Electron-deficient and polycenter bonds in the high-pressure γ-B28 phase of boron

The peculiar bonding situation in γ boron is characterized on the basis of an experimental electron-density distribution which is obtained by multipole refinement against low-temperature single-crystal x-ray diffraction data. A topological analysis of the electron-density distribution reveals one-electron-two-center bonds connecting neighboring icosahedral B(12) clusters. A unique polar-covalent two-electron-three-center bond between a pair of atoms of an icosahedral cluster and one atom of the interstitial B(12) dumbbell explains the observed charge separation in this high-pressure high-temperature polymorph of boron.     

Hydrothermal synthesis and structural characterization of novel α-Keggin unit-supported Cu(II)- and Mn(II)-bipyridine complexes from a <Emphasis Type="Italic">tri</Emphasis>-lacunary precursor

Blue [{Cu(2,2′-bipy)₂}₂{α-SiW₁₂O₄₀}] (bipy = bipyridyl) (1) and pale yellow [Mn(2,2′-bipy)₃]₂[α-SiW₁₂O₄₀] (2) have been synthesized hydrothermally and characterized by IR spectroscopy and single crystal X-ray structure analysis. In 1, the [α-SiW₁₂O₄₀]⁴⁻ ion acts as a bridge between the two [{Cu(2,2′-bipy)₂]²⁺ moieties via coordination through the terminal oxygen atoms, while in 2, the [Mn(2,2′-bipy)₃]²⁺ ion balances the charge on the polyoxo anion without forming any covalent bond. To the best of our knowledge, this is the first example of transition metal-mediated transformation of [α-SiW₉O₃₄]¹⁰⁻ to [α-SiW₁₂O₄₀]⁴⁻. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Kakeya-type sets in finite vector spaces

For a finite vector space V and a nonnegative integer r≤dim V, we estimate the smallest possible size of a subset of V, containing a translate of every r-dimensional subspace. In particular, we show that if K⊆V is the smallest subset with this property, n denotes the dimension of V, and q is the size of the underlying field, then for r bounded and r<n≤rq ^r−1, we have |V∖K|=Θ(nq ^n−r+1); this improves the previously known bounds |V∖K|=Ω(q ^n−r+1) and |V∖K|=O(n ² q ^n−r+1).     

Unusual formation of β-carboline dimers under Bischler-Napieralski reaction conditions: an old reaction with a new direction

l-N-Formyl tryptophan methyl ester (3) underwent a Bischler-Napieralski reaction with POCl₃ at room temperature or under microwave irradiation, resulting in the unusual formation of β-carboline dimers 5 and 6. Most importantly, acetylation using Ac₂O of each of the dimers 5 and 6 separately afforded 1-[3′-carbomethoxy-β-carbolinyl]-3-carbomethoxy-9-acetyl-β-carboline (7) as the only product, the structure of which was confirmed by X-ray crystallography studies.     

A local central limit theorem for triangles in a random graph

In this paper, we prove a local limit theorem for the distribution of the number of triangles in the Erdos‐Rényi random graph G(n, p), where is a fixed constant. Our proof is based on bounding the characteristic function of the number of triangles, and uses several different conditioning arguments for handling different ranges of t. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 48, 732–750, 2016     

A novel cation induced polymeric chain in Na8[{Cu(gly)2}2]{H2(H2W12O42)}]?·?24H2O: hydrothermal synthesis, spectroscopic characterization and X-ray structure analysis

A novel bis(glycinato)copper(II)paradodecatungstate Na₈[{Cu(gly)₂}₂]-{H₂(H₂W₁₂O₄₂)}] · 24H₂O (1) has been synthesized under hydrothermal conditions. The crystal structure of 1 reveals an infinite one-dimensional chain along the [100] direction and is built from paradodecatungstate (H₂W₁₂O₄₂)¹⁰⁻ clusters joined through [Cu(gly)₂] moieties. Parallel chains are interlinked by NaO₆ octahedra to generate a two-dimensional network.     

(1SR,2RS,5RS,6SR,8RS)‐7,7‐Dimethyltricyclo[6.2.1.01,6]undecane‐2,5,6‐triol: a supramolecular framework built from O—H⋯O hydrogen bonds

In the title compound, C₁₃H₂₂O₃, the asymmetric unit has two independent mol­ecules linked by a strong O—H?O hydrogen bond. The cyclo­hexane ring is trans fused to the cyclo­pentane ring bridged through an ethyl moiety. The hydroxyl groups act as donors as well as acceptors, resulting in an extensive two‐dimensional hydrogen‐bonded network in the (011) plane. Intermolecular O—H?O bonds between centrosymmetrically related mol­ecules form a four‐membered supramolecular assembly, leading to infinite chains parallel to the [01] direction, crosslinked in the [100] direction.     

A new half-condensed Schiff base compound: highly selective and sensitive pH-responsive fluorescent sensor

A new probe, 3-[(3-benzyloxypyridin-2-ylimino)methyl]-2-hydroxy-5-methylbenzaldehyde (1-H) behaves as a highly selective fluorescent pH sensor in a Britton-Robinson buffer at 25 °C. The pH titrations show a 250-fold increase in fluorescence intensity within the pH range of 4.2 to 8.3 with a pK(a) value of 6.63 which is valuable for studying many of the biological organelles.     

Short New Route to the Chiral Spiro‐Tetrahydrofuran Subunit Common to Some Terpenoids

Synthetic strategy based on a stereoselective iodoetherification reaction of a carvone‐derived hydroxyalkene unit has been developed for the asymmetric synthesis of the key spiro‐tetrahydrofuran subunit common to some naturally occurring terpenoids.