Role of resonances in building cross sections: Comparison between the Mittag–Leffler and the T‐matrix Green function expansion approaches

Peaks in collision cross sections are often interpreted as resonances. The complex dilation method, as well as other methods relying on analytic continuation of the scattering formalism, can be used to clarify whether these structures are true resonances in the sense that they are poles of the S‐matrix and the associated Green function. The performance of the Mittag–Leffler expansion and T‐matrix Green function expansion methods are formally and computationally compared. The two methods are applied to two model potentials. Eigenenergies, s‐wave residues, and cross sections are computed with both methods. The resonance contributions to the cross sections are further analyzed by removing the residue contributions from the Mittag–Leffler and Green function expansion sums, respectively. It is suggested that the contribution of a resonance to a cross section should be defined through its S‐matrix residue. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

A μ‐chloro‐bridged dinuclear ruthenium complex with 9H‐carbazole: the formation of one‐dimensional linear chains of star‐shaped edge‐fused rings

The title complex, di‐μ‐chloro‐bis­[chloro­(η⁶‐p‐cymene)ruthenium(II)]–9H‐carbazole (1/2), [Ru₂Cl₄(C₁₀H₁₄)₂]·2C₁₂H₉N, is composed of one [RuCl₂(η⁶‐p‐cymene)]₂ and two 9H‐carbazole mol­ecules. There are one‐half of a dinuclear complex and one 9H‐carbazole mol­ecule per asymmetric unit. In the dinuclear complex, each of the two crystallographically equivalent Ru atoms is in a pseudo‐tetra­hedral environment, coordinated by a terminal Cl atom, two bridging Cl atoms and the aromatic hydro­carbon, which is linked in a η⁶ manner; the Ru⋯Ru separation is 3.688 (3) Å. The title complex has a crystallographic centre of symmetry located at the mid‐point of the Ru⋯Ru line. Inter­molecular N—H⋯Cl and π–π stacking inter­actions are observed. These inter­actions form a four‐pointed star‐shaped ring and one‐dimensional linear chains of edge‐fused rings running parallel to the [100] direction, which stabilize the crystal packing.     

Standardisierung der dünnschichtchromatographischen Trennungen von Flechtensäuren zur Chemotaxonomie von Flechten

Zusammenfassung Die dünnschichtchromatographische Trennung von Flechtenextrakten zur Unterstützung der Taxonomie wurde in Bezug auf die Trennleistung und auf die Reproduzierbarkeit optimiert. Dabei wurden besonders gute Trennleistungen erhalten mit dem Flie?mittelgemisch Benzol:Dioxa:Eisessig=90∶25∶4 bei Verwendung von Kieselgel, dessen Aktivit?t durch eine Umgebung mit relativer Feuchte von 70% festgelegt wurde, und mit Methylenchlorid als Eluiermittel bei Verwendung von mit Oxals?ure impr?gniertem Kieselgel und antiparallelem Aktivit?tsgradienten. Eine hohe Reproduzierbarkeit der Trennungen wurde erreicht durch Verwendung der Vario-KS-Kammer nach Geiss, die die Einstellung einer definierten Schichtaktivit?t bzw. eines definierten Aktivit?tsgradienten und eine reproduzierbare Vorbedampfung der Schicht mit Flie?mittel erm?glicht. Es konnte gezeigt werden, da? durch unterschiedliche chromatographische Trennungen der gleichen Extrakte und durch die Verwendung verschiedener Anf?rbereagenzien die Identifizierung und damit die Aussagekraft für taxonomische Probleme steigt.

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Standardisation of the thin-layer chromatographic separation of lichen acids for the chemotaxonomy of lichens

Summary The thin-layer chromatography of lichen extracts for taxonomic studies has been optimized in relation to separation and to reproducibility. Especially good separations were found with benzene:dioxane:acetic acid (90∶25∶4) developer and silica gel thin-layer plates, whose activity was fixed by an ambient moisture content of 70%, and with methylene chloride developer and silica gel plates impregnated with oxalic acid and antiparallel activity gradient. High reproducibility of separation was obtained using the Geiss Vario-KS tank, which allows the activity of the plates or the activity gradient to be adjusted and which also allows reproducible exposure of plates to the vapour of developing solvents. By different chromatographic separations of the same extracts and by using different colour reactions the accuracy of identification for taxonomic studies has been improved.

