Synthesis,Spectral and Magnetic Properties,and Crystal Structures of Copper(II) Pyridinecarboxylate Adducts with N‐Heterocyclic Ligands

Synthesis and characterization of seven new complexes [Cu(2‐MeSnic)₂(CH₃OH)]₂ (where 2‐MeSnic is 2‐methylthionicotinate), [Cu(2‐MeSnic)₂L₂]₂ (where L is pyridine — py, ethylnicotinate — Etnic and butylnicotinate — Bunic), [Cu(2‐MeSnic)₂L₂(H₂O)₂] (where L is py and nicotinamide — nia) and [Cu(2‐MeSnic)₂(N‐Menia)₂(H₂O)₂]·2H₂O (where N‐Menia is N‐methylnicotinamide) are reported. The characterization were based on elemental analysis, infrared, electronic and EPR spectra, and magnetic susceptibility measurements over a temperature range of 1.8 — 300 K or 70 — 300 K. Three complexes of different type were studied by X‐ray analysis. The molecule of [Cu(2‐MeSnic)₂(CH₃OH)]₂ has dimeric paddle‐wheel cage structure with a tetragonal pyramidal arrangement around Cu^II. The dimer results from the fact that carboxyl groups of four 2‐MeSnic anions function as bridging in a syn‐syn arrangement. On the other hand [Cu(2‐MeSnic)₂(py)₂]₂ forms dimers with hexacoordinated Cu^II atoms in highly distorted coordination octahedra, each with two oxygen atoms of bridging carboxyl groups in an anti‐anti arrangement of two 2‐MeSnic anions, with two oxygen atoms of one asymmetrically chelating 2‐MeSnic anion and with two nitrogen atoms of two pyridine ligands. The temperature independent EPR spectrum for this complex exhibits an axial signal which corresponds to almost isolated S = ¹/₂ magnetic ions. Magnetic data for the dimer show a weak antiferromagnetic interaction between the two metal ions with J = —0.65 cm^—1. The Cu^II atom in complex [Cu(2‐MeSnic)₂(py)₂(H₂O)₂] is hexacoordinated in an elongated centrosymmetrical tetragonal‐bipyramidal arrangement (4 + 2). Based on the molecular structure the electronic, infrared, electron paramagnetic resonance spectra and magnetic properties are discussed and stereochemistry as well as the mode of ligand coordination in new solid complexes under study have been determined.     

On the central limit theorem for lacunary trigonometric series

Хорошо известно, что в ероятностное поведе ние лакунарного тригоно метрического ряда {cos 2πn _kx} тесно связ ано с «критическим» у словием лакунарности (*) $$\frac{{n_{k + 1} }}{{n_k }} \geqq 1 + \frac{{c_k }}{{\sqrt k }},c_k \to \infty $$ . Например, если выполн ено условие (*), то последовательность {cos2πn _kx} удовлетворяет центральной предель ной теореме, и при этом условие (*) не может быть ослабле но. Для последовательносте й, удовлетворяющих (*), и звестны и другие результаты по добного рода, в то время как для более медленно расту щих последовательносте й {n_k} не известно, по-видимому, ничего. В с татье развит метод, ко торый при помощи мартингально й техники позволяет проводить исследование систем {cos 2πn_kx} для последовательно стей, не удовлетворяю щих условию (*). Получено про стое объяснение условия (*), изучено, как «пропа-дает» центральная предель ная теорема при посте пенном ослаблении условия (*) и дока-заны некоторые центральн ые предельные теорем ы в отсутствие этого усл овия. Получены другие предельные те оремы для {cos 2πn_kx}, напри мер, закон повторного лог арифма и принципы инвариантн ости.     

