Cycle and circle tests of balance in gain graphs: Forbidden minors and their groups

We examine two criteria for balance of a gain graph, one based on binary cycles and one on circles. The graphs for which each criterion is valid depend on the set of allowed gain groups. The binary cycle test is invalid, except for forests, if any possible gain group has an element of odd order. Assuming all groups are allowed, or all abelian groups, or merely the cyclic group of order 3, we characterize, both constructively and by forbidden minors, the graphs for which the circle test is valid. It turns out that these three classes of groups have the same set of forbidden minors. The exact reason for the importance of the ternary cyclic group is not clear. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Facile one-pot synthesis of BINOL- and H8-BINOL-based aryl phosphites and their use in palladium catalysed asymmetric allylation

Novel P-monodentate aryl phosphite ligands have been synthesised in one step from (R)-BINOL, (R)-H₈-BINOL and (R)-H₈-3,3′-dibromo-BINOL. With the new aryl phosphites, up to 86% ee was observed in the asymmetric Pd-catalysed amination of 1,3-diphenyl-2-propenyl acetate with sodium diformylamide. In the enantioselective alkylation of 1,3-diphenyl-2-propenyl acetate with dimethyl malonate, up to 97% enantioselectivity was achieved.     

Longitudinal (1)H relaxation optimization in TROSY NMR spectroscopy

A general method to enhance the sensitivity of the multidimensional NMR experiments performed at high-polarizing magnetic field via the significant reduction of the longitudinal proton relaxation times is described. The method is based on the use of two vast pools of "thermal bath" 1H spins residing on hydrogens covalently attached to carbon and oxygen atoms in 13C,15N labeled and fully protonated or fractionally deuterated proteins to uniformly enhance longitudinal relaxation of the 1HN spins and concomitantly the sensitivity of multipulse NMR experiments. The proposed longitudinal relaxation optimization is implemented in the 2D [15N,1H]-LTROSY, 2D [15N,1H]-LHSQC and 3D LTROSY-HNCA experiments yielding the factor 2-2.5 increase of the maximal signal-to-noise ratio per unit time at 600 MHz. At 900 MHz, the predicted decrease of the 1HN longitudinal relaxation times can be as large as one order of magnitude, making the proposed method an important tool for protein NMR at high magnetic fields.     

Hydrogen‐bonded frameworks of bis(2‐carboxypyridinium) hexafluorosilicate and bis(2‐carboxyquinolinium) hexafluorosilicate dihydrate

In bis(2‐carboxypyridinium) hexafluorosilicate, 2C₆H₆NO₂⁺·SiF₆²⁻, (I), and bis(2‐carboxyquinolinium) hexafluorosilicate dihydrate, 2C₁₀H₈NO₂⁺·SiF₆²⁻·2H₂O, (II), the Si atoms of the anions reside on crystallographic centres of inversion. Primary inter‐ion interactions in (I) occur via strong N—H...F and O—H...F hydrogen bonds, generating corrugated layers incorporating [SiF₆]²⁻ anions as four‐connected net nodes and organic cations as simple links in between. In (II), a set of strong N—H...F, O—H...O and O—H...F hydrogen bonds, involving water molecules, gives a three‐dimensional heterocoordinated rutile‐like framework that integrates [SiF₆]²⁻ anions as six‐connected and water molecules as three‐connected nodes. The carboxyl groups of the cation are hydrogen bonded to the water molecule [O...O = 2.5533 (13) Å], while the N—H group supports direct bonding to the anion [N...F = 2.7061 (12) Å].     

Symmetric random walks in random environments

We consider a random walk on thed-dimensional lattice ^d where the transition probabilitiesp(x,y) are symmetric,p(x,y)=p(y,x), different from zero only ify–x belongs to a finite symmetric set including the origin and are random. We prove the convergence of the finite-dimensional probability distributions of normalized random paths to the finite-dimensional probability distributions of a Wiener process and find our an explicit expression for the diffusion matrix.     

Transition metal clusters and supported species with metal-carbon bonds from first-principles quantum chemistry

We discuss the impact of density functional electronic structure calculations for understanding the organometallic chemistry of transition metal (TM) surface complexes and clusters. Examples will cover three types of systems, mainly of interest in the context of heterogeneous catalysis: (i) supported carbonyl complexes of rhenium on MgO and of rhodium in zeolites, (ii) TM clusters with CO ligands and adsorbates, and (iii) metal clusters exhibiting chemical bonds with atomic carbon. The first group of case studies promotes the concept that surface groups of oxide supports are bonded to TM complexes in the same way as common (poly-dentate) ligands are bonded in coordination compounds. The second group of examples demonstrates various “ligand effects” of TM clusters. Finally, we illustrate how carbido centers stabilize TM clusters and modify the propensity for adsorption at the surface of such clusters.     

On Effective Conductivity on ℤ d Lattice

We study the effective conductivity _e for a random wire problem on the d-dimensional cubic lattice ^d , d2 in the case when random conductivities on bonds are independent identically distributed random variables. We give exact expressions for the expansion of the effective conductivity in terms of the moments of the disorder parameter up to the 5th order. In the 2D case using the duality symmetry we also derive the 6th order expansion. We compare our results with the Bruggeman approximation and show that in the 2D case it coincides with the exact solution up to the terms of 4th order but deviates from it for the higher order terms.