$$\omega $$ -Fibered Formations and Fitting Classes of Finite Groups

In this paper, we suggest a new functional approach to the study of group classes which enables us to describe all formations and Fitting classes of finite groups in the language of functions. The notions of -fibered formation and of -fibered Fitting class with direction are introduced. A direction is defined as a mapping of the set of all primes into the set of all nonempty Fitting formations. The existence of infinitely many mappings of this kind makes it possible to construct new forms of formations and Fitting classes for a given nonempty set . In particular, an -local formation is an -fibered formation with a direction such that for any prime p. In the paper we study some basic properties of -fibered formations and of -fibered Fitting classes with direction and obtain the structure of their minimal satellites for a given .     

Influence of the [2.1.1]-(2,6)-pyridinophane macrocycle ring size constraint on the structure and reactivity of copper complexes

The macrocycle [2.1.1]-(2,6)-pyridinophane (L) binds to CuCl to give a monomeric molecule with tridentate binding of the ligand but in a distorted tetrahedral "3 + 1" geometry, where one nitrogen forms a longer (by 0.12 A) bond to Cu. In dichloromethane solvent this pyridine donor undergoes facile site exchange with a second pyridine in the macrocycle, to give time-averaged mirror symmetry. Both experimental and density functional theory studies of the product of chloride abstraction, using NaBAr(F)(4) in CH(2)Cl(2), show that the Cu(+) binds in a trigonal pyramidal, not planar, arrangement in LCu(+). This illustrates the ability of macrocyclic ligand constraint to impose an electronically unfavorable geometry on 3-coordinate Cu(I). LCuBAr(F)(4) and a triflate analogue LCu(I)(OTf) readily react with oxygen in dichloromethane to produce, in the latter case, a hydroxo-bridged dimer [LCu(II)(micro-OH)](2)(OTf)(2), of the intact (unoxidized) ligand L. Since the analogous LCuCl does not react as fast with O(2) in CH(2)Cl(2), outer-sphere electron transfer is concluded to be ineffective for oxidation of cuprous ion here.     

Design of crystal packings of styrylheterocycles and [2+2] photocycloaddition reactions in their single crystals 7. Crystal structures of 4-styrylpyridine hydroperchlorates and solid-state [2+2] autophotocycloaddition reactions of these compounds

A series of 4-styrylpyridine hydroperchlorates were synthesized, and the [2+2] autophotocycloaddition (PCA) reaction in their polycrystalline films and single crystals resulting in the centrosymmetric rctt isomers of 1,2,3,4-tetrasubstituted cyclobutanes was investigated. Unlike neutral styrylpyridines, their protonated forms are better preorganized for the solid-state PCA reaction. According to the X-ray diffraction data, the cations of these compounds, like related styryl dyes, are mainly stacked in crystals in a head-to-head or head-to-tail fashion with equal probability. Only in the latter type of stacks, the PCA reaction is feasible as a single-crystal-to-single-crystal transformation. The crystal packing is stabilized by hydrogen bonds between organic cations and perchlorate anions, as well as by other weak directional interactions, for example, by S??S interactions, thus preventing the atomic displacements in the course of PCA. The completion of the PCA reaction in single crystals without their degradation was observed only for 15-crown-5-containing 4-styrylpyridine hydroperchlorate. The crystals of the latter compound are stabilized not by hydrogen bonds between the cations and anions but by N⁺-H??O(macrocycle) hydrogen bonds resulting in the formation of head-to-tail stacked dimers. In the crystals, these dimers are surrounded by a soft shell formed by rotationally and translationally mobile anions and benzene solvent molecules, as well as by conformationally flexible crown-ether moieties of adjacent dimer pairs. This leads to a decrease in the steric strain that occurs in the crystals in the course of PCA and prevents the degradation of single crystals. The PCA reaction is accompanied by the reduction in the crystal symmetry due to the doubling of the unit cell.     

Synthesis, structure, and properties of supramolecular charge-transfer complexes between bis(18-crown-6)stilbene and ammonioalkyl derivatives of 4,4'-bipyridine and 2,7-diazapyrene

4,4'-Bipyridine and 2,7-diazapyrene derivatives (A) having two ammonioalkyl N-substituents were synthesized. The complex formation of these compounds with bis(18-crown-6)stilbene (D) was studied by spectrophotometry, cyclic voltammetry, (1)H NMR spectroscopy, and X-ray diffraction analysis. In MeCN, π-donor D and π-acceptors A form supramolecular 1:1 (D·A) and 2:1 (D·A·D) charge-transfer complexes. The D·A complexes have a pseudocyclic structure as a result of ditopic binding of the ammonium groups to the crown-ether fragments. The better the geometric matching between the components, the higher the stability of the D·A complexes (log K up to 9.39). A key driving force of the D·A·D complex formation is the excessive steric strain in the precursor D·A complexes. The pseudocyclic D·A complexes involving the ammoniopropyl derivative of 4,4'-bipyridine were obtained as single crystals. Crystallization of the related ammonioethyl derivative was accompanied by transition of the D·A complexes to a structure of the (D·A)(m) coordination polymer type.     

