γ-sets and other singular sets of real numbers

A family of $\text{J}$ of open subsets of the real line is called an ω-cover of a set X iff every finite subset of X is contained in an element of $\text{J}$. A set of reals X is a γ-set iff for every ω-cover $\text{J}$ of X there exists $\text{〈D}{}_{\mathrm{n}}\text{: n < ω〉?}\text{J}{}^{\mathrm{\omega }}$ such that

In this paper we show that assuming Martin's axiom there is a γ-set X of cardinality the continuum.     

Macrocycles in the construction of acyclic stereochemistry

The conformations of macrocyclic intermediates provide a useful medium through which distant chiral centers may control chemical reactions. In this paper, we show that macrocycles made by cyclization of simple acyclic starting materials with an auxiliary spacer may be used to prepare stereochemically complex acyclic products.     

Raman spectrocopic studies on the vibrational relaxation of CH3CN in different environments

Comparison of the frequencies and half-widths of v₁ in a variety of solvents shows that dispersion forces make a significant contribution to the effective intermolecular potential. Measurements of τ_v^?1 and [ω²] in the CH₃CN/CD₃OD/CCl₄ system demonstrates that long-range (hydrogen-bonding?) potentials significantly affect the relaxation rate.     

Incoherent tunnelling of positive muons and trapping by vacancies in electron-irradiated aluminium

We have measured the transverse spin relaxation of positive muons ⁺ in Al single crystals after irradiation at 150 K with 3 MeV electrons. The relaxation functions agree with those expected for diffusion-limited trapping of the ⁺ in monovacancies. Between 215 K and 60 K the ⁺ diffusivity is well described by the Flynn-Stoneham law (multi-phonon incoherent tunnelling between ground states) with an activation enthalpyH _a = (30±2) meV. At lower temperatures, few-phonon (in particular one-phonon) processes become important. The decrease of the vacancy concentration by a factor of 100 during annealing between 227 K and 267 K has been studied.     

Reaction of nitric oxide at the beta-carbon of enamines. A new method of preparing compounds containing the diazeniumdiolate functional group

The reaction of nitric oxide (NO) with enamines has been investigated. Unlike previously reported reactions of NO as a free radical with alkenes, the electrophilic addition of NO to the beta-carbon of enamines results in the formation of compounds containing the diazeniumdiolate functional group (-[N(O)NO](-)). This reaction between NO and enamines has been shown to be quite general and a variety of enamine-derived diazeniumdiolates have been isolated and characterized. While enamines derived from aldehydes and ketones whose structures allow for sequential multiple electrophilic additions tended to undergo overreaction leading to unstable products, it has been shown that this complication may be overcome by suitable choice of reaction solvent. The products obtained may exist as zwitterionic iminium salts or as neutral species depending upon the structure of the parent enamine. The diazeniumdiolate derived from 1-(N-morpholino)cyclohexene is unique among the new compounds in that it spontaneously releases NO upon dissolution in buffered aqueous solution at pH 7.4 and 37 degrees C. While the total quantity of NO released by this material (ca. 7% of the theoretical 2 moles) is apparently limited by a competing reaction in which it hydrolyzes to an alpha-diazeniumdiolated carbonyl compound and the parent amine, this feature may prove to be of great value in the development of multiaction pharmaceuticals based upon this new type of NO-releasing compound. Reports of enzymatic (oxidative) release of NO from previously known carbon-bound diazeniumdiolates also suggest that analogues of these compounds may be useful as pharmaceutical agents. This new method of introducing the relatively rarely studied diazeniumdiolate functional group into organic compounds should lead to further research into its chemical and biological properties.     

Bis(m-phenylene)-32-crown-10-based cryptands, powerful hosts for paraquat derivatives

Four new bis(m-phenylene)-32-crown-10-based cryptands with different third bridges were prepared. Their complexes with paraquat derivatives were studied by proton NMR spectroscopy, mass spectrometry, and X-ray analysis. It was found that these cryptands bind paraquat derivatives very strongly. Specifically, a diester cryptand with a pyridyl nitrogen atom located at a site occupied by either water or a PF(6) anion in analogous complexes exhibited the highest association constant K(a) = 5.0 x 10(6) M(-1) in acetone with paraquat, 9000 times greater than the crown ether system. X-ray structures of this and analogous complexes demonstrate that improved complexation with this host is a consequence of preorganization, adequate ring size for occupation by the guest, and the proper location of the pyridyl N-atom for binding to the beta-pyridinium hydrogens of the paraquat guests. This readily accessible cryptand is one of the most powerful hosts reported for paraquats.     

