Dual pairs and representations of scattering amplitudes

A procedure for constructing scattering amplitudes for production processes that is exactly unitary, preserves the bosonic character of the many-particle states, and is invariant with respect to an underlying symmetry group is given. Two simple models, dealing with isospin internal symmetry and the two-dimensional Euclidean space group are presented which illustrate how scattering amplitudes can be represented as matrix elements of groups whose action commutes with the action of the invariance group on the relevant Fock space.Invited talk presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.Work supported in part by the Department of Energy.     

Synthesis and Catalytic Properties of Di- and Trinuclear Palladium Complexes with PCP-Pincer Ligands

Linear and branched conjugated pincer ligands having Ph₂P groups were synthesized: 3,3',5,5'- tetrakis(diphenylphosphinomethyl)diphenylacetylene, 3,3',5,5'-tetrakis(diphenylphosphinomethyl)diphenyldi- acetylene, 1,3,5-tris[3,5-bis(diphenylphosphinomethyl)phenylethynyl]benzene, and hexakis[3,5-bis(diphenylphosphinomethyl)phenylethynyl]benzene. Palladation of these ligands by heating with Pd(BF₄)₂(MeCN)₄ in boiling acetonitrile gave the corresponding di- and trinuclear ionic pincer palladium complexes. No individual complex was obtained from hexakis[3,5-bis(diphenylphosphinomethyl)phenylethynyl]benzene. The ionic com- plexes were converted into the corresponding chloride complexes by treatment with sodium chloride in a mixture of water with methylene chloride. The structure of the ionic palladium complex with 3,3',5,5'-tetrakis(diphenylphosphinomethyl)diphenylacetylene was established by X-ray analysis. The obtained palladium complexes exhibited a considerable catalytic activity in the Heck reaction of iodobenzene with ethyl acrylate and in the Michael addition of ethyl cyanoacetate with methyl vinyl ketone. The catalytic activity per palladium atom decreases as the number of palladium atoms in the complex increases.     

Novel P‐Stereogenic PCP Pincer‐Aryl Ruthenium(II) Complexes and Their Use in the Asymmetric Hydrogen Transfer Reaction of Acetophenone

Achiral P‐donor pincer‐aryl ruthenium complexes ([RuCl(PCP)(PPh₃)]) 4c , d were synthesized via transcyclometalation reactions by mixing equivalent amounts of [1,3‐phenylenebis(methylene)]bis[diisopropylphosphine] ( 2c ) or [1,3‐phenylenebis(methylene)]bis[diphenylphosphine] ( 2d ) and the N‐donor pincer‐aryl complex [RuCl{2,6‐(Me₂NCH₂)₂C₆H₃}(PPh₃)], ( 3 ; Scheme 2). The same synthetic procedure was successfully applied for the preparation of novel chiral P‐donor pincer‐aryl ruthenium complexes [RuCl(P*CP*)(PPh₃)] 4a , b by reacting P‐stereogenic pincer‐arenes (S,S)‐[1,3‐phenylenebis(methylene)]bis[(alkyl)(phenyl)phosphines] 2a , b (alkyl=ⁱPr or ^tBu, P*CHP*) and the complex [RuCl{2,6‐(Me₂NCH₂)₂C₆H₃}(PPh₃)], ( 3 ; Scheme 3). The crystal structures of achiral [RuCl(equation/tex2gif-sup-3.gifPCP)(PPh₃)] 4c and of chiral (S,S)‐[RuCl(equation/tex2gif-sup-6.gifPCP)(PPh₃)] 4a were determined by X‐ray diffraction (Fig. 3). Achiral [RuCl(PCP)(PPh₃)] complexes and chiral [RuCl(P*CP*)(PPh₃)] complexes were tested as catalyst in the H‐transfer reduction of acetophenone with propan‐2‐ol. With the chiral complexes, a modest enantioselectivity was obtained.     

Biosynthesis of anthecotuloide,an irregular sesquiterpene lactone from Anthemis cotula L. (Asteraceae) via a non-farnesyl diphosphate route

Retrobiosynthetic analysis of the allergenic sesquiterpene lactone, anthecotuloide, suggested that this natural product could be formed either by head to head condensation of geranyl diphosphate with dimethylallyl diphosphate, or from farnesyl diphosphate (FPP), the accepted regular sesquiterpene precursor via the rearrangement of a germacranolide precursor. Isotopic labelling of anthecotuloide has now been achieved by feeding [1-(13)C]-glucose, [U-13C6]-glucose and [6,6-(2)H2]-glucose to aseptically grown plantlets of Anthemis cotula(family Asteraceae). Analysis of labelling patterns and absolute 13C abundances using quantitative 13C NMR spectroscopy showed that the isoprene building blocks of this sesquiterpene are formed exclusively via the MEP terpene biosynthetic pathway. This was supported by results from an experiment using [U-13C6]-glucose. A deuterium labelling experiment using [6,6-(2)H2]-glucose supported the original proposal and showed that anthecotuloide is formed from a non FPP precursor. Isotope ratio mass spectrometry suggested that there were two pathways for sesquiterpene biosynthesis in A. cotula.     

