The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes

Quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis. We discuss a condition on the wave front set for the correspondingn-point distributions, called microlocal spectrum condition (SC). On Minkowski space, this condition is satisfied as a consequence of the usual spectrum condition. Based on Radzikowski's determination of the wave front set of the two-point function of a free scalar field, satisfying the Hadamard condition in the Kay and Wald sense, we construct in the second part of this paper all Wick polynomials including the energy-momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our microlocal spectrum condition.     

Fluorescent, Siderophore-Based Chelators. Design and Synthesis of a Trispyrenyl Trishydroxamate Ligand, an Intramolecular Excimer-Forming Sensing Molecule Which Responds to Iron(III) and Gallium(III) Metal Cations

Two pyrene-labeled hydroxylamines, 5-Bn and 5-Bz, O-protected with the benzyl and the benzoyl group, respectively, have been prepared for the generation of siderophore-based new chelators incorporating both the pyrene chromophore and the hydroxamic acid functionality. 5-Bz formed the starting point toward the synthesis of the tripod-shaped trishydroxamate, 1. That trichromophoric ligand displays remarkable fluorescence emission properties (dual emission: "monomer" and excimer type) which are markedly and selectively modified by binding Fe(NO(3))(3) and Ga(NO(3))(3). Ferric ions induce a quasi total quenching of the pyrene fluorescence, whereas the nonquenching Ga(III) cations are observed to affect the value of the excimer-to-monomer fluorescence intensity ratio. Ethylenediaminetetraacetic acid (EDTA) competition reactions yielded an estimated value of 3.8 for log K of the complex LFe in methanol/water (80/20 v/v), where K = ([LFe][H(+)](3))/([LH(3)][Fe(3+)]) and L is the ligand in its totally deprotonated form. Compound 1 is the prototype of a new class of photoresponsive molecular systems which could act as sensitive probes for metal cation detection and recognition.     

Metallic Conductivity in Metal Tetraaza [14]Annulene Iodides: The Crystal Structures of Dihydrodibenzo-[b,i]-1, 4, 8, 11-tetraazacyclotetradecinenickel and -palladium Iodides

Single crystals of dihydrodibenzo[b, i]-1, 4, 8, 11-tetraazacyclotetradecinenickel iodide show metallic conductivity between room temperature and approx. 110 K. The crystals are orthorhombic, space group I_bam with four formula units per cell of the following dimensions: a = 20.245, b = 13.416, c = 6.418 Å. The analogous palladium complex is isomorphous, the cell constants being a = 20.452, b = 13.430 and c = 6.499 Å. A number of other partially oxidized metal tetraaza [14]annulenes also show electrical conductivity.     

A theoretical investigation of the enantioselective hydrogenation mechanism of α-ketoesters

The enantioselective hydrogenation of α-ketoesters to α-hydroxyesters over Pt/Al₂O₃ catalysts modified by cinchona alkaloids is an interesting model reaction for the investigation of heterogeneous catalysis capable of producing optically active products. The aim of the present theoretical study is to rationalize the interaction between protonated cinchona alkaloids (modifiers) and methyl pyruvate (substrate) by investigating the possible weak complexes formed by these two species. For this purpose we use molecular mechanics and the AM1 semiempirical method. The optimization leads to two stable forms of the complexes, where the substrate is bound to the modifier via hydrogen bonding between the oxygen of the α-carbonyl of pyruvate and the quinuclidine nitrogen of the alkaloid. In such complexes the methyl pyruvate is transformed into a half-hydrogenated species which can be adsorbed on the platinum surface and, after hydrogenation, leads to methyl lactate product. The results show that adsorption of the complex leading to (R)-methyl lactate is more favorable than that of the corresponding system yielding (S)-methyl lactate, which may be the key for the enantio-differentiation.     

Determination of coplanar and non-coplanar polychlorinated biphenyls in human serum by gas chromatography with mass spectrometric detection: electron impact or electron-capture negative ionization?

A time- and cost-saving method for the congener-specific analysis of polychlorinated biphenyls (PCBs) in human serum has been developed and validated. After two fast extraction and clean-up steps, analyses were performed using gas chromatography coupled with mass spectrometry with single ion monitoring (GC/SIM-MS), either in electron impact (EI) or electron-capture negative ionization (ECNI) mode. For the determination of dioxin-like congeners, an improvement in EI-MS sensitivity is desirable and use of NI is thus preferred. The procedure was validated for 12 dioxin-like congeners by analyzing spiked samples on three different days and using (13)C(12)-labelled analogues as internal standards. When using an NCI source, the limit of quantification was assessed at 0.01 microg/L, except for PCBs #77 and #81, which cannot be reliably detected below 0.05 microg/L. For the lower chlorinated non-dioxin-like congeners, NI offers less selectivity because of limited fragmentation. Electron impact ionization and electron-capture negative ionization mode can therefore be considered to be complementary for the determination of PCB congeners in the general population.     

