High‐Frequency Fe–H Vibrations in a Bridging Hydride Complex Characterized by NRVS and DFT

High‐spin iron species with bridging hydrides have been detected in species trapped during nitrogenase catalysis, but there are few general methods of evaluating Fe?H bonds in high‐spin multinuclear iron systems. An ⁵⁷Fe nuclear resonance vibrational spectroscopy (NRVS) study on an Fe(μ‐H)₂Fe model complex reveals Fe?H stretching vibrations for bridging hydrides at frequencies greater than 1200 cm^?1. These isotope‐sensitive vibrational bands are not evident in infrared (IR) spectra, showing the power of NRVS for identifying hydrides in this high‐spin iron system. Complementary density functional theory (DFT) calculations elucidate the normal modes of the rhomboidal iron hydride core.     

Oxidative skeletal rearrangement of bicyclo[4.2.2]deca-2,4,7,9-tetraenes to bicyclo[4.3.1]deca-2,4,8-triene-7,10-diols and study of the antitumor activity of the products in vitro

Bicyclo[4.3.1]deca-2,4,8-triene-7,10-diols were synthesized in 76–85% yields by oxidative skeletal isomerization of the substituted bicyclo[4.2.2]deca-2,4,7,9-tetraenes of various structures on treatment with m-chloroperbenzoic acid. The structures of the obtained bicyclic unsaturated diols were reliably proven by modern spectral methods and X-ray diffraction. A high antitumor activity in vitro was found for bicyclo[4.3.1]deca-2,4,8-triene-7,10-diols against the Jurkat, K562, U937 and HL-60 tumor cell lines.     

Transformations of 5-(2-arylethynyl)-2-methyl-2H-tetrazoles under superelectrophilic activation

Reaction of 5-arylethynyl-2-methyl-2H-tetrazoles (acetylene tetrazoles) with arenes under the action of Brønsted superacid CF₃SO₃H or acidic zeolite HUSY CBV-720 gives rise to E-/Z-5-(2,2-diarylethenyl)-2-methyl-2H-tetrazoles, as products of hydroarylation of acetylene bond, in yields up to 98% with predominant formation of E-isomers. Cationic intermediates of these reactions have been studied theoretically by DFT calculations. Addition of CF₃SO₃H to the triple bond of acetylene tetrazoles leads to the corresponding E-/Z-vinyl triflates in high yields. Hydration of triple bond in these tetrazoles in H₂SO₄ results in the formation of 5-(2-aryl-2-oxoethyl)-2-methyl-2H-tetrazoles. Tandem hydroarylation-ionic hydrogenation of acetylene tetrazoles in the systems acid(CF₃SO₃H or AlCl₃)-arene-cyclohexane affords 5-(2,2-diarylethyl)-2-methyl-2H-tetrazoles.     

Split Orthogonal Arrays and Maximum Independent Resilient Systems of Functions

A system of (Boolean) functions in variables is called randomized if the functions preserve the property of their variables to be independent and uniformly distributed random variables. Such a system is referred to as -resilient if for any substitution of constants for any variables, where 0 i t, the derived system of functions in variables will be also randomized. We investigate the problem of finding the maximum number of functions in variables of which any form a -resilient system. This problem is reduced to the minimization of the size of certain combinatorial designs, which we call split orthogonal arrays. We extend some results of design and coding theory, in particular, a duality in bounding the optimal sizes of codes and designs, in order to obtain upper and lower bounds on . In some cases, these bounds turn out to be very tight. In particular, for some infinite subsequences of integers they allow us to prove that , , , , . We also find a connection of the problem considered with the construction of unequal-error-protection codes and superimposed codes for multiple access in the Hamming channel.     

Convergence of the Poincaré series for some classical Schottky groups

The Poincaré -series for a multiply connected circular region can be either convergent or divergent absolutely. In this paper we prove a uniform convergence result for such a region.

