Sobolev's inequality for Riesz potentials of functions in Morrey spaces of integral form

Morrey spaces have become a good tool for the study of existence and regularity of solutions of partial differential equations. Our aim in this paper is to give Sobolev's inequality for Riesz potentials of functions in Morrey spaces (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reversible photoswitching of the coordination numbers of silicon in organosilicon compounds bearing a 2-(phenylazo)phenyl group

Several organosilicon compounds bearing a 2-(phenylazo)phenyl group were synthesized from the corresponding chlorosilanes and 2-lithioazobenzene prepared by halogen-lithium transmetalation of 2-iodoazobenzene. Their structures were determined by (1)H, (13)C, (19)F, and (29)Si NMR spectra, UV-vis spectra, and X-ray crystallographic analyses. In the UV-vis spectra, silyl groups caused red shifts of both the n-pi and pi-pi transitions of the azo group compared with the transitions of the unsubstituted azobenzene. The E-isomers of the fluorosilanes showed an intramolecular interaction between a nitrogen atom of the azo group and the silicon atom, leading their intermediate structures between a distorted trigonal bipyramidal structure and a tetrahedral structure around the silicon atoms, which were revealed by the X-ray crystallographic analyses and the NMR spectra. On the other hand, silanes without fluorine atoms showed tetrahedral structures in the absence of such an interaction. The photoirradiation of the E-isomers of the fluorosilanes afforded reversibly the corresponding Z-isomers in good yields. The silicon atoms of the Z-isomers were found to be tetracoordinate in the absence of Si-N interactions by the (29)Si NMR spectra. The coordination numbers of the silicon atom of the fluorosilanes were reversibly switched between four and five by photoirradiation. These properties were compared to those of a tetrafluoro[2-(phenylazo)phenyl]silicate.     

Systematic study on the structures and reactivity of hydrazobenzenes and azobenzenes bearing a chalcogenophosphoryl group

Hydrazobenzenes 3-5 bearing a chalcogenophosphoryl group were synthesized by palladium-catalyzed cross-coupling reactions. Their X-ray crystallographic analyses and NMR and IR spectra showed the presence of intramolecular hydrogen bonds between the N-H protons and the chalcogenophosphoryl groups. The intermolecular hydrogen bonds in phosphine oxide 3 and selenide 5 were observed in the solid state. Phosphine oxide 3, sulfide 4, and selenide 5 constructed a dimeric structure, a discrete monomeric structure, and a chain structure, respectively. As the chalcogen atom changed, the crystalline structures of the 2-chalcogenophosphorylhydrazobenzenes also changed. The hydrogen bonds affected the oxidation reactions of the hydrazobenzenes, and oxidation of hydrazobenzenes bearing a lighter chalcogen atom was more difficult. For azobenzenes bearing a chalcogenophosphoryl group, X-ray crystallographic analyses and NMR spectra showed little interaction between the azo group and the chalcogenophosphoryl groups. However, in the UV-vis spectra, the red shifts of the absorption maxima due to the n --> pi transitions indicated intramolecular interactions in the excited state, in contrast to the corresponding 4-substituted azobenzenes. In addition, photoirradiation of phosphine oxide (E)-7 gave (Z)-7, whereas that of phosphine sulfide (E)-8 and phosphine selenide (E)-9 did not give (Z)-8 and (Z)-9, suggesting that heavy chalcogen atoms quench excited states by through-space interactions. Introduction of a chalcogenophosphoryl group at the 2-position had a significant effect on the structure, spectral properties, and reactivity of hydrazobenzenes and azobenzenes. Although azobenzene (E)-10 bearing a hydroxyphosphoryl group at the 2-position did not show hydrogen bonding in the crystalline state, its optical properties and photoisomerization ratio were different from those of (E)-7.     