(P-Bis(pentafluorophenyl) substituted) PCP-pincer Ru(II) complexes: A theoretical study of the molecular structure and electronic properties

The differences between the molecular structures of the PCP-pincer complex [RuCl{C₆H₃(CH₂P(C₆H₅)₂)₂-2,6}(PPh₃)] ([RuCl(PCP^H)(PPh₃)], 1) and its tetrakis-pentafluorophenyl substituted analogue [RuCl{C₆H₃(CH₂P(C₆F₅)₂)₂-2,6}(PPh₃)] ([RuCl(PCP^F20)(PPh₃)], 2) have been rationalised by performing calculations on the cations [Ru(PCP^H)(PPh₃)]⁺ (1cat) and [Ru(PCP^F20)(PPh₃)]⁺ (2cat). The molecular interactions between the chloride ligand and the axial rings, as found in 1 and 2, respectively, have been studied computationally in the model systems [(C₆X₅PH₂)₂Cl⁻] (X = H, F). The calculations on 2cat show that in 2 it is most likely the attractive electrostatic interaction between the chloride ligand and the fluorinated phenyl rings that forces the C_ipso atom to occupy an axial position rather than an equatorial one in the observed (X-ray of 2) square pyramidal arrangement. In 1, however, repulsive steric hindrance forces the PPh₃ ligand to take the apical position. The applicability of the TD-DFT method for the calculation of the electronic spectra of the PCP-pincer compounds 1 and 2 has been tested. The results indicate that the excitation energies calculated for both complexes are in a reasonable agreement with the experimental absorption maxima. However, for 1, all the calculated transition energies are underestimated.     

Dissipative evolution of quantum statistical ensembles and nonlinear response to a time-periodic perturbation

We present a detailed discussion of the evolution of a statistical ensemble of quantum mechanical systems coupled weakly to a bath. The Hilbert space of the full system is given by the tensor product between the Hilbert spaces associated with the bath and the bathed system. The statistical states of the ensemble are described in terms of density matrices. Supposing the bath to be held at some - not necessarily thermal - statistical equilibrium and tracing over the bath degrees of freedom, we obtain reduced density matrices defining the statistical states of the bathed system. The master equations describing the evolution of these reduced density matrices are derived under the most general conditions. On time scales that are large with respect to the bath correlation time and with respect to the reciprocal transition frequencies of the bathed system, the resulting evolution of the reduced density matrix of the bathed system is of Markovian type. The detailed balance relations valid for a thermal equilibrium of the bath are derived and the conditions for the validity of the fluctuation-dissipation theorem are given. Based on the general approach, we investigate the non-linear response of the bathed subsystem to a time-periodic perturbation. Summing the perturbation series we obtain the coherences and the populations for arbitrary strengths of the perturbation.Received: 26 November 2003, Published online: 30 January 2004PACS: 05.30.-d Quantum statistical mechanics - 33.35. + r Electron resonance and relaxation - 33.25. + k Nuclear resonance and relaxation     

Complex dynamic behavior of fluctuating smectic- A films as studied by scattering with coherent X-rays

Coherent dynamic x-ray scattering has been used to study the thermally excited layer fluctuations in freely suspended smectic films of the compound 4O.8. Using 8-keV x rays and films with a thickness around 0.3 &mgr;m we resolve relaxation times down to a few &mgr;s. A combination of damped and oscillatory behavior is observed for the layer undulations, which can be attributed to inertial effects. These are due to the surface contribution to the free energy which cannot be disregarded for thin films.     

Bis（ortho—）chelated Monoanionic Bisphosphinoaryl Ruthenium（Ⅱ）Complexes：Synthesis,Characterization and Reactivity

Bisphosphinoaryl ruthenium(Ⅱ）compounds are synthesized using two distinct synthetic routes.One route,direct cycloruthenation,consists of the reaction of the parent arene compound R-PCHP with [RuCl2(PPh3)3]in chlorinated solvents.However,this route suffers from major drawbacks because HCl is formed as well as free triphenylphoshine.The other route,the transcyclometalation reaction,involves the interconversion of one cyclometalated ligand metal complex,[RuCl(NCN)(PPh3)],into another complex,[RuCl(R-PCP)(PPh3)],with concomitant consumption and formation of the corresponding arenes R-PCHP and NCHN,respectively.