Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions

The ground state energy of an atom of nuclear chargeZe in a magnetic fieldB is exactly evaluated to leading order asZ in the following three regions:BZ ^4/3,BZ ^4/3 andZ ^4/3BZ³. In each case this is accomplished by a modified Thomas-Fermi (TF) type theory. We also analyze these TF theories in detail, one of their consequences being the nonintuitive fact that atoms are spherical (to leading order) despite the leading order change in energy due to theB field. This paper complements and completes our earlier analysis [1], which was primarily devoted to the regionsBZ ³ andBZ³ in which a semiclassical TF analysis is numerically and conceptually wrong. There are two main mathematical results in this paper, needed for the proof of the exactitude of the TF theories. One is a generalization of the Lieb-Thirring inequality for sums of eigenvalues to include magnetic fields. The second is a semiclassical asymptotic formula for sums of eigenvalues that isuniform in the fieldB.Work partially supported by U.S. National Science Foundation grant PHY90-19433 A02Work partially supported by U.S. National Science Foundation grant DMS 92-03829Work partially supported by the Heraeus Stiftung and the Research Fund of the University of Iceland.     

Nonresonant third-order susceptibility measurements in the nematic liquid crystal K18

We have observed a large nonresonant third-order nonlinear susceptibility, X ⁽³⁾ (-; , 0, 0) in the isotropic phase of a nematic liquid crystal 4-n-hexyl-4-cyanobiphenyl (K18). The highest value of X ⁽³⁾ obtained at 632.8 nm is 1.16274×10^-18 m²V^-2 corresponding to a temperature 29.3°C. The observed second-order pretransitional temperature T ^* from our measurements is 1.2°C below the first-order nematic to isotropic transition temperature. The dependence of the Kerr constant on (T-T ^*)^-1 is found to be in good agreement with the predictions of the Landau-de Gennes model.     

X-ray and molecular mechanics studies on the sesquiterpene lactone eupatocunin-o-bromobenzoate — An unusual case of disorder involving atropisomerism

The molecular structure of the cytotoxic sesquiterpene lactone eupatocunin has been determined by X-ray crystallographic analysis of theo-bromobenzoate derivative. Two structural isomers, arising from hindered rotation, are present within the single crystal. The molecules are disordered (ratio 0.750.25) with the bromine atom occupying alternate ortho positions on the aromatic ring. Molecular mechanics has been used to examine the energies of molecular conformation by torsion angle variation.     

Studies in alkylation. I. Synthesis and reactions of spiro[oxirane-2,4-piperidines]

Spiro[oxirane-2, 4′-piperidines] have been prepared by the action of dimethyloxosulfonium methylide on 4-piperidones. The spiro[oxirane-2,4′-piperidines] act as alkylating agents to introduce (4-hydroxy-4-piperidyl) methyl moieties onto heteroaromatic compounds such as 4(3H)-quinazolone.     

Nonrigid molecule effects in molecules with linear or nongeometrically equivalent equilibrium configurations

A theoretical study is made of the states of nonrigid molecules, extending earlier work to apply Longuet–Higgins' symmetry group of feasible permutation/inversions in two previously untreated cases. The first involves nonrigid molecule processes between different stereoisomers, that is between molecular equilibrium configurations of different geometrical shapes. The second takes into account nonrigid molecule processes in linear molecules. The theory is applied to the specific case of nonrigid molecule effects in the butyl ion C₄H (case i), and the form of the nonrigid molecule energy levels and spectra are determined. The theory is also applied to determine the nonrigid molecule energy levels in linear H₂F₂ (case ii).     

Determination of trace concentrations of citrate in aqueous systems

A fluorimetric method for the determination of citrate is described. Through a series of reactions, citrate is converted into citrazinic acid. The ammonium salt of this compound exhibits a fluorescence maximum at 430 nm when an excitation source of 340 nm is used. The method does not suffer from the normal interferences. The limit of detection is 0.01 μg ml^-, and the best working range is 0.1–10 μg ml^-1.     

Organic sonochemistry. Ultrasound-promoted coupling of organic halides in the presence of lithium wire

Alkyl, aromatic, benzylic and benzoyl halides have been successfully coupled in good yields using lithium wire suspended in tetrahydrofuran and ultrasound.     

Synthesis with migrating phenylthio groups: connective routes to 2-phenylthioallyl alcohols and 2-phenylthio enones

The title compounds may be made from bis(phenylthio) acetals and aldehydes by routes involving PhS migration.