Predicted stability and structure of (HXeCCH)n (n=2 or 4) clusters and of crystalline HXeCCH

Ab initio calculations predict the existence of the dimer and tetramer of HXeCCH. The interaction energies are -6.66 and -19.40 kcal mol-1 for the dimer and tetramer, respectively. For both complexes, larger blue shifts of the Xe-H stretching mode are found, while the Xe-C stretching modes are slightly redshifted. The stability and structure of HXeCCH crystals is predicted by density functional theory calculations with periodic boundary conditions. Strong electrostatic interactions are found between the monomers in the crystal. The results are first evidence for the existence of crystalline materials made of a novel class of noble gas molecules.     

Directed-sorting method for synthesis of bead-based combinatorial libraries of heterogeneous catalysts

The synthesis and analysis of inorganic material combinatorial libraries by a directed-sorting, split-pool bead method was demonstrated. Directed-sorting, split-pool, metal-loaded libraries were synthesized by adsorbing metal salts (H2PtCl6, SnCl2, CuCl2, and NiCl2) and metal standards (Pt, Cu, Ni in HCl) onto 2-mg porous gamma-alumina beads in 96- or 384-well plates. A matrix algorithm for the synthesis of bead libraries treated each bead as a member of a row or column of a given matrix. Computer simulations and manual tracking of the sorting process were used to assess library diversity. The bead compositions were analyzed by energy-dispersive X-ray spectroscopy, X-ray fluorescence spectroscopy, electron probe microanalysis, inductively coupled plasma atomic emission spectroscopy, and inductively coupled plasma mass spectroscopy. The metal-loaded beads were analyzed by laser-activated membrane introduction mass spectroscopy (LAMIMS) for catalytic activity using methylcyclohexane dehydrogenation to toluene as a probe reaction. The catalytic activity of individual beads that showed minimal (approximately 20% of that of Pt on alumina) to high conversion could be determined semiquantitatively by LAMIMS. This method, therefore, provides an alternative to screening using microreactors for reactors that employ catalysts in the form of beads. The directed-sorting method offers the potential for synthesis of focused libraries of inorganic materials through relatively simple benchtop split-pool chemistry.     

Derivatization-independent cholesterol analysis in crude lipid extracts by liquid chromatography/mass spectrometry: applications to a rabbit model for atherosclerosis

Direct measurement of various sterols in crude lipid extracts in a single experiment from limited biological samples is challenging. Current mass spectrometry (MS) based approaches usually require chemical derivatization before subjecting to MS analysis. Here, we present a derivatization-independent method for analyzing various sterols, including cholesterol and its congeners, using liquid chromatography and atmospheric pressure chemical ionization mass spectrometry. Based on the specific tandem mass spectrometry pattern of cholesterol, multiple reaction monitoring (MRM) transitions were used to quantify free cholesterol and its fatty acyl esters. Several cholesterol oxidation products could also be measured using the upfront liquid chromatography separation and specific MRM transitions. The method was validated alongside established enzymatic assays in measuring total cholesterol. As a proof of concept, we analyzed plasma sterols in rabbits administrated with a high cholesterol diet (HCD) which is a classical atherosclerotic model. Free cholesterol, cholesterol esters, 7-hydroxycholesterol, and 7-ketocholesterol were elevated in plasma of rabbits on HCD. This method could also serve as an excellent tool for quantitative analysis of other sterols such as ergosterol and sitosterol in other organisms beside mammalian. In Saccharomyces cerevisiae, our results indicated dramatic increases of the ratio of ergosterol esters to free ergosterol in both yeh2Δ and tgl1Δ cells, which are consistent with the function of the respective enzymes.     