     

Thek-partitioning problem

Thek-partitioning problem is defined as follows: Given a set of items {I ₁,I ₂,...,I _n} where itemIj is of weightwj 0, find a partitionS ₁,S ₂,...,S _m of this set with ¦S _i ¦ =k such that the maximum weight of all subsetsS _i is minimal,k-partitioning is strongly related to the classical multiprocessor scheduling problem of minimizing the makespan on identical machines. This paper provides suitable tools for the construction of algorithms which solve exactly the problem. Several approximation algorithms are presented for this NP-hard problem. The worst-case behavior of the algorithms is analyzed. The best of these algorithms achieves a performance bound of 4/3.     

Inequalities for Volumes of Simplices in Terms of Their Faces

By generalizing some well-known results, we first obtain an inequality involving the volume and product of s-contents of s-faces of an n-simplex. Using this we generalize two inequalities maximizing the volume of one or two simplices in terms of their edge lengths.     

Probing alkali coordination environments in alkali borate glasses by multinuclear magnetic resonance

Five series of binary alkali borate glasses were prepared to compare the alkali dependence of network and modifier short-range order. ¹¹B magic-angle spinning (MAS) NMR reveals that the fraction of four-coordinate boron depends strongly upon alkali type at high-alkali concentrations: heavier alkalis favour the formation of non-bridging oxygens, whereas lithium borates contain a much higher concentration of tetrahedral boron units. The alkali modifiers were observed directly by MAS NMR to measure the change in chemical shift with composition. All alkali peaks shift to higher frequency with increasing loading, indicative of decreasing average coordination numbers. Relative to their known chemical shift ranges, the heavier alkalis exhibit the greatest shifts, whereas the lithium shifts are subtle. This is interpreted in terms of the availability of charged and partially charged coordinating oxygens in the network. Moreover, the ¹³³Cs chemical shifts plateau at 40 mol%, implying that the Cs⁺ coordination number reaches a lower limit at this composition. This work demonstrates that NMR instrumentation and methodology have reached a level where even challenging nuclei like ³⁹K and ⁸⁷Rb can be probed to yield structural information in glasses.     

Synthesis and X-ray structural analysis of (2<Emphasis Type="Italic">Z</Emphasis>)-3(4-hydroxyphenyl)-2-pyridin-4-ylacrylonitrile and (2<Emphasis Type="Italic">Z</Emphasis>)-3-(3,5-di-<Emphasis Type="Italic">tert</Emphasis>-butyl-4-hydroxyphenyl)2-pyridin-4-ylacrylonitrile

Synthesis and X-ray structural investigations have been carried out for the two title compounds C₁₄H₁₀N₂O (3a) and C₂₂H₂₆N₂O (3b). Compound 3a crystallizes in the monoclinic space group P2₁/c, with a = 3.843(1) Å, b = 24.618(5) Å, c = 11.318(2) Å, = 92.61(3), V = 1069.7(4) Å,³ and Z = 4. Compound 3b crystallizes in the triclinic space group P-1, with a = 9.004(2) Å, b = 9.447(2) Å, c = 11.713(2) Å, = 76.70(3), = 83.12(3), = 82.16(3), V = 956.5(3) Å,³ and Z = 2. Both stilbazole derivatives have Z-geometry about the ethylene bridge which links the heterocyclic and aromatic rings. The molecular skeleton of 3a is slightly non-planar: the dihedral angles between the acrylonitrile linkage and the pyridine ring, and between this linkage and the p-hydroxyphenyl ring are 7.2(2) and 4.1(2), respectively. The molecular skeleton of 3b is less planar: the values of similar dihedral angles are 17.0(2) and 20.8(2), respectively. In the crystal of 3a, the molecules are packed in stacks along the a axis with head-to-head orientation. Intermolecular hydrogen bonds O=H s N and C=H s N link molecules into sheets parallel to (100) plane. In the crystals of 3b, the molecules have a head-to-tail orientation and intermolecular hydrogen bonds O=H s N link the molecules into infinite chains along [01-1] direction.