Photochemical and Acid-Catalyzed Rearrangements of 4-Carbomethoxy-4-methyl-3-(trimethylsilyl)-2,5-cyclohexadien-1-one

The synthesis of 4-carbomethoxy-4-methyl-3-(trimethylsilyl)-2,5-cyclohexadien-1-one (1) in 60% overall yield from benzaldehyde is described. Irradiation (366 nm) of 1 in benzene solution gave products of type A photorearrangement; e.g., diastereomers of the 4-(trimethylsilyl)- and 5-(trimethylsilyl)bicyclo[3.1.0]hex-3-en-2-ones 8 and 9. Bicyclohexenones 9a and 9b could not be isolated, but underwent acid-catalyzed protiodesilylative rearrangements on attempted chromatography (silica gel) to give a 1:1 mixture of (E)- and (Z)-4-(carbomethoxymethylmethylene)cyclopent-2-en-1-ones 12 and 13. Irradiation (366 nm) of either 12 or 13 resulted in photoisomerization to a photostationary state that was also a 1:1 mixture. Irradiation of 8a or 8b gave equivalent mixtures of phenols 14 and 15 by way of the type B oxyallyl zwitterion 17. The available experimental evidence suggests that both 9a and 9b undergo regiospecific photorearrangement to phenol 16 with no trace of 3-methyl-4-carbomethoxyphenol (19), the product of ipso substitution of the Me(3)Si group at C(4). Phenol 15 was isolated in 65% yield from the photoreaction of 1 in benzene with 20 equiv of CF(3)CO(2)H. The acid-catalyzed rearrangement of 1 to 3-carbomethoxy-4-methylphenol (21) occurs in 91% yield by way of CO(2)Me group rearrangement to C(3) to give the Me(3)Si-stabilized carbocation 23.     

Calix[6]arene-based cuprous "funnel complexes": a mimic for the substrate access channel to metalloenzyme active sites

Two calixarene-based model systems (a and b) for monocopper enzymes are compared. Both present a tris(pyridine) coordination site for Cu that mimics the imidazole-rich neutral binding site in enzymes. Upon reaction with 1 equiv of copper(I), the tridentate ligands gave rise to ill-defined unsymmetrical complexes. However, in the presence of an organonitrile RCN (R = Me, Et, Ph), tetrahedral species were obtained, with the nitrilo ligand included in the calixarene hydrophobic cone. System b presents a larger cavity than system a, with a wider opening thanks to the removal of three tBu groups from the calixarene structure. As a result, the recognition pattern for MeCN vs PhCN is inverted, and the relative affinity constants differ by 3 orders of magnitude. The mechanism of the acetonitrile exchange at the cuprous centers was studied by (1)H NMR spectroscopy. Thermodynamic and kinetic data show that it follows a dissociative pathway in both cases. The main differences between systems a and b stem from the presence of a door that entraps the guest in case a. In system b indeed, the removal of three calixarene tBu groups led to a 100-fold acceleration of the MeCN exchange rate. Hence, these supramolecular systems provide a rare and interesting model for the hydrophobic substrate channel giving access to a metalloenzyme active site.     

Immanant positivity for Catalan-Stieltjes matrices

We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices. To obtain these sufficient conditions, we construct new planar networks with a recursive nature for Catalan-Stieltjes matrices. As applications, we provide a unified way to produce inequalities for many combinatorial polynomials, such as the Eulerian polynomials, Schröder polynomials, and Narayana polynomials.     

Existence theorems for π/n vortex scattering

The analysis of 90° vortex-vortex scattering is extended to /n scattering in all head-on collisions ofn vortices in the Abelian Higgs model. A Cauchy problem with initial data that describe the scattering ofn vortices is formulated. It is shown that this Cauchy problem has a unique global finite-energy solution. The symmetry of the solution and the form of the local analytic solution then show that /n scattering is realized.     

A floating spherical Gaussian orbital model of molecular structure

The FSGO model has been used to make ab initio calculations of the geometrical structures of borazane and diborane. Where experimental data are available there is good agreement between calculated and observed values.

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Zusammenfassung Für ab initio-Rechnungen zur geometrischen Struktur des Borazans und Diborans wurde das FSGO-Modell benutzt. Soweit experimentelle Werte vorhanden sind, stimmen die berechneten und beobachteten Werte gut überein.

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Résumé La méthode FSGO a été utilisée pour effectuer des calculs ab-initio sur les structures géométriques du borazane et du diborane. Un bon accord est obtenu entre les valeurs calculées et les valeurs expérimentales existantes.