A family of diffusion processes on Sierpinski carpets

We construct a family of diffusions P ^α = {P ^x} on the d-dimensional Sierpinski carpet F^. The parameter α ranges over d _H < α < ∞, where d _H = log(3 ^d − 1)/log 3 is the Hausdorff dimension of the d-dimensional Sierpinski carpet F^. These diffusions P ^α are reversible with invariant measures μ = μ^[α]. Here, μ are Radon measures whose topological supports are equal to F^ and satisfy self-similarity in the sense that μ(3A) = 3^α·μ(A) for all A∈ℬ(F^). In addition, the diffusion is self-similar and invariant under local weak translations (cell translations) of the Sierpinski carpet. The transition density p = p(t, x, y) is locally uniformly positive and satisfies a global Gaussian upper bound. In spite of these well-behaved properties, the diffusions are different from Barlow-Bass' Brownian motions on the Sierpinski carpet. Received: 30 September 1999 / Revised version: 15 June 2000 / Published online: 24 January 2000     

Molecular Structure and Mutual Recognition Between Host and Guest Molecules Found in the Crystal Structures of Oxacalix[4]arenes Complexed with Xylene Isomers

The crystal structures of two complexes of oxacalix[4]arene derivatives {p-isopropyl-dihomooxacalix[4]arene (IOC-4)and p-tert-butyldihomooxacalix[4]arene(BOC-4)} with xylene isomers have been determined byX-ray diffraction method. Furthermore, in order toestimate the strength of the mutual interactionsbetween host (IOC-4 and BOC-4) and guest (o-, m-and p-xylene), the heat of complex formation forthe IOC-4 : xylene complexes was calculated using a molecularorbital method, and a differential scanningcalorimetric investigation was performed forthe BOC-4 : xylene complexes.     

RISM-SCF study of the free-energy profile of the Menshutkin-type reaction NH3+CH3Cl→NH3CH3++Cl− in aqueous solution

The free-energy profile for the Menshutkin-type reaction NH₃ + CH₃Cl → NH₃CH₃ ⁺ + Cl⁻ in aqueous solution is studied using the RISM-SCF method. The effect of electron correlation on the free-energy profile is estimated by the RISM-MP2 method at the HF optimized geometries along the reaction coordinate. Solvation was found to have a large influence on the vibrational frequencies at the reactant, transition state and product; these vibrational frequencies are utilized to calculate the zero-point energy correction of the free-energy profile. The computed barrier height and reaction exothermicity are in reasonable agreement with those of experiment and previous calculations. The change of solvation structure along the reaction path is represented by radial distribution functions between solute-solvent atomic sites. The mechanisms of the reaction are discussed from the view points of solute electronic and solvation structures. Received: 26 June 1998/Accepted: 28 August 1998 / Published online: 2 November 1998     

Enzymatic Precision Polymerization for Synthesis of Glycosaminoglycans and Their Derivatives

Hyaluronidase (HAase)-catalyzed polymerization was performed to provide synthetic hyaluronan (HA), chondroitin (Ch) and their derivatives. The 2-methyl oxazoline derivatives derived from their repeating disaccharides of N-acetylhyalobiuronate ( 1a ) and N-acetylchondrosine ( 3a ) were effectively polymerized by the enzyme, giving rise to synthetic HA and synthetic Ch in good yields through regio-selective and stereo-controlled ring-opening polyaddition. The oxazoline derivatives of 2-ethyl ( 1b , 3b ), 2-n-propyl ( 1c , 3c ), 2-isopropyl ( 1d , 3d ), 2-phenyl ( 1e , 3e ), 2-vinyl ( 1f , 3f ) and 2-isopropenyl ( 1g ) were synthesized and subjected to the enzymatic reaction. Monomers 1b , 1c , 1f , 3b and 3f were polymerized to corresponding polysaccharides 2b , 2c , 2f , 4b and 4f , all of which are unnatural glycosaminoglycans. Compounds 1d , 3c and 3d were also catalyzed by the enzyme, affording oligomers of 2d , 4c and 4d were produced in trace amounts. Monomers 1e , 1g and 3e were not catalyzed by HAase.     