Bidirectional transfer of phenyl and methyl groups between Pt(IV) and boron in platinum dipyridylborato complexes

In the presence of weakly Lewis basic DMSO methyl group migration between B and PtIV in dipyridylborato trihydrocarbyl PtIV complexes is reversible; the preferred direction of Ph group migration in THF solution is from PtIV to B.     

Stoichiometric aerobic PtII-Me bond cleavage in aqueous solutions to produce methanol and a PtII(OH) complex

Di(2-pyridyl)methanesulfonate ligand allows for facile aerobic oxidation of a PtIIMe complex into PtIVMe(OH)2 species and clean C-O reductive elimination of methanol from the latter in either acidic or basic aqueous solutions.     

Benzoaza-15-crown-5 ethers: synthesis,structure, and complex formation with metal and ethylammonium ions

Benzoaza-15-crown-5 ethers containing one or two nitrogen atoms in different positions of the macrocycle and bearing different substituents at these atoms were synthesized. The structures of azacrown ethers and their metal complexes were studied by X-ray diffraction. The stability constants of the complexes of azacrown ethers with Na⁺, Ca²⁺, Ba²⁺, Ag⁺, Pb²⁺, and EtNH₃ ⁺ ions were determined by ¹H NMR titration in MeCN-d₃. In free benzoazacrown ethers containing secondary nitrogen atoms bound to the benzene ring, as well as in N-acetyl derivatives, the N atoms are sp²-hybridized and have a planar geometry. The nitrogen lone pairs on the p orbitals are efficiently conjugated to the benzene ring or the carbonyl fragment of the acetyl group, which is unfavorable for the complex formation. In addition, the formation of complexes with benzoazacrown ethers containing secondary nitrogen atoms is hindered because the hydrogen atoms of the NH groups are directed to the center of the macrocyclic cavity. In benzoazacrown ethers bearing N-alkyl substituents or secondary nitrogen atoms distant from the benzene ring, the N atoms show a substantial contribution of the sp³-hybridized state and have a pronounced pyramidal configuration, which promotes the complex formation. The lead and calcium cations form the most stable complexes due to the high affinity of Pb²⁺ ions for O,N-containing ligands, a high charge density on these ions, and the better correspondence of the cavity size of the 15-membered macrocycles to the diameter of the Ca²⁺ ion. An increase in the stability of the complexes is observed mainly in going from monoazacrown ethers to diazacrown ethers containing identical substituents at the N atoms and in the following series of substituents: C(O)Me < H < Me < CH₂CO₂Et. In the case of the CH₂CO₂Et substituents, the carbonyl oxygen atom is also involved in the coordination to the cation. The characteristic features of the complexing ability of N-alkylbenzomonoaza-15-crown-5 ethers bearing the nitrogen atom conjugated to the benzene ring show that macro-cyclic ligands having this structure are promising as selective and efficient complexing agents for metal cations.     

Design of crystal packings of styrylheterocycles and [2+2] photocycloaddition reactions in their single crystals 6. Synthesis and crystal packings of neutral crown-containing and model styrylheterocycles

Neutral crown-containing and model styrylheterocycles of the 4-pyridine, 4-quinoline, and 9-acridine series were synthesized under acidic catalysis. The influence of the molecular geometry of these compounds, as well as of related styrylheterocycles of the 2-benzothiazole and benzobisthiazole series, on the formation of a particular crystal packing was investigated based on X-ray diffraction data. An extension of the conjugation system in the molecules can result in the sandwich-herringbone packing motif as the only one of the three packing motifs most typical of this class of compounds. This packing provides the preorganization of the structural units for the [2+2] photocycloaddition reaction. The styrylheterocycle containing the bulky 9-acridine moiety is nonplanar due to strong intramolecular steric interactions. The packing motifs formed by nonplanar molecules do not provide the preorganization of the molecules for the [2+2] photocycloaddition. The introduction of the crown ether moiety into the benzene ring of the styrylheterocycle can decrease the predictability of the packing motif as a result of the inclusion of solvent molecules capable of hydrogen bonding with the heteroatoms of the macrocycle in the crystal structure.