Complete reduction of fermion-antifermion Bethe-Salpeter equation with static kernel. II

Recent work with the Bethe-Salpeter (BS) equation for a $\text{spin}\text{-}\text{1}\text{2}$ fermion-antifermion system is developed further and extended in a number of ways. Static kernels are considered, as previously, but in the present case, the structure of the kernels serves to suppress completely all pair terms. The reduction of the 16 coupled integro-differential equations involving the BS bispinor wavefunctions can be carried out much more simply than before. The effective Hamiltonians of the eigenvalue equations which result for single scalar and vector wavefunctions are not only in formally closed operator form, correct to all orders in the coupling constant and $\text{v}\text{c}$, but have an explicit and simple structure. They depend at most linearly on the static potential, and also on powers of momentum and simple functions of the relativistic free-particle energies.Previous work is further generalized by the consideration of static four-vector interactions (vector gluons or photons) in an arbitrary “gauge” for equal mass particles and antiparticles on the one hand, and the fourth (scalar) component of a vector potential for unequal mass particle and antiparticle on the other hand, the latter in order to study the mass dependence of the effective interactions and of the wavefunctions.Spin-orbit, spin-spin, and tensor interactions are expected to arise from the Breit-like four-vector interactions in conventional $\text{v}\text{c}$ expansions, but the present results are correct to all orders in $\text{v}\text{c}$. Furthermore, such types of interactions also arise, as previously, for the case of a Coulomb-like potential, for which they are not, at first guess, expected. In the unequal mass case, an interesting new type of effective tensor interaction is also generated which serves to mix triplet and singlet states.Various special “gauges” are considered in the equal mass case. The general structure of the BS amplitude is also discussed, and specifically developed in some detail in perturbation theory for the ground state of positronium.While the current work should be considered as a general examination of the properties of a large class of BS equations of the Coulomb-Dirac or Breit-type, two areas for specific applications immediately come to mind: the calculation of positronium energy levels to very high order and the study of quark-antiquark binding involving both like and unlike quarks.     

Dual Radon transforms on affine Grassmann manifolds

Fix , and let and denote the affine Grassmann manifolds of - and -planes in . We investigate the Radon transform associated with the inclusion incidence relation. For the generic case and n$">, we will show that the range of this transform is given by smooth functions on annihilated by a system of Pfaffian type differential operators. We also study aspects of the exceptional case .

     

Synthesis and theoretical studies on rare three-coordinate lead complexes

A series of beta-diketiminate lead halide complexes has been synthesised LPbCl (2), LPbBr (3) and LPbI (4) (L = {N(2,6-(i)Pr(2)C(6)H(3))C(Me)}2CH]), which includes a rare example of a three-coordinate lead iodide (4). The chloride and bromide complexes, 2 and 3, are relatively stable in both the solid and solution states, only slowly decomposing to elemental lead over the course of a month in solution, the lead iodide 4 appears to be less stable and decomposes after 3 d in the solid state at ambient temperatures. The lead chloride complex 2 was treated with KN(SiMe3)2 to yield an unusual terminal lead amide complex LPbN(SiMe3)2 (5). Unlike three-coordinate beta-diketiminate transition metal-halide complexes, the ligands are present in a pyramidal arrangement around the lead centre, commonly attributed to the presence of a stereochemically active lone pair. We have investigated the influence of this lone pair on the geometry of the metal halide complexes 2-4, as well as the isostructural germanium and tin complexes (6 and 7, respectively) using DFT calculations. The lone pair in the lead complexes is significantly more diffuse than in the tin and germanium analogues and only a small amount of hybridisation between the 6s and 6p orbitals is observed.     

Nonlocal behavior of an electron in the ring-opening of cyclobutene

The nonlocal behavior of an electron in the ring-opening of cyclobutene is analyzed using the sharing amplitude and tools based thereupon. The sharing amplitude is a generalization of the absolute value squared of the wave function (a probability density according to the Born interpretation) to a measure that gives, for a single particle in a many particle system, both the relative phase of a wavelike quantity between any two space/spin points and a measure of the distribution of that quantity between those points. The sharing indices are related to the absolute value squared of the amplitude, thereby ensuring that the amplitude and the indices are consistent. To provide prototypical behavior of the sharing quantities in single and double bonds and to identify nonbonding and antibonding behavior, these tools are used to describe single electron behavior in ethane and ethylene, in the latter including separate σ and π contributions and two excited states. Similar analyses of the single and double carbon-carbon bonds in the reactant cyclobutene and in the product s-cis-butadiene (a planar transition state allowing for σ and π separation) are carried out. Comparisons are made to the prototypical molecules. The sharing quantities in the locally stable forms of s-gauche-butadiene are then considered. A remnant of the bond that is broken in cyclobutene is found in a form that is consistent with a conrotatory ring-opening, a behavior suggested by Woodward and Hoffmann on the basis of the symmetry of the highest occupied molecular orbital in the product, but here without appeal to only that molecular orbital. Finally, the nonlocal behavior of an electron during the breaking and making of bonds in the reaction is discussed for several geometries along the reaction path.     

Simultaneous chromatography and electrophoresis: two-dimensional planar separations

Single-dimension separations are routinely coupled in series to achieve two-dimensional separations, yet little has been done to simultaneously exploit multiple dimensions during separation. In this work, simultaneous chromatography and electrophoresis is introduced and evaluated for its potential to achieve two-dimensional separations. In simultaneous chromatography and electrophoresis, chromatography occurs via capillary action while an orthogonal electric field concurrently promotes electrophoresis in a second dimension. A novel apparatus with a dual solvent reservoir was designed to apply the concurrent electric field. Various compounds were used to characterize the apparatus and technique, i.e., vitamins, amino acids, and dyes. Improved separation is reported with equivalent analysis times in comparison to planar chromatography alone. The feasibility of simultaneously employing chromatography and electrophoresis in two dimensions is discussed.

Glycoconjugates of gadolinium complexes for MRI applications

Examples of C-4 symmetric, medium MW conjugates incorporating 12 glucose or galactose groups linked via four dendritic wedges to a central Gd complex have been characterised; their enhanced relaxivity is interpreted in terms of effective motional coupling and large contributions from second sphere water molecules.     

Maristentorin, a novel pigment from the positively phototactic marine ciliate Maristentor dinoferus, is structurally related to hypericin and stentorin

The photoreceptor pigment of the heterotrich ciliate, Maristentor dinoferus, has been characterized. It is structurally similar to those of Stentor coeruleus and Blepharisma japonicum but differs significantly in that it bears no aromatic hydrogens. The structure of the pigment, maristentorin, is based upon the hypericin skeleton, and its spectra are nearly identical to those of hypericin but shifted toward the red. Within experimental error, its fluorescence lifetime is identical to that of hypericin, approximately 5.5 ns in dimethylsulfoxide. It is remarkable that while the pigments are structurally similar in S. coeruleus and M. dinoferus, in the former there is an abrupt photophobic response, whereas in the latter there is a slow response toward light. The roles of the hypericin-like pigments in the heterotrich ciliates are discussed as potentially analogous in Maristentor.     

Sauerstoff

Ohne Zusammenfassung     

ChemInform Abstract: Copper(I) and Copper(II) Coordination Structure under Hydrothermal Conditions at 325 °C: An X‐Ray Absorption Fine Structure and Molecular Dynamics Study.

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