Selective monobenzoylation of 1,2- and 1,3-diols catalyzed by Me2SnCl2 in water (organic solvent free) under mild conditions

We have developed an efficient method for selective monobenzoylation of 1,2- and 1,3-diols in water catalyzed by Me(2)SnCl(2). Treatment of 1,2- and 1,3-diols with benzoyl chlorides, DMT-MM, and potassium carbonate in the presence of a catalytic amount of Me(2)SnCl(2) and DMAP in water at room temperature gave monobenzoates in up to 97% yield.     

Ammonium-directed olefinic epoxidation: kinetic and mechanistic insights

The ammonium-directed olefinic epoxidations of a range of differentially N-substituted cyclic allylic and homoallylic amines (derived from cyclopentene, cyclohexene, and cycloheptene) have been investigated, and the reaction kinetics have been analyzed. The results of these studies suggest that both the ring size and the identity of the substituents on nitrogen are important in determining both the overall rate and the stereochemical outcome of the epoxidation reaction. In general, secondary amines or tertiary amines with nonsterically demanding substituents on nitrogen are superior to tertiary amines with sterically demanding substituents on nitrogen in their ability to promote the oxidation reaction. Furthermore, in all cases examined, the ability of the (in situ formed) ammonium substituent to direct the stereochemical course of the epoxidation reaction is either comparable or superior to that of the analogous hydroxyl substituent. Much slower rates of ring-opening of the intermediate epoxides are observed in cyclopentene-derived and cycloheptene-derived allylic amines as compared with their cyclohexene-derived allylic and homoallylic amine counterparts, allowing for isolation of these intermediates in both of the former cases.     

Fixed point theorems and convergence theorems for generalized nonspreading mappings in Banach spaces

In this paper, we first prove a general fixed point theorem for nonlinear mappings in a Banach space. Then we prove a nonlinear mean convergence theorem of Baillon??s type and a weak convergence theorem of Mann??s type for 2-generalized nonspreading mappings in a Banach space.     

Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces

Let H be a real Hilbert space and let T: H→2^H be a maximal monotone operator. In this paper, we first introduce two algorithms of approximating solutions of maximal monotone operators. One of them is to generate a strongly convergent sequence with limit vT⁻¹0. The other is to discuss the weak convergence of the proximal point algorithm. Next, using these results, we consider the problem of finding a minimizer of a convex function. Our methods are motivated by Halpern's iteration and Mann's iteration.     

An economical approach for peptide synthesis via regioselective C–N bond cleavage of lactams

An economical, solvent-free, and metal-free method for peptide synthesis via C–N bond cleavage using lactams has been developed. The method not only eliminates the need for condensation agents and their auxiliaries, which are essential for conventional peptide synthesis, but also exhibits high atom economy. The reaction is versatile because it can tolerate side chains bearing a range of functional groups, affording up to >99% yields of the corresponding peptides without racemisation or polymerisation. Moreover, the developed strategy enables peptide segment coupling, providing access to a hexapeptide that occurs as a repeat sequence in spider silk proteins.

An economical, solvent-free, and metal-free method for peptide synthesis via C–N bond cleavage using lactams has been developed.     

In Situ Tracking of Dynamic NO Capture through a Crystal-to-Crystal Transformation from a Gate-Open-Type Chain Porous Coordination Polymer to a NO-Adducted Discrete Isomer