Cobalt-catalyzed trimethylsilylmethylmagnesium-promoted radical alkenylation of alkyl halides: a complement to the Heck reaction

A cobalt complex, [CoCl2(dpph)] (DPPH = [1,6-bis(diphenylphosphino)hexane]), catalyzes an intermolecular styrylation reaction of alkyl halides in the presence of Me3SiCH2MgCl in ether to yield beta-alkylstyrenes. A variety of alkyl halides including alkyl chlorides can participate in the styrylation. A radical mechanism is strongly suggested for the styrylation reaction. The sequential isomerization/styrylation reactions of cyclopropylmethyl bromide and 6-bromo-1-hexene provide evidence of the radical mechanism. Crystallographic and spectroscopic investigations on cobalt complexes reveal that the reaction would begin with single electron transfer from an electron-rich (diphosphine)bis(trimethylsilylmethyl)cobalt(II) complex followed by reductive elimination to yield 1,2-bis(trimethylsilyl)ethane and a (diphosphine)cobalt(I) complex. The combination of [CoCl2(dppb)] (DPPB = [1,4-bis(diphenylphosphino)butane]) catalyst and Me3SiCH2MgCl induces intramolecular Heck-type cyclization reactions of 6-halo-1-hexenes via a radical process. On the other hand, the intramolecular cyclization of the prenyl ether of 2-iodophenol would proceed in a fashion similar to the conventional palladium-catalyzed transformation. The nonradical oxidative addition of carbon(sp2)-halogen bonds to cobalt is separately verified by a cobalt-catalyzed cross-coupling reaction of alkenyl halides with Me3SiCH2MgCl with retention of configuration of the starting vinyl halides. The cobalt-catalyzed intermolecular radical styrylation reaction of alkyl halides is applied to stereoselective variants. Styrylations of 1-alkoxy-2-bromocyclopentane derivatives provide trans-1-alkoxy-2-styrylcyclopentane skeletons, one of which is optically pure.     

Determination of Kamlet-Taft solvent parameters pi* of high pressure and supercritical water by the UV-Vis absorption spectral shift of 4-nitroanisole

Kamlet-Taft solvent parameters, pi*, of high pressure and supercritical water were determined from 16-420 degrees C based on solvatochromic measurements of 4-nitroanisole. For the measurements, an optical cell that could be used at high temperatures and pressures was developed with the specification of minimal dead space. The low dead space cell allowed us to measure the absorption spectra of 4-nitroanisole at high temperature conditions before appreciable decomposition occurred. The behavior of pi* in terms of water density (pi* = 1.77rho- 0.71) was found to be linear, except in the near critical region, in which deviations were observed that could be attributed to local density augmentation. Excess density, which was defined as the difference between local density and bulk density, showed a maximum near the critical density of water. The frequencies of UV-Vis spectra of 4-(dimethylamino)benzonitrile and N,N-dimethyl-4-nitroaniline were correlated with pi* based on a linear solvation energy relationship (LSER) theory. Local density augmentation around 4-nitroanisole and that around 4-(dimethylamino)benzonitrile were similar but the augmentation observed around N,N-dimethyl-4-nitroaniline was larger.     

A potential intermediate for the aza-Corey-Chaykovsky reaction: synthesis, structure, and thermolysis of a pentacoordinate 1,2-thiazetidine 1-oxide

Thermolysis of a pentacoordinate 1lambda(6),2-thiazetidine, which was synthesized for the first time and characterized by X-ray crystallographic analysis, gave the corresponding aziridine and a cyclic sulfinate almost quantitatively. The potential intermediacy of a 1lambda(6),2-thiazetidine was suggested in the aza-Corey-Chaykovsky reaction.     

Lewis acid-catalyzed tri- and difluoromethylation reactions of aldehydes

The first Lewis acid-catalyzed trifluoromethylation reactions of aldehydes with Me3SiCF3 under TiF4/DMF, Ti(O iPr)4/DMF and Cu(OAc)2/dppp/toluene conditions are described. We have successfully applied this methodology to the difluoromethylation of aldehydes using Me3SiCF2SePh, Me3SiCF2P(O)OEt2 and Me3SiCF2SPh.