A note on the random greedy independent set algorithm

Let r be a fixed constant and let be an r‐uniform, D‐regular hypergraph on N vertices. Assume further that for some . Consider the random greedy algorithm for forming an independent set in . An independent set is chosen at random by iteratively choosing vertices at random to be in the independent set. At each step we chose a vertex uniformly at random from the collection of vertices that could be added to the independent set (i.e. the collection of vertices v with the property that v is not in the current independent set I and contains no edge in ). Note that this process terminates at a maximal subset of vertices with the property that this set contains no edge of ; that is, the process terminates at a maximal independent set. We prove that if satisfies certain degree and codegree conditions then there are vertices in the independent set produced by the random greedy algorithm with high probability. This result generalizes a lower bound on the number of steps in the H‐free process due to Bohman and Keevash and produces objects of interest in additive combinatorics. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 479–502, 2016     

Fabrication of Super-Sized Metal Inorganic-Organic Hybrid Glass with Supramolecular Network via Crystallization-Suppressing Approach

Metal coordination compound (MCC) glasses [e.g., metal-organic framework (MOF) glass, coordination polymer glass, and metal inorganic-organic complex (MIOC) glass] are emerging members of the hybrid glass family. So far, a limited number of crystalline MCCs can be converted into glasses by melt-quenching. Here, we report a universal wet-chemistry method, by which the super-sized supramolecular MIOC glasses can be synthesized from non-meltable MOFs. Alcohol and acid were used as agents to inhibit crystallization. The MIOC glasses demonstrate unique features including high transparency, shaping capability, and anisotropic network. Directional photoluminescence with a large polarization ratio (≈47 %) was observed from samples doped with organic dyes. This crystallization-suppressing approach enables fabrication of super-sized MCC glasses, which cannot be achieved by conventional vitrification methods, and thus allows for exploring new MCC glasses possessing photonic functionalities.     

Ab initio calculations on low-lying electronic states of SnCl(2)- and Franck-Condon simulation of its photodetachment spectrum

Geometry optimization and harmonic vibrational frequency calculations have been carried out on low-lying doublet and quartet electronic states of stannous (tin(II)) dichloride anion (SnCl(2)(-)) employing the CASSCF and RCCSD(T) methods. The small-core fully-relativistic effective core potential, ECP28MDF, was used for Sn in these calculations, together with valence basis sets of up to augmented correlation-consistent polarized-valence quintuple-zeta (aug-cc-pV5Z) quality. The ground electronic state of SnCl(2)(-) is determined to be the X(2)B(1) state, with the A(2)B(2) and ?(4)Sigma state, calculated to be ca. 1.50 and 2.72 eV higher in energy respectively. The electron affinities of the X(1)A(1) and ?(3)B(1) states of SnCl(2) have been computed to be 1.568+/-0.007 and 4.458+/-0.002 eV respectively, including contributions of core correlation and extrapolation to the complete basis set limit. The SnCl(2) (X(1)A(1)) + e <-- SnCl(2)(-) (X(2)B(1)) and SnCl(2) (?(3)B(1)) + e <-- SnCl(2)(-) (X(2)B(1)) photodetachment bands have been simulated with computed Franck-Condon factors, which include an allowance for anharmonicity and Duschinsky rotation.     

Pseudouridines in rRNA helix 69 play a role in loop stacking interactions

The (1)H NMR spectra of RNAs representing E. coli 23S rRNA helix 69 with [1,3-(15)N]pseudouridine modification at specific sites reveal unique roles for pseudouridine in stabilizing base-stacking interactions in the hairpin loop region.     

Screening for cocrystallization tendency: the role of intermolecular interactions

Pharmaceutical cocrystals have rapidly emerged as a new class of API solids with great promise and advantages. Much work has been focused on exploring the crystal engineering and design strategies that facilitate formation of cocrystals of APIs and ligands/cocrystal formers. However, fewer attempts have been made to understand the equilibrium phase behavior and phase transition kinetics of the cocrystallizing solutions. This limited knowledge on the solution physical chemistry often leads to difficulty in screening for potential molecular pairs of API and ligand that form cocrystals effectively. In this study, the long-time self-diffusivities measured using pulsed gradient spin-echo nuclear magnetic resonance (PGSE NMR) are used to characterize the particle interactions in solutions for pharmaceutical cocrystallizing systems. For the pairs of API and ligand that produce cocrystals, the heteromeric attractions between API and ligand are found to be stronger than the homomeric attractions between API molecules and between ligand molecules, suggesting that an energetically favorable condition is induced for the formation of cocrystals. To the best of our knowledge, this is the first report of using the pair contribution of the self-diffusivity as a screening tool for cocrystal formation.     

