2-dibromodiborane(4) ( 6 ) and trimethylphosphine with potassium graphite. The X-ray structure of 1 shows the two anthryl rings to be parallel and their π(C₁₄) systems perpendicular to the diborene π(B=B) system. This twisted conformation allows for intercalation of the relatively high-lying π(B=B) orbital and the low-lying π* orbital of the anthryl moiety with no significant conjugation, resulting in a small HOMO–LUMO gap (HLG) and ultimately a C−H borylation of the anthryl unit. The HLG of 1 was estimated to be 1.57 eV from the onset of the long wavelength band in its UV/Vis absorption spectrum (THF, λ_onset=788 nm). The oxidation of 1 with elemental selenium afforded diboraselenirane 8 in quantitative yield. By oxidative abstraction of one phosphine ligand by another equivalent of elemental selenium, the B−B and C¹−H bonds of 8 were cleaved to give the cyclic 1,9-diborylanthracene 9 .     

Influence of methyl‐modified silyl groups on the properties of polymers and Si/B/N/C ceramics derived from N‐silylated borazine derivatives

Thermal silazane cleavage of dichloroboryldisilylamines (SiCl_mMe_3?m)N(SiMe₃)(BCl₂) (1: m = 1; 2: m = 2) at 196 °C leads to the borazine derivates [(SiCl_mMe_3?m)NB(Cl_nMe_1?n)]₃ (3: m = 1, n = 0.185; 4: m = 2, n = 0.111) characterized by NMR and IR spectroscopy and mass spectrometry. Single‐crystal X‐ray diffraction structure analyses reveal (BN)₃ units with unusual twisted boat conformations in both compounds. Additionally, more detailed studies are done to clear up the function of the by‐products (SiCl_mMe_3?m)N(SiClMe₂)(BClMe) formed during the cyclization step leading to asymmetrically boron substituted borazine derivatives. The single‐source precursors 3 and 4 were cross‐linked with methylamine producing polymers 3P and 4P, which were transformed into black amorphous materials with ceramic yields of 20.8 % and 50.3 %, respectively. Ceramic 4C (Si_1.00B_0.98 N_2.55 C_1.37O_0.05) was further investigated by ¹¹B and ²⁹Si magic angle spinning (MAS) NMR spectroscopy. A combined study of high‐temperature TG analyses and X‐ray powder diffraction analyses confirms the thermal stability of 4C up to 1670 °C. Copyright © 2012 John Wiley & Sons, Ltd.     

Iron-Catalyzed Halogen Exchange of Trifluoromethyl Arenes**

The facile production of ArCF₂X and ArCX₃ from ArCF₃ using catalytic iron(III)halides is reported, which constitutes the first iron-catalyzed halogen exchange for non-aromatic C−F bonds. Theoretical calculations suggest direct activation of C−F bonds by iron coordination. ArCX₃ and ArCF₂X products of the reaction are synthetically valuable due to their diversification potential. In particular, chloro- and bromodifluoromethyl arenes (ArCF₂Cl, ArCF₂Br respectively) provide access to a myriad of difluoromethyl arene derivatives (ArCF₂R). To optimize for mono-halogen exchange, a statistical method called Design of Experiments was used. Optimized parameters were successfully applied to electron rich and electron deficient aromatic substrates, and to the late stage diversification of flufenoxuron, a commercial insecticide. These methods are highly practical, being run at convenient temperatures and using inexpensive common reagents.     

Boundedness properties in function spaces

Some boundedness properties of function spaces (considered as topo- logical groups) are studied.     

Synthesis of phenanthridine and phenanthridinone derivatives based on Pd‐catalyzed C–H activation

This review article provides an overview of the most recent and exciting developments in palladium‐catalyzed C–H activation and mechanistic aspects of these catalytic reactions as the fast‐growing field for the synthesis of phenanthridine derivatives.     

Functions averages over the roots of unity,cauchy problems and addition formulas

An averaging operator over the roots of unity is defined on a class of analytic functions and its algebraic and analytic properties are investigated. A Cauchy like integral formula for this is obtained. This operator and its properties are then employed to solve higher order Cauchy problems, to derive addition formulas for hypergeometric functions and to obtain integral representations for special classes of hypergeometric functions.     

Cohomological uniqueness of the Cauchy problem solutions for the Einstein equation

In this paper we analyze the Cauchy problem for the Einstein equation in the case of a non-characteristic initial hypersurface. To find the correct notions for the characteristic and Cauchy data we introduce a complex, which we call the Einstein complex. Then the Cauchy problem acquires correctness in terms of the associated spectral sequence. We define the Cauchy data in such way that they allow us to reconstruct a cohomologously unique formal solution.     

Analysis for some properties of discrete time Markov decision processes

This paper investigates properties of the optimality equation and optimal policies in discrete time Markov decision processes with expected discounted total rewards under weak conditions that the model is well defined and the optimality equation is true. The optimal value function is characterized as a solution of the optimality equation and the structure of optimal policies is also given.     

Dihedral angle study in Hesperidin using NMR Spectroscopy

Hesperidin is flavonoid molecule found in citrus fruits (Citrus reticulata), especially difficult to extract, classify and characterize. Present work is to study the unresolved relative configuration of Hesperidin through the dihedral angle, coupling constant and different NMR techniques. The Karplus equation and its modifications have been originated from the valence bond theory and associated with dihedral angle and coupling constant. The result data set of calculated dihedral angle can probe significant method to assign the virtual configuration of natural products and also resolved stereochemistry of Hesperidin at C‐2 position in. Copyright © 2016 John Wiley & Sons, Ltd.