Quantum mechanics in noninertial reference frames: Violations of the nonrelativistic equivalence principle

In previous work we have developed a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group that includes transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as is the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. A special feature of these previously constructed representations is that they all respect the non-relativistic equivalence principle, wherein the fictitious forces associated with linear acceleration can equivalently be described by gravitational forces. In this paper we exhibit a large class of cocycle representations of the Galilean line group that violate the equivalence principle. Nevertheless the classical mechanics analogue of these cocycle representations all respect the equivalence principle.     

Effect of emulsion drop-size distribution upon coalescence in simple shear flow: a population balance study

A population balance is used to examine the effect of the shape of the initial drop-size distribution of an emulsion upon its short and long-time evolution in simple shear flow. Initial distributions that are monodisperse, multidisperse, lognormal, bimodal, multimodal, and step functions are considered. At short times, it is shown that the rate of coalescence decreases by up to 25% for step distributions and up to 75% for lognormal distributions as the width of the distribution increases. Bimodal, multidisperse and multimodal distributions show intermediate decreases in the rate of coalescence, between these two values, with increases in the distribution width. Furthermore, it is found that the initial rate of coalescence is strongly dependent upon the presence of large drops. As the number fraction of large droplets within the distribution increases, the rate of coalescence also increases. At long times, all distributions move toward an asymptotic distribution shape in which the frequency of drops decreases algebraically with drop diameter at small drop diameters, and decreases exponentially with drop diameter at large drop diameters. Though portions of each distribution showed the expected asymptotic scaling behavior at long times, each asymptotic distribution nevertheless retains 'fingerprints' of the respective initial distribution. Overall, the rate of coalescence for a system is bounded by the initial rate, which is a function of the initial distribution shape, and the asymptotic rate, which is dependent upon the long-time scaling behavior. Finally, it is shown that the resolution with which the drop-size distribution of an emulsion is experimentally measured can have a significant effect upon predicted rates of coalescence.     

Template-Directed Synthesis of Macroheterocycles by Ring-Closing Metathesis of Olefin-Substituted Pyridines in the Coordination Sphere of a Triplatinum Complex

Mono- and tris-3,5- and 2,6-pyridinediyl-containing macroheterocycles were synthesized by metathesis of olefin-substituted pyridines in the coordination sphere of mono- and tris-platinum complexes, respectively. Tris(2,6-pyridinediyl)-containing macroheterocycles were hydrogenated over palladium catalyst. The hydrogenated macrocycle was used as ligand for the triplatinum template. The structure of the resulting complex was established by X-ray analysis.     

Hydroxy- and mercaptopyridine pincer platinum and palladium complexes generated by silver-free halide abstraction

A silver-free route has been employed for the synthesis of a number of Pd and Pt complexes supported by an NCN "pincer" ligand (NCN = [2,6-(Me2NCH2)2C6H3]-) via halide abstraction. This was achieved by the use of o-, m-, and p-hydroxypyridines or o- and p-mercaptopyridines in basic ethanol solutions. The acidic OH or SH protons are removed to generate the formally anionic ligands. X-ray crystal structure determination of these complexes shows that the bonding of the substituted pyridine ligands occurs exclusively through the pyridine N for hydroxypyridines and exclusively through the thiol S in mercaptopyridines. In the hydroxypyridine case, the ortho and para isomers tautomerize to generate pyridone structures with a covalent M-N bond, whereas the m-hydroxypyridine complex, which is unable to tautomerize, is found to still be bound through the pyridine N but in a zwitterionic structure. The mercaptopyridine complexes are the first reported examples of pincer-ligated Pd and Pt thiolate species. The pyridine ligands can be quantitatively exchanged for chloride by reaction with excess NH4Cl, a potentially useful chemical switch for ligation/decomplexation of this ligand type.     

A novel heteroditopic terpyridine-pincer ligand as building block for mono- and heterometallic Pd(II) and Ru(II) complexes