Probing surface charge potentials of clay basal planes and edges by direct force measurements

The dispersion and gelation of clay suspensions have major impact on a number of industries, such as ceramic and composite materials processing, paper making, cement production, and consumer product formulation. To fundamentally understand controlling mechanisms of clay dispersion and gelation, it is necessary to study anisotropic surface charge properties and colloidal interactions of clay particles. In this study, a colloidal probe technique was employed to study the interaction forces between a silica probe and clay basal plane/edge surfaces. A muscovite mica was used as a representative of 2:1 phyllosilicate clay minerals. The muscovite basal plane was prepared by cleavage, while the edge surface was obtained by a microtome cutting technique. Direct force measurements demonstrated the anisotropic surface charge properties of the basal plane and edge surface. For the basal plane, the long-range forces were monotonically repulsive within pH 6-10 and the measured forces were pH-independent, thereby confirming that clay basal planes have permanent surface charge from isomorphic substitution of lattice elements. The measured interaction forces were fitted well with the classical DLVO theory. The surface potentials of muscovite basal plane derived from the measured force profiles were in good agreement with those reported in the literature. In the case of edge surfaces, the measured forces were monotonically repulsive at pH 10, decreasing with pH, and changed to be attractive at pH 5.6, strongly suggesting that the charge on the clay edge surfaces is pH-dependent. The measured force profiles could not be reasonably fitted with the classical DLVO theory, even with very small surface potential values, unless the surface roughness was considered. The surface element integration (SEI) method was used to calculate the DLVO forces to account for the surface roughness. The surface potentials of the muscovite edges were derived by fitting the measured force profiles with the surface element integrated DLVO model. The point of zero charge of the muscovite edge surface was estimated to be pH 7-8.     

Dirhenium carbonyl complexes bearing 2-vinylpyridine,morpholine and 1-methylimidazole ligands

Treatment of the labile compound [Re₂(CO)₈(MeCN)₂] with 2-vinylpyridine in refluxing benzene affords exclusively the new compound [Re₂(CO)₈(μ-η¹:η²-NC₅H₄CHCH₂)] (1) in 39% yield in which the μ-η¹:η²-vinylpyridine ligand is coordinated to one Re atom through the nitrogen and to the other Re atom via the olefinic double bond. Reaction of [Re₂(CO)₈(MeCN)₂] with morpholine in refluxing benzene furnishes two compounds, [Re₂(CO)₉(η¹-NC₄H₉O)] (2) and [Re₂(CO)₈(η¹-NC₄H₉O)₂] (3) in 5% and 29% yields, respectively. Reaction of [Re₂(CO)₈(MeCN)₂] with 1-methylimidazole gives [Re₂(CO)₈{η¹-NC₃H₃N(CH₃)}₂] (4) and the mononuclear compound fac-[ReCl(CO)₃{η¹-NC₃H₃N(CH₃)}₂] (5) in 18% and 26% yields, respectively. In the disubstituted compounds 2 and 4, the heterocyclic ligands occupy equatorial coordination sites. The mononuclear compound 5 consists of three CO groups, two N coordinated η¹-1-methylimidazole ligands and a terminal Cl ligand. The XRD structures of complexes 1, 3 and 5 are reported.     

Formations of mixed-valence oxovanadiumV,IV citrates and homocitrate with N-heterocycle chelated ligand

Dimeric mixed-valence oxovanadium citrate [V 2O 3(phen) 3(Hcit)].5H 2O ( 1) (H 4cit = citric acid, phen = 1,10-phenanthroline) was isolated from a weak acidic medium. It could be converted quantitatively into a tetrameric oxovanadium citrate adduct of 1,10-phenanthroline [V 2O 3(phen) 3(Hcit) 2(phen) 3O 3V 2].12H 2O ( 2). This was supported by the trace of infrared spectra and X-ray diffraction patterns. The two compounds feature a bidentate citrate group that chelates only to one vanadium center through their negatively charged alpha-alkoxy and alpha-carboxy oxygen atoms, while the other beta-carboxy and beta-carboxylic acid groups are free to participate in strong intramolecular and intermolecular hydrogen bonding [2.45(1) in 1 and 2.487(2) A in 2], respectively. This is also the case of homocitrato vanadate(V/IV) [V 2O 3(phen) 3( R, S-H 2homocit)]Cl.6H 2O ( 3) (H 4homocit = homocitric acid), which features a binding mode similar to that found in the R-homocitrato iron molybdenum cofactor of Mo-nitrogenase. Moreover, the homocitrato vanadate(V) [VO 2(phen) 2] 2[V 2O 4( R,S-H 2homocit) 2].4H 2O.2C 2H 5OH ( 4) is isolated as a molecular precursor for the formation of mixed-valence complex 3. The V-O alpha-alkoxy and V-O alpha-carboxy bond distances of homocitrate complexes 3 and 4 are 1.858(4) and 1.968(6) av and 2.085(4) and 1.937(5) A, respectively. They are shorter than those of homocitrate to FeVco (2.15 A). The gamma-carboxy groups of coordinated homocitrato complexes 3 and 4, and the free homocitrate salt Na 3(Hhomocit).H 2O ( 5), form strong hydrogen bonds with the chloride ion and the water molecule [2.982(5) in 3, 2.562(9) in 4, and 2.763(1) A in 5], respectively.     

Solvent dependence of the charge-transfer properties of a quaterthiophene–anthraquinone dyad

An electron donor–acceptor dyad (quaterthiophene–anthraquinone) mediates ultrafast intramolecular photoinduced charge separation and consequent charge recombination when in polar or moderately polar solvents. Alternatively, non-polar media completely impedes the initial photoinduced electron transfer by causing enough destabilization of the charge-transfer state and shifting its energy above the energy of the lowest locally excited singlet state. Furthermore, femtosecond transient-absorption spectroscopy reveals that for the solvents mediating the initial photoinduced electron-transfer process, the charge recombination rates were slower than the rates of charge separation. This behavior of donor–acceptor systems is essential for solar-energy-conversion applications. For the donor–acceptor dyad described in this study, the electron-transfer driving force and reorganization energy place the charge-recombination processes in the Marcus inverted region.