Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

Structure,Chirality, and Formation of Giant Icosahedral Fullerenes and Spherical Graphitic Onions

We describe the topology, structure, and stability of giant fullerenes exhibiting various symmetries (I, I _h , D _2h , T). Our results demonstrate that it is possible to create two new families of nested chiral icosahedral (I) fullerenes namely C₂₆₀@C₅₆₀@C₉₈₀@C₁₅₂₀@, ...,and C₁₄₀@C₃₈₀@C₇₄₀@C₁₂₂₀@ ..., which exhibit interlayer separations of ca. 3.4 Å. These chiral fullerenes are thought to possess metalliclike conduction properties. We discuss in detail the transformation of polyhedral graphitic particles into quasispherical nested giant fullerenes by reorganization of carbon atoms, which result in the formation of additional pentagonal and heptagonal carbon rings. These spherical structures are metastable and we believe they could be formed under extreme conditions, such as those produced by high-energy electron irradiation. There is circumstantial experimental evidence for the presence of heptagonal rings within these spherical fullerenes.     

Synthesis and axial ligation behaviour of sterically hindered Zn(II)-porphyrin liquid crystals

A new class of low melting liquid crystalline octaalkyloxyporphyrins have been synthesised. Their Zn(II)-complexes display an interesting ligation behaviour towards amines (of varying shapes and sizes), ascribed to the steric hindrance or hydrophobic pockets on both the faces of the porphryin as evidenced from the crystal structure of Zn(II)-octabutyloxyporphyrin.     

About the calculation of exchange coupling constants in polynuclear transition metal complexes

The application of theoretical methods based on the density functional theory with hybrid functionals provides good estimates of the exchange coupling constants for polynuclear transition metal complexes. The accuracy is similar to that previously obtained for dinuclear compounds. We present test calculations on simple model systems based on H. He and CH(2). He units to compare with Hartree-Fock and multiconfigurational results. Calculations for complete, nonmodeled polynuclear transition metal complexes yield coupling constants in very good agreement with available experimental data.     

Percolation in strongly correlated systems: The massless Gaussian field

We derive a number of new results for correlated nearest neighbor site percolation onZ ^d. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance –, has a nontrivial percolation behavior: sites on whichS _x h percolate if and only ifh _c . with0 _c < . This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.     

Improved asymptotic analysis of the average number of steps performed by the self-dual simplex algorithm

In this paper we analyze the average number of steps performed by the self-dual simplex algorithm for linear programming, under the probabilistic model of spherical symmetry. The model was proposed by Smale. Consider a problem ofn variables withm constraints. Smale established that for every number of constraintsm, there is a constantc(m) such that the number of pivot steps of the self-dual algorithm,(m, n), is less thanc(m)(lnn) ^m(m+1) . We improve upon this estimate by showing that(m, n) is bounded by a function ofm only. The symmetry of the function inm andn implies that(m, n) is in fact bounded by a function of the smaller ofm andn. Parts of this research were done while the author was visiting Stanford University, XEROX- PARC, Carnegie-Mellon University and Northwestern University and was supported in part by the National Science Foundation under Grants MCS-8300984, ECS-8218181 and ECS-8121741.     

Synthesis of new axially dissymmetric ligand with large perfluoroalkyl groups

A new axially dissymmetric ligand with large perfluoroalkyl groups, 2,2′-bis(1-hydroxy-1H-perfluorooctyl)biphenyl (1c), which could not be obtained by the coupling reaction of the aryl bromide using copper powder, was synthesized successfully by the coupling reaction using Ni(COD)₂. This ligand showed much higher asymmetric induction in the reaction of diethylzinc with benzaldehyde than the trifluoromethyl (1a) or pentafluoroethyl (1b) analogues.     

Biphenyl-tricarbonylchrom-komplexe, 9. Mitt.: Synthesen,chromatographische Enantiomerentrennung,Circulardichroismus und Chiralität von mono- und bis-(Tricarbonylchrom)-Komplexen di- und tetrasubstituierter sowie überbrückter Biphenyle

Chiral title compounds have been resolved by medium pressure liquid chromatography (MPLC) on triacetylcellulose in ethanol. Whereas a quantitative separation was achieved for16 and20, a recycling technique had to be applied to1,4,6,10 and15 leading to a 100% e.e. for1,6 and15 and to ca. 60% e.e. for4 and10.An unambiguous assignment of the chirality (+)-(R) _a -(S) _m for tricarbonylchromium-6,6-dimethyl-diphenicacid dimethylester (4) was deduced both from the photochemical decomplexation to (-)-5 with the known chirality (R) _a (whose e.e. was determined by MPLC on triacetylcellulose) and by comparison of the¹H-n.m.r. spectra of4 and5 thereby proving the structure 4 for the former.Other chiralities both for mono and bis(tricarbonylchromium)biphenyl complexes were established by chemical correlations and comparison of the CD spectra with those of key compounds.

Herrn Prof. Dr.H. Tuppy mit besten Wünschen zum 60. Geburtstag gewidmet.     

2-(2-Hydroxyaryl)cinnamic amides: a new class of axially chiral molecules

The syntheses of several differently substituted amides formally derived from a chiral amine, either E-2-(2-hydroxyphenyl)cinnamic acid or both E- and Z-2-(2-hydroxynaphthyl)cinnamic acid, are reported. These molecules display a restricted rotation about the C₂-C_aryl bond. The barriers to rotation about the C₂-C_aryl bond were measured by the dynamic ¹H NMR and were found to vary between 11.8 and 24.5 kcal mol⁻¹, depending on the substitution. In particular, E-2-(2-hydroxynapthyl)cinnamic amides, displayed a high barrier to rotation (ΔG_c^‡=24.4 kcal mol⁻¹) and could be isolated in both diastereomerically pure forms at room temperature. The X-ray structure of one E-2-(2-hydroxynapthyl)cinnamic amide, was resolved, enabling for the determination of the absolute configuration of the chiral axis (aR).