Computer-assisted choice of discrete spacers for anionic isotachophoresis separations

In isotachophoresis (ITP), the sample constituents migrate, depending on their concentrations in the loaded sample, either in fully developed zones or in the boundary layers between the zones of constituents of the corresponding effective mobilities. The latter (spike) migration mode is analytically beneficial in selective detections of trace analytes, especially, when appropriately chosen discrete spacers minimize detection interferences due to matrix constituents. To facilitate a search for suitable mixtures of discrete spacers, a two-step calculation procedure was developed in this work. Using a pool of discrete spacers consisting of 42 anionic and zwitterionic constituents, this procedure was shown effective in the anionic ITP separations performed at pH = 6.5-10.0. Besides the predictions of the migration orders, it was helpful in identifying the spacing constituents that could cause resolution problems due to an uncertainty with which pH of the leading electrolyte solution is known. The ionic mobility and pKa data, taken for the spacing constituents from the literature and the ones obtained from the ITP experiments carried out in this work, were used in the calculations performed in a context with the choice of spacers. Although the data obtained from the ITP experiments provided better results, small uncertainties with which they were acquired (attributable to fluctuations in the experimental conditions) set practical limits in the calculation based choice of multi-component mixtures of the spacing constituents.     

Synthese und Charakterisierung von Aquapentachloroplatinaten(IV) – Struktur von [K(18-Krone-6)][PtCl5(H2O)]

Synthesis and Characterization of Aquapentachloroplatinates(IV) – Structure of [K(18-crown-6)][PtCl₅(H₂O)] The crown ether complex of the aquapentachloroplatinic acid of the composition [H₁₃O₆][PtCl₅(H₄O₂)] · 2(18-cr-6) ( 2 ) reacts with K₂CO₃ and [NⁿBu₄]OH in aqueous solution to give [K(18-cr-6)][PtCl₅(H₂O)] ( 5 a ) and [NⁿBu₄][PtCl₅(H₂O)] · ¹/₂ (18-cr-6) · H₂O ( 5 b ), respectively. Both compounds were characterized by microanalysis, vibrational (IR, Raman) and NMR (¹H, ¹³C, ¹⁹⁵Pt) spectroscopy. The X-ray structure analysis of 5 a (orthorhombic, pnma; a = 16,550(4), b = 18,044(3), c = 7,415(1) Å; Z = 4; R1 = 0,0183; wR2 = 0,0414) reveals that the crystal is threaded by chains built up of [PtCl₅(H₂O)]^? and [K(18-cr-6)]⁺ units. There are tight K …? Cl contacts (d(K? Cl1)) = 3,0881(9) Å and O_W? H? O_cr hydrogen bridges (d(O1 …? O2) = 2,806(3) Å) between these units. The coordination polyhedron [PtCl₅O] has approximately C_4v symmetry.     

Expedient and Diastereodivergent Assembly of Terpenoid Decalin Subunits having Quaternary Stereocenters through Organocatalytic Robinson Annulation of Nazarov Reagent

We report an expedient approach to highly functionalized cis‐ and trans‐decalines that could function as key structural subunits toward the synthesis of various classes of terpenoids. Key to the strategy is an organocatalyzed Robinson annulation reaction of the Nazarov reagent that affords chiral enone building blocks with high enantioselectivities. The quaternary carbon stereogenic center can direct the subsequent reactions and allow the rapid and diastereoconvergent assembly of complex decalines with contiguous stereocenters.     

An expansion formula for fractional derivatives of variable order

In this work we extend our previous results and derive an expansion formula for fractional derivatives of variable order. The formula is used to determine fractional derivatives of variable order of two elementary functions. Also we propose a constitutive equation describing a solidifying material and determine the corresponding stress relaxation function.     

Synthesis and Stereochemistry of Some new Derivatives of 1,2-O-Cyclohexylidene-α-D-Xylofuranuronic Acid

Abstract

1,2-O-Cyclohexylidene-α-d-xylofuranuronic acid (2) has been converted into its 3-O-acetyl derivative and consecutively to the corresponding acid chloride and ethyl ester. Direct reaction of 2 with ethanol in the presence of p-to-luene sulphonic acid gave the ethyl ester. Reaction of 2 with phosphorus pentachloride in dry ether gave the acid chloride of 1,2-O-cyclohexylidene-3-O-dichlorophosphoryl–α-d-xylofuranuronic acid. Conformational data have been obtained from ¹H and ¹³C NMR measurements.