     

Fluxional processes in diamagnetic and paramagnetic allyl dicarbonyl and 2-methylallyl dicarbonyl molybdenum histidinato complexes as revealed by spectroscopic data and density functional calculations

This work describes a detailed study on the structure and dynamics of pseudooctahedral low-valent complexes of the type [Mo(His-N(epsilon)-R)(eta-2-R'-allyl)(CO)(2)] (His=N(delta),N,O-L-histidinate; R=H, R'=H (1); R=C(2)H(4)CO(2)Me, R'=H (2); R=H, R'=Me (3); R=C(2)H(4)CO(2)Me, R'=Me (4)). These diamagnetic 18-electron complexes were comprehensively characterized spectroscopically and by X-ray crystallography. In the solid state, the (substituted) allyl ligand is in an endo position in all compounds, but it is trans to the His-N(delta) atom in 1 and 2, whereas it is trans to the carboxylate O atom for the 2-Me-allyl compounds 3 and 4. In solution, both isomers are present in a solvent-dependent equilibrium. The third isomer (allyl trans to His-NH(2)) is not spectroscopically observed in solution. This is in agreement with the results from density functional (DFT) computations (BPW 91 functional) for 1 and 3, which predict a considerably higher energy (+6.3 and +5.9 kJ mol(-1), respectively) for this isomer. A likely path for isomerization is calculated, which is consistent with the activation energy determined by variable temperature NMR measurements. At least for 3, the preferred path involves several intermediates and a rotation of the 2-Me-allyl ligand. For the paramagnetic 17-electron congeners, DFT predicts the exo isomer of 3(+) with the 2-Me-allyl ligand trans to the carboxylate O atom to be by far the most stable isomer. For 1(+), an endo-exo equilibrium between the isomers with the allyl ligand trans to the carboxylate O atom is suggested. These suggestions are confirmed by EPR spectroscopy on the electrochemically generated species, which show signals for one- (4) and two- (2) metal-containing compounds. The appearance of the EPR spectra may be rationalized by inspection of the SOMOs from DFT calculations of the species in question. The notion of a metal-centered oxidation is also substantiated by IR spectroelectrochemistry and by UV/Vis spectra of the 17-electron complexes. Upon depleting the metal of electron density, the stretching vibrations of the carbonyl ligands shift more than 100 cm(-1) to higher wavenumbers, and the carbonyl vibration of the metal-coordinated carboxylate shifts by about 50 cm(-1). A color change from yellow to green upon oxidation is observed visually and quantified by the appearance of a new band at 622 nm (2(+)) and 546 nm (4(+)), respectively.     

Ferrocenoyl peptides with sulfur-containing side chains: synthesis, solid state and solution structures

The synthesis and full characterization of a number of amino acid and dipeptide derivatives with sulfur-containing side chains derived from ferrocene carboxylic acid and ferrocene-1,1′-dicarboxylic acid is presented. In particular, compounds Fc-CO-(Aaa)_n-OMe (4) and Fe[C₅H₄-CO-(Aaa)_n-OMe]₂ (3) with (Aaa)_n = Cys(Bzl) (a), Cys(Bzl)-Cys(Bzl) (b), Cys(p-OMe-Bzl) (c), Cys(p-OMe-Bzl)-Cys(p-OMe-Bzl) (d), Met (e), and Met-Met (f) were prepared. Also, the free acid derivatives Fe[C₅H₄-CO-Met-OH]₂ (6e) and Fc-CO-Met-OH (7e) were prepared and characterized. The solid state structures of 3a, 4b, and 4e were determined by single crystal X-ray diffraction. Compound 3a shows a 1,3′ substitution pattern on the Cp rings in the solid state. Structures in solution were determined by NMR, IR and CD spectroscopy, with particular emphasis on the question of hydrogen bonding and helical chirality of the metallocene. As an example, the full assignment for the Cp signals in the disubstituted derivative 3a was achieved by simulation of the ¹H NMR signals from the cyclopentadienyl ring in combination with 2D-NOESY spectra. In solution, 3a has the known 1,2′ substitution pattern, which is stabilized by intramolecular hydrogen bonds.     

