The three space problem in topological groups

We study compact, countably compact, pseudocompact, and functionally bounded sets in extensions of topological groups. A property P is said to be a three space property if, for every topological group G and a closed invariant subgroup N of G, the fact that both groups N and G/N have P implies that G also has P. It is shown that if all compact (countably compact) subsets of the groups N and G/N are metrizable, then G has the same property. However, the result cannot be extended to pseudocompact subsets, a counterexample exists under p=c. Another example shows that extensions of groups do not preserve the classes of realcompact, Dieudonné complete and μ-spaces: one can find a pseudocompact, non-compact Abelian topological group G and an infinite, closed, realcompact subgroup N of G such that G/N is compact and all functionally bounded subsets of N are finite. Several examples given in the article destroy a number of tempting conjectures about extensions of topological groups.     

Bounded sets in topological groups and embeddings

We show that the existence of a non-metrizable compact subspace of a topological group G often implies that G contains an uncountable supersequence (a copy of the one-point compactification of an uncountable discrete space). The existence of uncountable supersequences in a topological group has a strong impact on bounded subsets of the group. For example, if a topological group G contains an uncountable supersequence and K is a closed bounded subset of G which does not contain uncountable supersequences, then any subset A of K is bounded in G?(K?A). We also show that every precompact Abelian topological group H can be embedded as a closed subgroup into a precompact Abelian topological group G such that H is bounded in G and all bounded subsets of the quotient group G/H are finite. This complements Ursul's result on closed embeddings of precompact groups to pseudocompact groups.     

On the effect of montmorillonite in the curing reaction of epoxy nanocomposites

The procedure for the fabrication of epoxy-based polymer layered silicate nanocomposites is important in respect of the nanostructure that is developed. To further our understanding of this, the influence of an organically modified clay (montmorillonite, MMT) on the curing kinetics of an epoxy resin has been studied by differential scanning calorimetry. Clay loadings of 10 and 20 mass% are used, and isothermal as well as dynamic cures have been investigated. For both cure schedules the effect of the MMT is to advance the reaction. Kinetic analysis yields values for the activation energy, but shows that the reaction cannot be described simply by the usual autocatalytic equation. The glass transition of the cured nanocomposites is lower than that for the cured neat resin, a result that is attributed to homopolymerisation taking place in addition to the epoxy–amine reaction.     

Multivariate resolution of NMR labile signals by means of hard- and soft-modelling methods

One of the difficulties frequently encountered when studying acid–base equilibria with NMR spectroscopy is the labile behaviour of the measured signal, which hinders the application of bilinear multivariate data analysis methods. In this work, a mathematical transformation is proposed for the conversion of NMR labile signals to inert signals, which make possible the application of multivariate data analysis methods, based on bilinear data models. The procedure has been applied to the analysis of NMR data corresponding to the acid–base equilibria of nucleotides dCMP and dGMP. Both hard-modelling (EQUISPEC) and soft-modelling (MCR-ALS) approaches have been applied for the analysis and resolution of transformed bilinear NMR data matrices.     

Syntheses and Structural Aspects of Cyclodextrin/Dialkylamine Inclusion Compounds

We report the syntheses and structural aspects of cyclodextrin host–guest inclusion compounds containing linear secondary alkylamines (dipropyl, dibutyl, dipentyl, dihexyl, and dioctyl) at 25 °C. Elemental analysis, ¹³C CP-MAS NMR spectroscopy, and powder X-ray diffraction analysis confirm the inclusion process. The basic host structure of the products is similar to that of typical cyclodextrin inclusion systems. ¹³C MAS NMR experiments show a different resonance pattern for the confined guest molecules with respect to the amine in the liquid phase. The presence of different resonance signals for the homologous carbon atoms of both dialkylamine branches is evidence for the non-symmetric location of the amine in the cyclodextrin channels.     

Weak intramolecular proton-hydride and proton-fluoride interactions: experimental (NMR, X-ray) and DFT studies of the bis(NBH(3)) and bis(NBF(3)) adducts of 1,3-dimethyl-1,3-diazolidine

