Metal-catalyzed silacyclopropanation of mono- and disubstituted alkenes

As an alternative to the strongly reducing conditions necessary for the formation of silacyclopropanes, silylene transfer was developed as a mild, functional group tolerant method of silacyclopropanation. Complex silacyclopropanes were formed from functionalized alkenes using cyclohexane di-tert-butyl silacyclopropane, 1, as the source of t-Bu(2)Si. Di-tert-butyl silylene can be generated from 1 through the use of a catalytic amount of a metal salt. At -27 degrees C, silver triflate catalyzes the transfer of t-Bu(2)Si from 1 to mono- and disubstituted alkenes stereospecifically and diastereoselectively. In situ functionalization of silacyclopropanes with catalytic zinc bromide and methyl formate provides for an expedient one-flask synthesis of complex oxasilacyclopentanes from alkenes.     

Interlacing of zeros of shifted sequences of one-parameter orthogonal polynomials

We study the interlacing property of zeros of Laguerre polynomials of adjacent degree, where the free parameters differ by an integer, and of the same degree, where the free parameter is shifted continuously. Similar interlacing results are proven for the positive zeros of Gegenbauer polynomials. Research by Kathy Driver is supported by the National Research Foundation of South Africa under grant number 2053730. Research by Kerstin Jordaan is partially supported by the National Research Foundation of South Africa under grant number 2054423.     

Convergence of theU(1)4 lattice gauge theory to its continuum limit

It is shown that in four space-time dimensions the compactU(1) lattice gauge theory with general energy function converges to a renormalized free electromagnetic field on the current sector as the lattice spacing approaches zero, provided the coupling constant is sufficiently large. For the Wilson energy function, it is possible, by judicious choice of the Gibbs state, to get convergence for arbitrary coupling strengths. Furthermore, for all but a countable number of values of the coupling constant, the limit exists and is independent of the particular state chosen to define the lattice model.This research was supported in part by an Alfred P. Sloan Foundation Doctoral Dissertation Fellowship and in part by N.S.F. Grant Nos. DMS 84-01997 and DMS-8610730(1)     

Stabilizing CO on Au with NO2: electronegative species as promoters on coinage metals?

CO adsorption on NO(2)-predosed Au[111] reveals an unexpected attractive coadsorbate interaction, associated with an unprecedented blueshift of the CO stretch frequency, a sizeable attenuation of the infrared NO(2) symmetric stretch band, and a (sq.rt(7) x sq.rt(7))R19 degrees structure characterized by scanning tunneling microscopy and low energy electron diffraction. Density functional calculations allow us to rationalize these observations, and point towards a general pattern of behavior for electronegative coadsorbates on coinage metals, with important implications for catalytic promotion.     

Trajectories of the zeros of hypergeometric polynomials F(−n, b; 2b; z) for b < − 1/2

In a previous paper [2] we studied the zeros of hypergeometric polynomials F(−n, b; 2b; z), where b is a real parameter. Making connections with ultraspherical polynomials, we showed that for b > − 1/2 all zeros of F(−n, b; 2b; z) lie on the circle |z − 1| = 1, while for b < 1 − n all zeros are real and greater than 1. Our purpose now is to describe the trajectories of the zeros as b descends below the critical value − 1/2 to 1 − n. The results have counterparts for ultraspherical polynomials and may be said to “explain” the classical formulas of Hilbert and Klein for the number of zeros of Jacobi polynomials in various intervals of the real axis. These applications and others are discussed in a further paper [3].     

YM2:Continuum expectations,lattice convergence,and lassos

The two dimensional Yang-Mills theory (YM₂) is analyzed in both the continuum and the lattice. In the complete axial gauge the continuum theory may be defined in terms of a Lie algebra valued white noise, and parallel translation may be defined by stochastic differential equations. This machinery is used to compute the expectations of gauge invariant functions of the parallel translation operators along a collection of curvesC. The expectation values are expressed as finite dimensional integrals with densities that are products of the heat kernel on the structure group. The time parameters of the heat kernels are determined by the areas enclosed by the collectionC, and the arguments are determined by the crossing topologies of the curves inC. The expectations for the Wilson lattice models have a similar structure, and from this it follows that in the limit of small lattice spacing the lattice expectations converge to the continuum expectations. It is also shown that the lasso variables advocated by L. Gross [36] exist and are sufficient to generate all the measurable functions on the YM₂-measure space.     

Rh2(II)-catalyzed nitro-group migration reactions: selective synthesis of 3-nitroindoles from β-nitro styryl azides

Rhodium carboxylate complexes (1 mol %) catalyze the migration of electron-withdrawing groups to selectively produce 3-substituted indoles from β-substituted styryl azides. The relative order of migratorial aptitude for this transformation is ester ? amide < H < sulfonyl < benzoyl ? nitro.     

Brønsted Acidity and the Medium: Fundamentals with a Focus on Ionic Liquids

Fundamental aspects of Brønsted acidity in ionic liquid systems, in relation to those of simple protic molecules in the gas phase, pure protic molecules in the condensed phase and solutions of protic molecules in molecular systems, are presented. The variety of acidities possible, beyond those observed in aqueous systems, is emphasised and discussed in terms of differences of solvent levelling, ionisation, dissociation, homo‐/hetero‐conjugate ion speciation and the stabilisation of proton‐transfer products from solvent to solvent. It is argued that data regarding aqueous systems do not necessarily explain acid/base behaviour in other liquids satisfactorily. Methods of measuring acidity are reviewed, particularly by spectrophotometry and electrochemistry and recommendations proffered for estimating speciation and acidity of ionic liquids of various complexities.