A Study of PbTiO3 Crystallization in Pure and Composite Nanopowders Prepared by the Sol-Gel Technique

Summary.  In this investigation the crystallization of PbTiO₃ upon annealing of pure nanopowders and PbTiO₃–SiO₂ (1:1 v/v) nanocomposite powders prepared by the sol-gel technique was studied. Using X-ray diffraction phase analysis, the start of PbTiO₃ crystallization in pure PbTiO₃ powders was detected at 400°C. Distinct crystallization of PbTiO₃ in PbTiO₃–SiO₂ nanocomposites starts at 700°C, whereas SiO₂ remains amorphous. There are indications that an interface interaction between the PbTiO₃ and the SiO₂ phase plays an important role in hindering the crystallization of PbTiO₃. The particle size (size of coherently scattering regions) was estimated from the broadening of the X-ray diffraction line profiles. The average size of PbTiO₃ nanocrystallites increases with temperature and time of annealing, the influence of temperature being more significant than that of the annealing time. Differential scanning calorimetry confirmed the results of the X-ray diffraction with respect to the start of the crystallization. Laser beam scattering and scanning electron microscopy provided the statistical distribution of the grain size and the morphology of the powder grains, showing that each grain of the powders contains several nanocrystallites (coherently scattering regions). Received October 4, 2001. Accepted (revised) December 14, 2001     

Self-consistent solution of the Dyson equation for atoms and molecules within a conserving approximation

We have calculated the self-consistent Green's function for a number of atoms and diatomic molecules. This Green's function is obtained from a conserving self-energy approximation, which implies that the observables calculated from the Green's functions agree with the macroscopic conservation laws for particle number, momentum, and energy. As a further consequence, the kinetic and potential energies agree with the virial theorem, and the many possible methods for calculating the total energy all give the same result. In these calculations we use the finite temperature formalism and calculate the Green's function on the imaginary time axis. This allows for a simple extension to nonequilibrium systems. We have compared the energies from self-consistent Green's functions to those of nonselfconsistent schemes and also calculated ionization potentials from the Green's functions by using the extended Koopmans' theorem.     

Specific labeling of cell surface proteins with chemically diverse compounds

The specific and covalent labeling of fusion proteins with synthetic molecules opens up new ways to study protein function in the living cell. Here we present a novel method that allows for the specific and exclusive extracellular labeling of proteins on the surfaces of live cells with a large variety of synthetic molecules including fluorophores, protein ligands, or quantum dots. The approach is based on the specific labeling of fusion proteins of acyl carrier protein with synthetic molecules through post-translational modification catalyzed by phosphopantetheine transferase. The specificity and versatility of the labeling should allow it to become an important tool for studying and manipulating cell surface proteins and for complementing existing approaches in cell surface engineering.     

Das chlorsilylsubstituierte Silanimin Bu2SiNSiClBu2

In the thermolysis of the silaterazolines silatetrazoline ^tBu₂SiNSiCl^tBu₂ · ^tBu₃SiN₃ the silanimine ^tBu₂SiNSiCl^tBu₂ and the silyl azide ^tBu₃SiN₃ are formed quantitatively. The silanimine ^tBu₂SiNSiCl^tBu₂ has been trapped with Et₃NHF, Me₃NHCl, water, 1-butene, 2,3-dimethyl-1,3-butadiene, isobutene, methylvinyl ether, and ^tBu₂SiClN₃. The structure of the disiloxane (^tBu₂SiCl-NH-Si^tBu₂)₂O and of the bis(di-tert-butylchlorsilyl)-substituted silatetrazoline ^tBu₂SiNSiCl^tBu₂ · ^tBu₂SiClN₃ has been determined by X-ray structure analysis.     

Bianchi type V perfect fluid cosmologies

Bianchi type V solutions of the Einstein equations are studied using the Hamiltonian approach. Explicit expressions depending on a single quadrature are given for the metric components in the general orthogonal perfect fluid case. It is shown that the quadrature can be evaluated in terms of elementary or elliptic integrals when the parameter in the equation of statep=(–1) takes the values 1, 10/9, 4/3, 14/9, 5/3, 2.