Bis(NBH(3)), bis(NBF(3)), and NBF(3)/NBH(3) adducts 1-3 were prepared from 1,3-dimethyl-1,3-diazolidine and characterized by the (1)H, (13)C, (11)B, (19)F, 2D (1)H(-13)C HETCOR and NOESY NMR spectra. The structures and conformations of the adducts were established by the variable-temperature (1)H NMR spectra, the X-ray diffraction method (adduct 2A), and density functional calculations at different theoretical levels. The experimental and theoretical data have revealed that bis adducts 1-3 prefer trans orientations of the borane groups (1A, 2A, 3A) in solution, the solid state, and the gas phase. The studies have shown that the energetic preference of trans adducts with respect to cis compounds, decreasing as 2A (2.9 kcal/mol) > 3A (2.7 kcal/mol) > 1A (1.4 kcal/mol), is dictated by spatially repulsive interactions between the CH(3), BH(3), and BF(3) groups. The results of DFT calculations agree well with an experimental trans/cis isomeric ratio of 9:1 determined in solutions of adduct 1. The calculated geometry and energy, as well as the topological analysis of electronic densities, show that trans adducts 1-3 should exist in gas phase as twist conformations T-2 stabilized by the intramolecular C-H(delta+)...(-delta)H-B or C-H(delta+)...(-delta)F-B interactions. These interactions are characterized as closed-shell. The energy of one proton-hydride and proton-fluoride intramolecular contact, estimated as 1.9 (1A-T-2) and 0.7 (2A-T-2) kcal/mol, respectively, classifies the "elongated" intramolecular interactions CH(delta+)...(-delta)HB and CH(delta+)...(-delta)FB as weak ones. It has been established that, on going from gas phase to a condensed phase (solution and solid), the twist-conformations T-2 transform to conformations T-1, probably by intermolecular dipole-dipole interactions. The data presented in this work show that despite a weakness of the "elongated" proton-hydride and proton-fluoride interactions, they can play a significant role in the stabilization of conformational molecular states, especially when cooperativity is in action.     

Crystal structure oftrans-ethyl(1,5,6-trimethylbenzimidazole)-bis(dimethylglyoximato)cobalt(III). Relationships between structural and spectroscopic properties in compounds of the general formulae [Co(dmgH)2(R)(1,5,6-Me3Bzm)]

Summary The synthesis and x-ray crystal structure oftrans-[Co(dmgH)₂(Et)(1,5,6-Me₃Bzm)] where dmgH=dimethylglyoximate(–1), and 1,5,6-Me₃Bzm=1,5,6-trimethylbenzimidazole, is reported. The compound C₁₉H₂₆N₆O₄Co is monoclinic, space group P2₁/n;a=11.700(4);b=24.205(6);c=8.500(3) Å and =101.63(3)°. D(calcd) 1.299 g cm^–3; Z=4 and R=0.066 for 2359 independent reflections. Comparison of Co-N(axial ligand) bond lengths for compounds of general formulaetrans-[Co(dmgH)₂(R)(L)], with L=pyridine or 1,5,6-trimethylbenzimidazole and R=CH(CN)Cl, CH₂NO₂, Me, Et,i-Pr, cyclo-hexyl or adamantyl is made. The Co–N(1,5,6-Me₃Bzm) bond lengths of the trimethylbenzimidazole derivatives show a fairly linear relationship with the electronic parameter of the axial R group, derived from the¹³C-n.m.r. spectra of their pyridine analogues. The influence of steric effects on the properties of these Co^III compounds is discussed.     

Synthesis,Spectroscopic and EPR Results and Crystal Structure of Copper(II) Formato Derivatives with Pyrazine and Dimethylpyrazines

The complexes of copper formato with pyrazine and dimethylpyrazines: Cu(HCOO)₂(pyrz) ( 1 ), Cu₂(HCOO)₄(pyrz) ( 2 ), Cu₂(HCOO)₄(2,3‐Me₂pyrz) ( 3 ), Cu₂(HCOO)₄(2,5‐Me₂pyrz) ( 4 ), and Cu₂(HCOO)₄(2,6‐Me₂pyrz)₂ ( 5 ) have been synthesized and characterized by chemical analysis and IR and electronic spectro scopies. The three‐dimensional structure of compound 1 consists of –Cu–pyrz–Cu–pyrz– chains joined by bridging formate groups coordinated, in configuration syn‐anti, to two copper atoms. The coordination around the copper atom is orthorhombic with two Cu–O distances of 2.374(1) Å, two Cu–O of 1.952 Å and two Cu–N of 2.080 Å. Compound 5 is formed by molecular dimers with the [Cu₂(μ‐HCOO)₄] unit, two copper atoms and four syn‐syn fomate groups, and two ligands coordinated to the copper atoms in the axial positions. In compounds 2 and 3 chains of [Cu₂(μ‐HCOO)₄] dimers with pyrz or 2,3‐Me₂pyrz as bridging ligands are formed. The EPR signal of 1 is orthorhombic (g = 2.23, 2.20 and 2.06). In the EPR spectra of 2 – 5 compounds the triplet (S = 1) signals are observed. The g_?, g_∥ and D values are been calculated.     