Synthesis and characterization of two quaternary thorium chalcophosphates: Cs4Th2P6S18 and Rb7Th2P6Se21

Two new thorium chalcophosphates have been synthesized by the reactive flux method and characterized by single-crystal X-ray diffraction, diffuse reflectance, and Raman spectroscopy: Cs4Th2P6S18 (I); Rb7Th2P6Se21 (II). Compound I crystallizes as colorless blocks in the triclinic space group P1 (No. 2) with a = 12.303(4) A, b = 12.471(4) A, c = 12.541(4) A, alpha = 114.607(8) degrees, beta = 102.547(6) degrees, gamma = 99.889(7) degrees, and Z = 2. The structure consists of (Th2P6S18)(4-) layers separated by layers of cesium cations and only contains the (P2S6)(4-) building block. Compound II crystallizes as red blocks in the triclinic space group P1 (No. 2) with a = 11.531(3) A, b = 12.359(4) A, c = 16.161(5) A, alpha = 87.289(6) degrees, beta = 75.903(6) degrees, gamma = 88.041(6) degrees, and Z = 2. The structure consists of linear chains of (Th2P6Se21)(7-) separated by rubidium cations. Compound II contains both the (PSe4)(3-) and (P2Se6)(4-) building blocks. Both structures may be derived from two known rare earth structures where a rare earth site is replaced by an alkali or actinide metal to form these novel structures. Optical band gap measurements show that compound I has a band gap of 2.8 eV and compound II has a band gap of 2.0 eV. Solid-state Raman spectroscopy of compound I shows the vibrations expected for the (P2S6)(4-) unit. Raman spectroscopy of compound II shows the vibrations expected for both (PSe4)(3-) and (P2Se6)(4-) units. Our work shows the remarkable diversity of the actinide chalcophosphate system and demonstrates the phase space is still ripe to discover new structures.     

Reactivity of rhenium(V) oxo Schiff base complexes with phosphine ligands: rearrangement and reduction reactions

The symmetric rhenium(V) oxo Schiff base complexes trans-[ReO(OH2)(acac2en)]Cl and trans-[ReOCl(acac2pn)], where acac2en and acac2pn are the tetradentate Schiff base ligands N,N'-ethylenebis(acetylacetone) diimine and N,N'-propylenebis(acetylacetone) diimine, respectively, were reacted with monodentate phosphine ligands to yield one of two unique cationic phosphine complexes depending on the ligand backbone length (en vs pn) and the identity of the phosphine ligand. Reduction of the Re(V) oxo core to Re(III) resulted on reaction of trans-[ReO(OH2)(acac2en)]Cl with triphenylphosphine or diethylphenylphosphine to yield a single reduced, disubstituted product of the general type trans-[Re(III)(PR3)2(acac2en)]+. Rather unexpectedly, a similar reaction with the stronger reducing agent triethylphosphine yielded the intramolecularly rearranged, asymmetric cis-[Re(V)O(PEt3)(acac2en)]+ complex. Reactions of trans-[Re(V)O(acac2pn)Cl] with the same phosphine ligands yielded only the rearranged asymmetric cis-[Re(V)O(PR3)(acac2pn)]+ complexes in quantitative yield. The compounds were characterized using standard spectroscopic methods, elemental analyses, cyclic voltammetry, and single-crystal X-ray diffraction. The crystallographic data for the structures reported are as follows: trans-[Re(III)(PPh3)2(acac2en)]PF6 (H48C48N2O2P2Re.PF6), 1, triclinic (P), a = 18.8261(12) A, b = 16.2517(10) A, c = 15.4556(10) A, alpha = 95.522(1) degrees , beta = 97.130(1) degrees , gamma = 91.350(1) degrees , V = 4667.4(5) A(3), Z = 4; trans-[Re(III)(PEt2Ph)2(acac2en)]PF6 (H48C32N2O2P2Re.PF6), 2, orthorhombic (Pccn), a = 10.4753(6) A, b =18.4315(10) A, c = 18.9245(11) A, V = 3653.9(4) A3, Z = 4; cis-[Re(V)O(PEt3)(acac2en)]PF6 (H33C18N2O3PRe.1.25PF6, 3, monoclinic (C2/c), a = 39.8194(15) A, b = 13.6187(5) A, c = 20.1777(8) A, beta = 107.7730(10) degrees , V = 10419.9(7) A3, Z = 16; cis-[Re(V)O(PPh3)(acac2pn)]PF6 (H35C31N2O3PRe.PF6), 4, triclinic (P), a = 10.3094(10) A, b =12.1196(12) A, c = 14.8146(15) A, alpha = 105.939(2) degrees , beta = 105.383(2) degrees , gamma = 93.525(2) degrees , V = 1698.0(3) A3, Z = 2; cis-[Re(V)O(PEt2Ph)(acac2pn)]PF6 (H35C23N2O3PRe.PF6), 5, monoclinic (P2(1)/n), a = 18.1183(18) A, b = 11.580(1) A, c = 28.519(3) A, beta = 101.861(2) degrees , V = 5855.9(10) A(3), Z = 4.     

