Weyl's geometry and physics

It is proposed to remove the difficulty of nonitegrability of length in the Weyl geometry by modifying the law of parallel displacement and using standard vectors. The field equations are derived from a variational principle slightly different from that of Dirac and involving a parameter . For =0 one has the electromagnetic field. For <0 there is a vector meson field. This could be the electromagnetic field with finite-mass photons, or it could be a meson field providing the missing mass of the universe. In cosmological models the two natural gauges are the Einstein gauge and the cosmic gauge. With the latter the universe has a fixed size, but the sizes of small systems decrease with time and their masses and energies increase, thus producing the Hubble effect. The field of a particle in this gauge is investigated, and it leads to an interesting solution of the Einstein equations that raises a question about the Schwarzschild solution.     

Many-particle tracking with nanometer resolution in three dimensions by reflection interference contrast microscopy

We have developed and characterized a method, based on reflection interference contrast microscopy, to simultaneously determine the three-dimensional positions of multiple particles in a colloidal monolayer. To evaluate this method, the interaction of 6.8 microm (+/-5%) diameter lipid-derivatized silica microspheres with an underlying planar borosilicate substrate is studied. Measured colloidal height distributions are consistent with expectations for an electrostatically levitated colloidal monolayer. The precision of the method is analyzed using experimental techniques in addition to computational bootstrapping algorithms. In its present implementation, this technique achieves 16 nm lateral and 1 nm vertical precision.     

Dinuclear zinc(II) double-helicates of homochirally substituted bis(dipyrromethene)s

[structure: see text] A series of bis(dipyrromethene)s substituted with aromatic amide and aliphatic ester homochiral auxiliaries have been prepared and complexed with zinc(II) ions to form double-helical dinuclear complexes. CD analysis of the crude complexes revealed that the helicates formed in a diastereoselective manner. The helicates have been resolved into their constituent M and P helices by HPLC, indicating that the helical sense of the complexes is stable to racemization.     

P840-Reaction Centers from Chlorobium tepidum–Quinone Analysis and Functional Reconstitution into Lipid Vesicles

Membranes of Chlorobium tepidum contain about 35, 45 and2–10 molecules of menaquinone-7, chlorobium quinone (1′-oxo-menaquinone-7) and of the polar menaquinone (probably 1′-OH-menaquinone-7) per reaction center, respectively. None of these quinones was retained during the isolation of P840-reaction centers beyond the detection limit of about 0.2 quinones per reaction center, neither in the core complex nor in functionally intact reaction center preparations. The latter is shown to catalyze the formation of an electrochemical proton gradient in the presence of ascorbate and phenazinium methosulfate, when it is incorporated into lipid vesicles.     

Solution and solid-state structure of the anion [Ag(2)[closo-CB(11)H(12)](4)](2-)

Addition of the carbene 1,3-dimesitylimidazol-2-ylidene (IMes) to a toluene solution of Ag[closo-CB(11)H(12)] results in the formation of the complex [(IMes)(2)Ag](2)[Ag(2)[closo-CB(11)H(12)](4)], the anionic component of which contains two silver(I) centers bridged by two carboranes in addition to one terminally bound carborane on each metal, in the solid-state. Comparison of the observed (11)B[(1)H] NMR chemical shifts of [(IMes)(2)Ag](2)[Ag(2)[closo-CB(11)H(12)](4)] or Ag[closo-CB(11)H(12)] with [NBu(4)][closo-CB(11)H(12)] in CD(2)Cl(2) demonstrates that the silver ion interacts significantly with the cage in solution. Theoretical investigations using the ab initio/GIAO/NMR method of [closo-CB(11)H(12)](-) and Na[closo-CB(11)H(12)] as model geometries for the silver salts support experimental evidence for these Ag...[BH] interactions in solution.     

Anion radical [2 + 2] cycloaddition as a mechanistic probe: stoichiometry- and concentration-dependent partitioning of electron-transfer and alkylation pathways in the reaction of the Gilman reagent Me2CuLi.LiI with bis(enones)

