Ellagitannin chemistry. Evolution of a three-component coupling strategy for the synthesis of the dimeric ellagitannin coriariin A and a dimeric gallotannin analogue

The total synthesis of the dimeric ellagitannin coriariin A is reported. The key reaction to access the dimeric framework was realized early in the synthesis pathway via a bis acylation reaction of a dehydrodigalloyl diacid with 2 equiv of a glucopyranose trichloroacetimidate. The glucose rings were subsequently functionalized, culminating in a double oxidative cyclization to form stereoselectively both (S)-HHDP ester units. This bis acylation strategy was also employed to prepare a gallotannin analogue of coriariin A whose earlier synthesis by orthoquinone dimerization was plagued by yield-limiting side reactions.     

Universality in lattice models of dynamic arrest: introduction of an order parameter

We introduce an order parameter for dynamical arrest. Dynamically available volume (unoccupied space that is available to the motion of particles) is expressed as holes for the simple lattice models we study. Near the arrest transition the system is dilute in holes, so we expand dynamical quantities in a series of hole density. Unlike the situation when presented in particle density, all cases of simple models that we examine have a quadratic dependence of the diffusion constant on hole density. This observation implies that in certain regimes ideal dynamical arrest transitions may possess a hitherto unnoticed degree of universality.     

Hyperaromatic stabilization of arenium ions

Benzene-cis- and trans-1,2-dihydrodiols undergo acid-catalyzed dehydration at remarkably different rates: k(cis)/k(trans) = 4500. This is explained by formation of a β-hydroxycarbocation intermediate in different initial conformations, one of which is stabilized by hyperconjugation amplified by an aromatic no-bond resonance structure (HOC(6)H(6)(+) ? HOC(6)H(5) H(+)). MP2 calculations and an unfavorable effect of benzoannelation on benzenium ion stability, implied by pK(R) measurements of -2.3, -8.0, and -11.9 for benzenium, 1-naphthalenium, and 9-phenanthrenium ions, respectively, support the explanation.     

Tricritical point in heterogeneous k-core percolation

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k(i). In this Letter we identify a binary mixture of heterogeneous k-cores which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erd?s-Rényi networks and 2D square lattices.     

Hyperaromatic stabilization of arenium ions: a remarkable cis stereoselectivity of nucleophilic trapping of β-hydroxyarenium ions by water

Cis- and trans-1,2-dihydrodiol isomers of benzene undergo acid-catalyzed dehydration to form phenol. In principle the isomeric substrates react through a common β-hydroxybenzenium (cyclohexadienyl) carbocation. Notwithstanding, the isomers show a large difference in reactivity, k(cis)/k(trans) = 4500. This difference is reduced to k(cis)/k(trans) = 440 and 50 for the 1,2-dihydrodiols of naphthalene and 9,10-dihydrodiols of phenanthrene, respectively, and to 6.9 for the dihydrodiols of the nonaromatic 7,8-double bond of acenaphthylene. Because the difference in stabilities of cis- and trans-dihydrodiols should be no more than 2-3-fold, these results imply a high cis stereoselectivity for nucleophilic trapping of a β-hydroxyarenium cation by water in the reverse of the carbocation-forming reaction. This is confirmed by studies of the 10-hydroxy-9-phenanthrenium ion generated from aqueous solvolyses of the trans-9,10-bromohydrin derivative of phenanthrene and the monotrichloroacetate ester of the phenanthrene cis-9,10-dihydrodiol. The cis stereoselectivity of forward and reverse reactions is explained by the formation (in the "forward" reaction) of different conformations of carbocation from cis- and trans-dihydrodiol reactants with respectively β-C-H and β-C-OH bonds in pseudoaxial positions with respect to the charge center of the carbocation optimal for hyperconjugation. Formation of different conformations is constrained by departure of the (protonated) OH leaving group from a pseudoaxial position. The difference in stability of the carbocations is suggested to stem (a) from the greater hyperconjugative ability of a C-H than a C-OH bond and (b) from enhanced conjugation arising from the stabilizing influence of an aromatic ring in the no-bond resonance structures representing the hyperconjugation (C(6)H(6)OH(+) ? C(6)H(5)OH H(+)). This is consistent with an earlier suggestion by Mulliken and a demonstration by Schleyer that the benzenium ion is subject to hyperconjugative aromatic stabilization. It is proposed that, in analogy with the terms homoconjugation and homoaromaticity, arenium ions should be considered as "hyperaromatic".     

Lattice model of glasses

Glass-forming liquids have been extensively studied in recent decades, but there is still no theory that fully describes these systems, and the diversity of treatments is in itself a barrier to understanding. Here we introduce a new simple model that (possessing both liquid-crystal and glass transition) unifies different approaches, producing most of the phenomena associated with real glasses, without loss of the simplicity that theorists require. Within the model we calculate energy relaxation, nonexponential slowing phenomena, the Kauzmann temperature, and other classical signatures. Moreover, the model reproduces a subdiffusive exponent observed in experiments of dense systems. The simplicity of the model allows us to identify the microscopic origin of glassification, leaving open the possibility for theorists to make further progress.     

Ab initio studies on ONH3, ONF3 and OCF 3 − , using polarization functions and configuration interaction methods

SCF geometry optimizations, using double-zeta basis sets with polarization functions, either as d-orbitals or bond functions, were performed on ONH₃, ONF₃, and OCF ₃ ^? . The bonding in these molecules is discussed with the help of orbital density plots and Mulliken population analyses. ONF₃ can be explained as donor-acceptor product of O with NF₃. For OCF ₃ ^? , diffuse functions have also been added to the basis set. The CF distance is predicted to be 1.39 Å, in qualitative agreement with the known infrared spectrum. With the best basis set, the NF distance of ONF₃ is too short by 0.08 Å at the SCF level. A geometry optimization by the configuration-interaction method gives the NF distance as well as the ON distance in excellent agreement with experimental results.     

A new area-maximization proof for the circle

Conclusion  Finally, we compare the trianglesT _i with the isosceles triangles which would be obtained by slicing the circle by the same procedure. Since they all have the same short base length and the same angle opposite the base, the isosceles triangles composing the circle have more area than the trianglesT _i. Because the latter triangles cover all ofR ₁ (perhaps even with overlap and/or extension beyondR ₁), we see that the area of the quarter-circle is greater than that ofR ₁, and thus the circle's entire area is greater than that of our original regionR.     

The angle criterion

We complete the proof of the angle conjecture on when a pair of orientedm-planes is area-minimizing. The nonzero sum (oriented union)P ₁+P ₂ is area-minimizing if and only if the characterizing angles between them satisfy the inequality

Area-minimizing subsurfaces of Scherk's singly periodic surface and the catenoid

An unbounded portion of the catenoid and a class of subsurfaces of Scherk's singly periodic surface defined over nonconvex domains are shown to be area-minimizing. Mathematics Subject Classification (1991) Primary 49Q05 Secondary 53A10, 30C45