A palladium-catalyzed Stille coupling reaction was employed as a versatile method for the synthesis of a novel terpyridine-pincer (3, TPBr) bridging ligand, 4'-{4-BrC6H2(CH2NMe2)2-3,5}-2,2':6',2' '-terpyridine. Mononuclear species [PdX(TP)] (X = Br, Cl), [Ru(TPBr)(tpy)](PF6)2, and [Ru(TPBr)2](PF6)2, synthesized by selective metalation of the NCNBr-pincer moiety or complexation of the terpyridine of the bifunctional ligand TPBr, were used as building blocks for the preparation of heterodi- and trimetallic complexes [Ru(TPPdCl)(tpy)](PF6)2 (7) and [Ru(TPPdCl)2](PF6)2 (8). The molecular structures in the solid state of [PdBr(TP)] (4a) and [Ru(TPBr)2](PF6)2 (6) have been determined by single-crystal X-ray analysis. Electrochemical behavior and photophysical properties of the mono- and heterometallic complexes are described. All the above di- and trimetallic Ru complexes exhibit absorption bands attributable to (1)MLCT (Ru --> tpy) transitions. For the heteroleptic complexes, the transitions involving the unsubstituted tpy ligand are at a lower energy than the tpy moiety of the TPBr ligand. The absorption bands observed in the electronic spectra for TPBr and [PdCl(TP)] have been assigned with the aid of TD-DFT calculations. All complexes display weak emission both at room temperature and in a butyronitrile glass at 77 K. The considerable red shift of the emission maxima relative to the signal of the reference compound [Ru(tpy)2]2+ indicates stabilization of the luminescent 3MLCT state. For the mono- and heterometallic complexes, electrochemical and spectroscopic studies (electronic absorption and emission spectra and luminescence lifetimes recorded at room temperature and 77 K in nitrile solvents), together with the information gained from IR spectroelectrochemical studies of the dimetallic complex [Ru(TPPdSCN)(tpy)](PF6)2, are indicative of charge redistribution through the bridging ligand TPBr. The results are in line with a weak coupling between the {Ru(tpy)2} chromophoric unit and the (non)metalated NCN-pincer moiety.     

Trimetallic FePd2 and FePt2 4-ferrocenyl-NCN pincer complexes

Ferrocene-bridged NCN pincer complexes of structural type Fe(η⁵-C₅H₄-4-NCN-1-MX)₂ (X = I: 6, M = Pd; 7, M = Pt; X = Cl: 8, M = Pt; NCN = [4-C₆H₂(CH₂NMe₂)₂-2,6]⁻) are accessible by the subsequent reaction of Fe(η⁵-C₅H₄-4-NCNH)₂ (4) with ⁿBuLi and [PtCl₂(SEt₂)₂] (synthesis of 8) or treatment of Fe(η⁵-C₅H₄-4-NCN-1-I)₂ (5) with [Pd₂(dba)₃] (synthesis of 6) or [Pt(tol)₂(SEt₂)]₂ (synthesis of 7) (dba = dibenzylidene acetone, tol = 4-tolyl). In addition, the Sonogashira cross-coupling of Fe(η⁵-C₅H₄I)₂ (1) with HCC-4-NCNH (2) gives Fe(η⁵-C₅H₄-CC-4-NCNH)₂ (3). The reaction behavior of 3 towards ^tBuLi is reported as well.Cyclovoltammetric studies show that the ferrocene entity can be oxidized reversibly. The Fe(II)/Fe(III) potential decreases with increasing electron density at the NCN pincer units due to the presence of the M-halide moiety (M = Pd, Pt).The solid state structure of Fe(η⁵-C₅H₄-4-NCN-1-PdI)₂ (6) is presented. In 6 the Fe(η⁵-C₅H₄)₂ unit connects two NCN-PdI pincer entities with palladium in a square-planar environment. The cyclopentadienyl ligands show a staggered conformation. The C₆H₂ rings are tilted by 23.5(3)° towards the C₅H₄ entities and the C₆H₂ plane is almost coplanar with the coordination plane (10.3(3)°).     

Canonical variables for crossing multiparticle amplitudes

Canonical variables for arbitrary multiparticle amplitudes are defined which have the property that under crossing all variables except two energies stay in their physical domain.     

Aminoarenethiolate-copper(I)-catalyzed amination of aryl bromides

[reaction, structure: see text] Aminoarenethiolate-copper(I) complexes are known to be efficient catalysts for carbon-carbon bond formation. Here, we show the first examples that these thiolate-copper(I) complexes are efficient for carbon-nitrogen bond formation reactions as well. N-Arylation of benzylamine and imidazole with bromobenzene was achieved either in NMP as solvent or under solvent-free conditions in the presence of 2.5 mol % of aminoarenethiolate-copper(I) complex only.     

Covariant electroweak nucleon form factors in a chiral constituent-quark model

Results for the proton and neutron electric and magnetic form factors as well as the nucleon axial and induced pseudoscalar form factors are presented for the chiral constituent-quark model based on Goldstone-boson exchange dynamics. The calculations are performed in a covariant framework using the point-form approach to relativistic quantum mechanics. The direct predictions of the model yield a remarkably consistent picture of the electroweak nucleon structure. Received: 28 February 2002 / Accepted: 14 March 2002     

Untersuchung der Photochemie von Polyenen mit Hilfe von mikroprozessor-gesteuerter HPLC

Ohne Zusammenfassung

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Photochemical examination of polyenes by microprocessor controlled HPLC

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Wir danken Frau Prof. Breyer-Pfaff für die Moglichkeit, im Institut für Toxikologie Densitogramme aufnehmen zu konnen, und der Deutschen Forschungsgemeinschaft für personelle und finanzielle Unterstiitzung.