Studies on the Enzymatic Acylation of Quinic Acid,Shikimic Acid,Shikimic Acid,and Their Derivatives in Organic Solvents

Quinic acid ( 1a ), shikimic acid ( 2 ), and their derivatives were acylated in organic solvents by several lipases and by the protease subtilisin Carlsberg. The most satisfactory results were obtained with methyl (or benzyl) quinate ( 7a (or 8a )) and lipase from Chromobacterium viscosum adsorbed on Celite, which showed an overshelming preference towards the acylation of OH–C(4). Under optimized conditions, the syntehtically useful 4-O -acetylquinate 8d was isolated in ca. 90% yield. On the other hand, acylation of methyl shikimate ( 10a ) showed no regioselectivity with any of the enzymes tested. A possible rationale for the different behavior of Chromobacterium viscosum lipase towards 7a and 10a is given, comparing the conformations of these two molecules, as deducted from ¹H-NMR and molecular-mechanics calculation.     

Surface-enhanced Raman scattering from crystal violet adsorbed on a silver electrode

SERS from crystal violet (CV) on a Ag electrode was investigated under preresonance and resonance conditions. The excitation profile of the chemisorbed species is like that of dissolved molecules but intensities are ≈ 1000 times larger. The Raman enhancement is ≈ 10⁸ and exhibits a specific potential dependence even in the absence of adsorption-desorption process. At potentials where reduction of CV occurs leuco crystal violet was detected.     

Algebraic study of chiral anomalies

The algebraic structure of chiral anomalies is made globally valid on non-trivial bundles by the introduction of a fixed background connection. Some of the techniques used in the study of the anomaly are improved or generalized, including a systematic way of generating towers of descent equations.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under contract DE-AC03-76SF00098 and in part by the National Science Foundation under research grant PHY81-18547     

Structure and dynamics of ND3BF3 in the solid and gas phases: a combined NMR,neutron diffraction,and Ab initio study

The decrease in D-->A bond lengths, previously reported for some Lewis acid/base complexes, in going from the gas to the solid phases is investigated by obtaining an accurate crystal structure of solid ND(3)BF(3) by powder neutron diffraction. The B-N internuclear distance is 1.554(3) A, 0.118 A shorter than the most recent gas-phase microwave value and 0.121 A shorter than the single molecule geometry optimized (1.672 A, CISD/6-311++G(d,p)) bond length. The crystal structure also shows N-D.F-B hydrogen bonds. The effects of this change in structure and of intermolecular hydrogen-bonding on nuclear magnetic shielding (i.e., chemical shifts) and the nuclear quadrupolar coupling constants (QCC) are investigated by ab initio molecular orbital and density functional theory calculations. These calculations show that the nitrogen ((15)N and (14)N) and boron ((11)B and (10)B) chemical shifts should be rather insensitive to changes in r(BN) and that the concomitant changes in molecular structure. Calculations on hydrogen-bonded clusters, based on the crystal structure, indicate that H-bonding should also have very little effect on the chemical shifts. On the other hand, the (11)B and (14)N QCCs show large changes because of both effects. An analysis of the (10)B[(19)F] line shape in solid ND(3)(10)BF(3) yields a (11)B QCC of +/-0.130 MHz. This is reasonably close an earlier value of +/-0.080 MHz and the value of +/-0.050 MHz calculated for a [NH(3)BF(3)](4) cluster. The gas-phase value is 1.20 MHz. Temperature-dependent deuterium T(1) measurements yield an activation energy for rotation of the ND(3) group in solid ND(3)BF(3) of 9.5 +/- 0.1 kJ/mol. Simulations of the temperature-dependent T(1) anisotropy gave an E(a) of 9.5 +/- 0.2 kJ/mol and a preexponential factor, A, of 3.0 +/- 0.1 x 10(12) s(-)(1). Our calculated value for a [NH(3)BF(3)](4) cluster is 16.4 kJ/mol. Both are much higher than the previous value of 3.9 kJ/mol, from solid-state proton T(1) measurements.