An Experimental Study of Three-Phase Trapping in Sand Packs

The trapped saturations of oil and gas are measured as functions of initial oil and gas saturation in water-wet sand packs. Analogue fluids—water, octane and air—are used at ambient conditions. Starting with a sand-pack column which has been saturated with brine, oil (octane) is injected with the column horizontal until irreducible water saturation is reached. The column is then positioned vertically and air is allowed to enter from the top of the column, while oil is allowed to drain under gravity for varying lengths of time. At this point, the column may be sliced and the fluids analyzed by gas chromatography to obtain the initial saturations. Alternatively, brine is injected through the bottom of the vertical column to trap oil and gas, before slicing the columns and measuring the trapped or residual saturations by gas chromatography and mass balance. The experiments show that in three-phase flow, the total trapped saturations of oil and gas are considerably higher than the trapped saturations reported in the literature for two-phase systems. It is found that the residual saturation of oil and gas combined could be as high as 23 %, as opposed to a maximum two-phase residual of only 14 %. For very high initial gas saturations, the residual gas saturation, up to 17 %, was also higher than for two-phase displacement. These observations are explained in terms of the competition between piston-like displacement and snap-off. It is also observed that less oil is always trapped in three-phase flow than in two-phase displacement, and the difference depends on the amount of gas present. For low and intermediate initial gas saturations, the trapped gas saturation rises linearly with initial saturation, followed by a constant residual, as seen in two-phase displacements. However, at very high initial gas saturations, the residual saturation rises again.     

On the probability of independent sets in random graphs

Let k be the asymptotic value of the independence number of the random graph G(n, p). We prove that if the edge probability p(n) satisfies p(n) ? n^?2/5ln^6/5n then the probability that G(n, p) does not contain an independent set of size k ? c, for some absolute constant c > 0, is at most exp{?cn²/(k⁴p)}. We also show that the obtained exponent is tight up to logarithmic factors, and apply our result to obtain new bounds on the choice number of random graphs. We also discuss a general setting where our approach can be applied to provide an exponential bound on the probability of certain events in product probability spaces. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 22: 1–14, 2003     

On smoothed analysis in dense graphs and formulas

We study a model of random graphs, where a random instance is obtained by adding random edges to a large graph of a given density. The research on this model has been started by Bohman and colleagues (Random Struct Algor 3 ; Random Struct Algor 4 ). Here we obtain a sharp threshold for the appearance of a fixed subgraph and for certain Ramsey properties. We also consider a related model of random k‐SAT formulas, where an instance is obtained by adding random k‐clauses to a fixed formula with a given number of clauses, and derive tight bounds for the non‐satisfiability of the thus‐obtained random formula. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

The number of Hamiltonian decompositions of regular graphs

A Hamilton cycle in a graph Γ is a cycle passing through every vertex of Γ. A Hamiltonian decomposition of Γ is a partition of its edge set into disjoint Hamilton cycles. One of the oldest results in graph theory is Walecki’s theorem from the 19th century, showing that a complete graph K _n on an odd number of vertices n has a Hamiltonian decomposition. This result was recently greatly extended by Kühn and Osthus. They proved that every r-regular n-vertex graph Γ with even degree r = cn for some fixed c > 1/2 has a Hamiltonian decomposition, provided n = n(c) is sufficiently large. In this paper we address the natural question of estimating H(Γ), the number of such decompositions of Γ. Our main result is that H(Γ) = r ^(1+o(1))nr/2. In particular, the number of Hamiltonian decompositions of K _n is \({n^{\left( {1 + o\left( 1 \right)} \right){n^2}/2}}\).     

Random subgraphs of properly edge-coloured complete graphs and long rainbow cycles

We study the upper tail of the number of arithmetic progressions of a given length in a random subset of {1,..., n}, establishing exponential bounds which are best possible up to constant factors in the exponent. The proof also extends to Schur triples, and, more generally, to the number of edges in random induced subhypergraphs of ‘almost linear’ k-uniform hypergraphs.