Optimal control of gas adsorption properties in metal–organic frameworks (MOFs) or porous coordination polymers (PCPs) remains a great challenge in the field of materials science. An efficient strategy to capture electron-acceptor-type gas molecules such as nitrogen monooxide (NO) is to use host–guest interactions by utilizing electron-donor-type MOFs/PCPs as host frameworks. Herein, we focus on a highly electron-donating chain compound by using the paddlewheel-type [Ru₂^II,II] complex [Ru₂(2,4,5-Me₃PhCO₂)₄] (2,4,5-Me₃PhCO₂⁻=2,4,5-trimethylbenzoate) with the phenazine (phz) linker: [Ru₂(2,4,5-Me₃PhCO₂)₄(phz)] ( 1 ). Compound 1 exhibited a specific gated adsorption for NO under gas pressures greater than 60 kPa at 121 K, which finally resulted in approximately seven molar equivalents being taken up at 100 kPa followed by four molar equivalents remaining under vacuum at 121 K; its Rh isomorph ( 2 ) with weaker donation ability was inactive for NO. When the sample of 1 ⊃4 NO was heated to room temperature, the compound underwent a crystal-to-crystal phase transition to give [Ru₂(2,4,5-Me₃PhCO₂)₄(NO)₂](phz) ( 1 -NO), involving a post-synthetic nitrosylation on the [Ru₂] unit, accompanied by an eventful site-exchange with phz. This drastic event, which is dependent on the NO pressure, temperature, and time, was coherently monitored by using several different in situ techniques, revealing that the stabilization of NO molecules in nanosized pores dynamically and stepwisely occurred with the support of strong electronic/magnetic host–guest interactions.     

On the Formulation of the Feynman Path Integral Through Broken Line Paths

We study the formulation of the Feynman path integral through broken line paths in non-relativistic quantum mechanics. This formulation is very familiar to us and well known to be useful. But its rigorous meaning is given little except for special cases. In the present paper, using the ideas in the theory of difference methods and the theory of pseudo-differential operators, we show rigorously for some class of potentials that this formulation is well defined and that this Feynman path integral gives the probability amplitude, i.e., the solution of the Schr?dinger equation. Received: 21 August 1996 / Accepted: 13 February 1997     

Formation mechanism of the Si(1 1 1)7×7 reconstruction studied by scanning tunneling microscopy: Zipper-like restructuring in the sequential size changes of isolated single faulted-halves

The formation mechanism of the 7×7 reconstruction on annealed Si(1 1 1) surfaces has been demonstrated at the atomic level. In situ observations of unreconstructed regions (‘1×1’) on terraces after rapid quenching to 380 °C were done using scanning tunneling microscopy (STM) with a scanning speed of 1.7 s per frame. In the narrow ‘1×1’ regions, we imaged isolated single-faulted (F) halves of the dimer-adatom-stacking-fault (DAS) structure from “birth” to “death”. During “life”, the isolated single F-halves frequently changed their size. The size changes between odd-sized F-halves always took place through even-sized F-halves of intermediate sizes: 5×5-F^′↔6×6-F↔7×7-F^′↔8×8-F↔9×9-F^′↔10×10-F↔11×11-F^′↔12×12-F↔13×13-F^′, where the 5×5-F^′, 7×7-F^′ and so forth are irregular-type structures of the odd-sized F-halves. Even-sized F-halves and the irregular-type structures are necessary in the size changes, whereas the regular-type structures have never been involved. Lifetimes of the 10×10-F, 8×8-F, and 6×6-F at 380 °C are about 10.5, 6, and 2-3 s, respectively, which are much shorter than those of the isolated irregular-type structures of the odd-sized F-halves. With the aid of room temperature STM images of a rapidly quenched surface, we determined the atomic structures of the even-sized F-halves. We have proposed a sequential size change (SSC) model, including undiscovered parts of the size changes ‘1×1’ ↔2×2-F↔3×3-F^′↔4×4-F↔5×5-F^′, as the formation and decay mechanism of isolated single F-halves in the ‘1×1’ region. The SSC model has the following sequence: ‘1×1’ ↔ 2×2-F↔3×3-F^′↔4×4-F↔5×5-F^′↔6×6-F↔7×7-F^′↔8×8-F↔9×9-F^′↔10×10-F↔11×11-F^′↔12×12-F↔13×13-F^′. It was found by collecting statistics of size-change directions that one of two equivalent sides of the irregular-type structures, which have a mirror symmetry, is involved in the size changes thus indicating that other parts of the F-halves remain unchanged. Based on such findings, we have proposed the atomic processes for bond-rearrangements in the SSC model. The bond-rearrangements proceed along one side of a triangular F-half by breaking the existing dimers and forming new dimers like a “zipper”. Proposed atomic processes of the zipper-like restructuring are illustrated by a ball-and-stick model. The reason for the appearance of the even-sized F-halves and the irregular-type structures of the odd-sized ones is discussed in terms of the energy barrier heights along a reaction path in the size change of single F-halves.