Exposure of easily reduced aromatic bis(enones) 1a-1e to the methyl Gilman reagent Me(2)CuLi.LiI at 0 degrees C in tetrahydrofuran solvent provides the products of tandem conjugate addition-Michael cyclization, 2a-2e, along with the products of [2 + 2] cycloaddition, 3a-3e. Complete partitioning of the Gilman alkylation and [2 + 2] cycloaddition pathways may be achieved by adjusting the loading of the Gilman reagent, the rate of addition of the Gilman reagent, and the concentration of the reaction mixture. The Gilman alkylation manifold is favored by the rapid addition of excess Gilman reagent at higher substrate concentrations, while the [2 + 2] cycloaddition manifold is favored by slow addition of the same Gilman reagent at lower concentrations and loadings. Notably, [2 + 2] cycloaddition to form 3a-3e is catalytic in Gilman reagent. Kinetic data reveal that the ratio of 2a and 3a changes such that the cycloaddition pathway becomes dominant upon increased consumption of Gilman reagent. These data suggest a concentration-dependent speciation of the Gilman reagent and differential reactivity of the aggregates present at higher and lower concentrations. While the species present at higher concentration induce Gilman alkylation en route to products 2a-2e, the species present at lower concentration provide products of catalytic [2 + 2] cycloaddition, 3a-3e. Moreover, upon electrochemical reduction of the bis(enones) 1a-1e, or chemically induced single-electron transfer from arene anion radicals, the very same [2 + 2] cycloadducts 3a-3e are formed. The collective data suggest that [2 + 2] cycloadducts 3a-3e arising under Gilman conditions may be products of anion radical chain cyclobutanation that derive via electron transfer (ET) from the Me(2)CuLi.LiI aggregate(s) present at low concentration. These observations provide a link between the Gilman alkylation reaction and related ET chemistry and suggest these reaction paths are mechanistically distinct. This analysis is made possible by the recent observation that easily reduced bis(enones) are subject to intramolecular [2 + 2] cycloaddition upon cathodic reduction or chemically induced ET from arene anion radicals, and is herewith showcased as a novel method of testing for the intermediacy of enone anion radicals.     

Ruthenium(II) dendrimers containing carbazole-based chromophores as branches

Three new luminescent and redox-active Ru(II) complexes containing novel dendritic polypyridine ligands have been synthesized, and their absorption spectra, luminescence properties (both at room temperature in fluid solution and at 77 K in rigid matrix), and redox behavior have been investigated. The dendritic ligands are made of 1,10-phenanthroline coordinating subunits and of carbazole groups as branching sites. The first and second generation species of this novel class of dendritic ligands (L1 and L2, respectively; see Figure 1 for their structural formulas) have been prepared and employed. The metal dendrimers investigated are [Ru(bpy)(2)(L1)](2+) (1; bpy = 2,2'-bipyridine), [Ru(bpy)(2)(L2)](2+) (2), and [Ru(L1)(3)](2+) (3; see Figure 2). For the sake of completeness and comparison purposes, also the absorption spectra, redox behavior, and luminescence properties of L1 and L2 have been studied, together with the properties of 3,6-di(tert-butyl)carbazole (L0) and [Ru(bpy)(2)(phen)](2+) (4, phen = 1,10-phenanthroline). The absorption spectra of the free dendritic ligands show features which can be assigned to the various subunits (i.e., carbazole and phenanthroline groups) and additional bands at lower energies (at lambda > 300 nm) which are assigned to carbazole-to-phenanthroline charge-transfer (CT) transitions. These latter bands are significantly red-shifted upon acid and/or zinc acetate addition. Both L1 and L2 exhibit relatively intense luminescence at room temperature in fluid solution (lifetimes in the nanosecond time scale, quantum yields of the order of 10(-2)-10(-1)) and at 77 K in rigid matrix (lifetimes in the millisecond time scale). Such a luminescence is assigned to CT states at room temperature and to phenanthroline-centered pi-pi triplet levels at 77 K. The room-temperature luminescence of L1 and L2 is totally quenched by acid or zinc acetate. The metal dendrimers exhibit the typical absorption and luminescence properties of Ru(II) polypyridine complexes. In particular, metal-to-ligand charge-transfer (MLCT) bands dominate the visible absorption spectra, and formally triplet MLCT levels govern the excited-state properties. Excitation spectroscopy evidences that all the light absorbed by the dendritic branches is transferred with unitary efficiency to the luminescent MLCT states in 1-3, showing that the new metal dendrimers can be regarded as efficient light-harvesting antenna systems. All the free ligands and metal dendrimers exhibit a rich redox behavior (except L2 and 3, whose redox behavior was not investigated because of solubility reasons), with clearly attributable reversible carbazole- and metal-centered oxidation and polypyridine-centered reduction processes. The electronic interaction between the carbazole redox-active sites of the dendritic ligands is affected by Ru(II) coordination.     

Mechanochemical Formation,Solution Rearrangements,and Catalytic Behavior of a Polymorphic Ca/K Allyl Complex

Without solvents present, the often far-from-equilibrium environment in a mechanochemically driven synthesis can generate high-energy, non-stoichiometric products not observed from the same ratio of reagents used in solution. Ball milling 2 equiv. K[A’] (A’=[1,3-(SiMe₃)₂C₃H₃]⁻) with CaI₂ yields a non-stoichiometric calciate, K[CaA’₃], which initially forms a structure ( 1 ) likely containing a mixture of pi- and sigma-bound allyl ligands. Dissolved in arenes, the compound rearranges over the course of several days to a structure ( 2 ) with only η³-bound allyl ligands, and that can be crystallized as a coordination polymer. If dissolved in alkanes, however, the rearrangement of 1 to 2 occurs within minutes. The structures of 1 and 2 have been modeled with DFT calculations, and 2 initiates the anionic polymerization of methyl methacrylate and isoprene; for the latter, under the mildest conditions yet reported for a heavy Group 2 species (one-atm pressure and room temperature).