Reactions of polymers having β-alkoxyenoate moieties in the main chain

The hydrolysis and the substitution reaction of the main chain of the polymer having β-alkoxyenoate moieties in the main chain are described. The hydrolysis of the polymer prepared from 2,2-dimetylpropylene-1,3-bis(propiolate) and p-xylene glycol under acidic conditions proceeded smoothly to obtain diols in quantitative yield by the cleavage of both ester and vinyl ether moieties. On the other hand, carboxylic acids were obtained by the hydrolysis of the polymer under alkaline conditions. The aminolysis with pyrrolidine gave the β-aminoenoate by the selective fission of vinyl ether moieties in quantitative yield. Furthermore, a polymer having β-aminoenoate moieties in the main chain was obtained by the reaction with piperazine via the displacement of the main chain. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 787–793, 1997     

Density functional theory of chemical reactivity indices in some ion—molecule reaction systems

Three isoelectronic reactions, proton transfer (PT ), hydrogen abstraction (HA ), and electron transfer (ET ), of NH⁺₃ with NH,₃ H₂O, and HF have been studied using ab initio molecular orbital calculations. For the reaction of NH⁺₃ + H₂O, the energy of the transition state (TS) is higher than that of the reactants. This is consistent with the experimental observation that the rate constant is less than the average dipole orientation (ADO) rate constant. It seems reasonable that the reaction rate for the reaction NH⁺₃ + H₂O would hardly depend on the v₂ mode of NH⁺₃ at least for low-lying excited states (E_int≤ 0.714 eV) of the v₂ mode, because the v₂ mode contributes mainly to the normal mode orthogonal to the reaction coordinate at the TS . This is consistent with experimental observation. A similar prediction can be made for the NH⁺₃ + HF reaction. The electron-transfer processes for the HA reactions have been examined in terms of the intrinsic reaction coordinate (IRC ). The order of reactivity with NH⁺₃ is NH₃ > H₂O > HF. It is found that the degree of the electron transfer and the reactivity are correlated with the absolute hardness (η) of NH₃, H₂O, and HF. This is in accord with the softness as the chemical reactivity index in the density functional theory. © 1996 John Wiley & Sons, Inc.     

Recent advances in olefin polymerization

Various metallocenes were tested for syndiotactic polymerization of propylene. Reduction in the amount of costly methylalumoxane (MAO) or replacement with the other components was accomplished. Small modifications in the metallocene ligands brought about remarkable differences in the resulting catalysts concerning their storage stability, H₂ response as well as stereo-specificity. Syndiotactic polypropylene (SPP) in the melt state behaves very differently compared to isotactic polypropylene (IPP). The notion that these polymers have different distributions of molecular entanglements are pursued, and verified for the first time. Excellent dispersibility of other olefin polymers in SPP matrix contributed to improve the usefulness of SPP.     

Iron-Catalyzed Biomimetic Dimerization of Tryptophan-Containing Peptides

Biomimetic oxidative dimerization of tryptophan derivatives in aqueous media with oxygen as a bulk oxidant catalyzed by an iron octacarboxy phthalocyanine complex was established. The discovery of the extremely active iron catalyst enables aerobic enzyme-mimetic oxidation to be performed in a flask. This method was applicable to the oxidative dimerization of a wide range of tryptophan derivatives, including various dipeptides and oligopeptides, with remarkable functional-group tolerance without the protection of the amino acid residues. Furthermore, oxidative dimerization of tryptophan derivatives bearing dioxopiperazine units enabled the convergent total synthesis of five natural pyrroloindole compounds and unnatural congeners. The established chemical method provides facile access to a broad range of dimerized peptides with a unique scaffold to link two turn structures, which will serve as a powerful tool to create new small- and medium-sized-molecules as drug candidates.