Synthesis and Characterization of Heterodinuclear IrCo, RuCo, IrNi, and RuNi Complexes Containing Pyrazolate and Pyrazolylborate Ligands

Treatment of the metallo ligands [ML(pz)(2)(Hpz)] (pz = pyrazolate; L = C(5)Me(5), M = Ir (1); L = mesitylene, M = Ru (3)) with [M'Cl{HB(3-i-Pr-4-Br-pz)(3)}] (M' = Co (4), Ni (5)) yields heterodinuclear complexes of formula [LM(&mgr;-pz)(2)(&mgr;-Cl)M'{HB(3-i-Pr-4-Br-pz)(3)}] (L = C(5)Me(5); M = Ir; M' = Co (6), Ni (7). L = mesitylene; M = Ru; M' = Co (8)). The related complex [Ru(eta(6)-p-cymene)(pz)(2)(Hpz)] (2) reacts with equimolar amounts of 4 or 5 to give mixtures of the corresponding bis(&mgr;-pyrazolato) &mgr;-chloro complexes [(eta(6)-p-cymene)Ru(&mgr;-pz)(2)(&mgr;-Cl)M'{HB(3-i-Pr-4-Br-pz)(3)}] (M' = Co (9), Ni (10)) and the triply pyrazolato-bridged complexes [(eta(6)-p-cymene)Ru(&mgr;-pz)(3)M'{HB(3-i-Pr-4-Br-pz)(3)}] (M' = Co (11), Ni (12)). Complex 1 reacts with 5 in the presence of KOH to give the IrNi complex [(eta(5)-C(5)Me(5))Ir(&mgr;-pz)(3)Ni{HB(3-i-Pr-4-Br-pz)(3)}] (13) whereas its reaction with 4 and KOH rendered the bis(&mgr;-pyrazolato) &mgr;-hydroxo complex [(eta(5)-C(5)Me(5))Ir(&mgr;-pz)(2)(&mgr;-OH)Co{HB(3-i-Pr-4-Br-pz)(3)}] (14). The molecular structure of the heterobridged IrCo complex (6) and those of the homobridged RuNi (12) and IrNi (13) complexes have been determined by X-ray analyses. Compound 6 crystallizes in the monoclinic space group P2(1)/n, with a = 10.146(5) ?, b = 18.435(4) ?, c = 22.187(13) ?, beta = 97.28(4) degrees, and Z = 4. Complex 12 is monoclinic, space group P2(1), with a = 10.1169(7) ?, b = 21.692(2) ?, c = 11.419(1) ?, beta = 112.179(7) degrees, and Z = 2. Compound 13 crystallizes in the monoclinic space group Cc, with a = 13.695(2) ?, b = 27.929(6) ?, c = 13.329(2) ?, beta = 94.11(4) degrees, and Z = 4. All the neutral complexes 6, 12, and 13 consist of linear M.M'.B backbones with two (6) or three (12, 13) pyrazolate ligands bridging the dimetallic M.M' units and three substituted 3-i-Pr-4-Br-pz groups joining M' to the boron atoms. The presence in the proximity of the first-row metal M' of the three space-demanding isopropyl substituents of the pyrazolate groups induces a significant trigonal distortion of the octahedral symmetry, yielding clearly different M'-N bond distances on both sides of the ideal octahedral coordination sphere of these metals.     

Advantages of the Ns group in the reactions of N-SO2R inosines with benzylamine and with NH3

The reactivity of N¹-alkylsulfonyl- and N¹-arylsulfonyl-2′,3′,5′-tri-O-acetylinosine with benzylamine and with ¹⁵NH₃, regarding the attack on C2, has been shown to be in the order CF₃SO₂ (Tf) > 2,4-(NO₂)₂C₆H₃SO₂ (DNs) ? 4-NO₂C₆H₄SO₂ (pNs) ≈ C₆F₅SO₂ (PFBs) > 2-NO₂C₆H₄SO₂ (Ns) ? CH₃SO₂ (Ms) > 4-CH₃C₆H₄SO₂ (Ts) > 2,4,6-(CH₃)₃C₆H₂SO₂ (Mts). In spite of its intermediate reactivity, the Ns group is the most appropriate, since in this case the formation of by-products is minimised during the ring-opening and ring-closing steps of the process. Another advantage of the Ns group is thus disclosed.