An Inverse Problem in Periodic Diffractive Optics: Reconstruction of Lipschitz Grating Profiles

We consider the problem of recovering a two-dimensional periodic structure from scattered waves measured above the structure. Following an approach by Kirsch and Kress, this inverse problem is reformulated as a nonlinear optimization problem. We develop a theoretical basis for the reconstruction method in the case of an arbitrary Lipschitz grating profile. The convergence analysis is based on new perturbation and stability results for the forward problem.     

Cobalt-Catalyzed Intramolecular Hydroacylation Involving Cyclopropane Cleavage

A simple cobalt-diphosphine catalyst has been found to efficiently promote intramolecular cyclization of ortho-cyclopropylvinyl- and cyclopropylidenemethyl-substituted benzaldehydes into benzocyclooctadienone and benzocycloheptadienone derivatives, respectively. This ring-opening hydroacylation likely involves aldehyde C−H oxidative addition, olefin insertion, cyclopropane cleavage by β-carbon elimination, and C−C bond-forming reductive elimination, as was supported by mechanistic experiments and DFT calculations.     

Synthesis of Seven-Membered Benzolactones by Nickel-Catalyzed C−H Coupling of Benzamides with Oxetanes

A NiCl₂(PEt₃)₂-catalyzed regioselective C−H coupling of 8-aminoquinoline-derived benzamides with oxetanes has been developed. The reaction proceeds with concomitant removal of the 8-aminoquinoline auxiliary to directly form the corresponding seven-membered benzolactones, which frequently occur in natural products and bioactive molecules. Additionally, no stereochemical erosion is observed during the course of the reaction, and the use of enantioenriched and substituted oxetane thus provides a new avenue to the optically active benzolactone.     

Detailed Analysis of the Crystal Structures and Magnetic Properties of a Dysprosium(III) Phthalocyaninato Sextuple-Decker Complex: Weak f–f Interactions Suppress Magnetic Relaxation

In the research field of single-molecule magnets (SMMs), lanthanoid–lanthanoid interactions, so-called f–f interactions, are known to affect the SMM properties, although their magnitudes are small. In this article, an SMM with very weak f–f interactions is reported, and the effects of the interactions on the SMM properties are discussed. X-ray structural analysis of the Dy^III-Cd^II-phthalocyaninato sextuple-decker complex (Dy₂Cd₃) reveals that the intramolecular Dy−Dy length in Dy₂Cd₃ is more than 13 Å, which is longer than the intermolecular Dy−Dy length. Even though the two Dy^III ions are far apart, intermolecular ferromagnetic dipole–dipole interactions are observed in Dy₂Cd₃. From detailed analysis of ac magnetic susceptibilities, quantum tunneling of the magnetization (QTM) in Dy₂Cd₃ is partially suppressed owing to the existence of very weak Dy−Dy interactions. Our results show that even very weak Dy−Dy interactions act as a dipolar bias, suppressing QTM.     

One-Pot Synthesis of Enantioenriched β-Amino Secondary Amides via an Enantioselective [4+2] Cycloaddition Reaction of Vinyl Azides with N-Acyl Imines Catalyzed by a Chiral Brønsted Acid

A catalytic enantioselective synthesis of β-amino secondary amides was achieved using vinyl azides as the enamine-type nucleophile and chiral N-Tf phosphoramide as the chiral Brønsted acid catalyst through a five-step sequential transformation in one pot. The established sequential transformation involves an enantioselective [4+2] cycloaddition reaction of vinyl azides with N-acyl imines as the key stereo-determining step that is efficiently accelerated by a chiral N-Tf phosphoramide catalyst in a highly enantioselective manner in most cases. Further generation of the iminodiazonium ion intermediate through ring opening of the cycloaddition product and subsequent skeletal rearrangement involving Schmidt-type 1,2-aryl group migration followed by recyclization of the resulting nitrilium ion were also initiated by the same acid catalyst. Final acid hydrolysis of the recyclized products in the same pot gave rise to enantioenriched β-amino amides through C−C bond formation at the α-position of the secondary amides.     

Effect of ammonium groups on the properties and alkaline stability of poly(arylene ether)‐based anion exchange membranes

Five kinds of ammonium groups functionalized partially fluorinated poly(arylene ether) block copolymer membranes were prepared for investigating the structure–property relationship as anion exchange membranes (AEMs). Consequently, the pyridine (PYR)‐modified membrane showed the highest alkaline and hydrazine stability in terms of the conductivity, water uptake, and dry weight. The chloromethylated precursor block copolymers were reacted with amines, such as trimethylamine, N‐butyldimethylamine, 1‐methylimidazole, 1,2‐dimethylimidazole, and PYR to provide the target quaternized poly(arylene ether)s. The structures of the polymers, as well as model compounds and oligomers were well characterized by ¹H NMR spectra. The obtained AEMs were subjected to water uptake and hydroxide ion conductivity measurements and stabilities in aqueous alkaline and hydrazine media. The pyridinium‐functionalized quaternized polymers membrane showed the highest alkaline and hydrazine stability with minor losses in the conductivity, water uptake, and dry weight. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 383–389