Structural properties of ultra-small thorium and uranium dioxide nanoparticles embedded in a covalent organic framework

We report the structural properties of ultra-small ThO₂ and UO₂ nanoparticles (NPs), which were synthesized without strong binding surface ligands by employing a covalent organic framework (COF-5) as an inert template. The resultant NPs were used to observe how structural properties are affected by decreasing grain size within bulk actinide oxides, which has implications for understanding the behavior of nuclear fuel materials. Through a comprehensive characterization strategy, we gain insight regarding how structure at the NP surface differs from the interior. Characterization using electron microscopy and small-angle X-ray scattering indicates that growth of the ThO₂ and UO₂ NPs was confined by the pores of the COF template, resulting in sub-3 nm particles. X-ray absorption fine structure spectroscopy results indicate that the NPs are best described as ThO₂ and UO₂ materials with unpassivated surfaces. The surface layers of these particles compensate for high surface energy by exhibiting a broader distribution of Th–O and U–O bond distances despite retaining average bond lengths that are characteristic of bulk ThO₂ and UO₂. The combined synthesis and physical characterization efforts provide a detailed picture of actinide oxide structure at the nanoscale, which remains highly underexplored compared to transition metal counterparts.

ThO₂ and UO₂ nanoparticles synthesized using a COF-5 template exhibit unpassivated surfaces and provide insight into nanoscale properties of actinides.     

Rh(II) and Rh(I) two-legged piano-stool complexes: structure,reactivity, and electronic properties

The ligand 1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene, 3, was used to synthesize a mononuclear Rh(II) complex [(eta(1):eta(6):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh][PF(6)](2), 6+, in a two-legged piano-stool geometry. The structural and electronic properties of this novel complex including a single-crystal EPR analysis are reported. The complex can be cleanly interconverted with its Rh(I) form, allowing for a comparison of the structural properties and reactivity of both oxidation states. The Rh(I) form 6 reacts with CO, tert-butyl isocyanide, and acetonitrile to form a series of 15-membered mononuclear cyclophanes [(eta(1):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh(CO)(3)][PF(6)] (8), [(eta(1):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh(CNC(CH(3))(3))(2)][PF(6)] (10), and [(eta(1):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh(CO)(CH(3)CN)][PF(6)] (11). The Rh(II) complex 6+ reacts with the same small molecules, but over shorter periods of time, to form the same Rh(I) products. In addition, a model two-legged piano-stool complex [(eta(1):eta(6):eta(1)-1,4-bis[3-(diphenylphosphino)propoxy]-2,3,5,6-tetramethylbenzene)Rh][B(C(6)F(5))(4)], 5, has been synthesized and characterized for comparison purposes. The solid-state structures of complexes 5, 6, 6+, and 11 are reported. Structure data for 5: triclinic; P(-)1; a = 10.1587(7) A; b = 11.5228(8) A; c = 17.2381(12) A; alpha = 96.4379(13) degrees; beta = 91.1870(12) degrees; gamma = 106.1470(13) degrees; Z = 2. 6: triclinic; P(-)1; a = 11.1934(5) A; b = 12.4807(6) A; c = 16.1771(7) A; alpha = 81.935(7) degrees; beta = 89.943(1) degrees; gamma = 78.292(1) degrees; Z = 2. 6+: monoclinic; P2(1)/n; a = 11.9371(18) A; b = 32.401(5) A; c = 12.782(2) A; beta = 102.890(3) degrees; Z = 4. 11: triclinic; P(-)1; a = 13.5476(7) A; b = 13.8306(7) A; c = 14.9948(8) A; alpha = 74.551(1) degrees; beta = 73.895(1) degrees; gamma = 66.046(1) degrees; Z = 2.     

Synthesis and small molecule reactivity of uranium(IV) alkoxide complexes with both bound and pendant N-heterocyclic carbene ligands

The syntheses of two tetravalent uranium alkoxide-carbene complexes are reported, [UIL3], and [UL4] where L = OCMe2CH2[1-C(NCHCHNiPr)]. The latter shows dynamic behaviour of the alkoxycarbene ligands in solution at room temperature, and the crystal structure of [UL4] shows that one carbene group remains uncoordinated. The unbound N-heterocyclic carbene group is trapped by a range of reagents such as 16-valence-electron metal carbonyl fragments and BH3 moieties, forming, for example, [UL3(mu-L)W(CO)5], [UL2(mu-L)2Mo(CO)4], and [UL(n)(L-BH3)(4-n)] (n = 1-4), demonstrating the potential for these hemilabile electropositive metal-carbene complexes to participate in the bifunctional activation of small molecules.     

Bimetallic reactivity. One-site addition two-metal oxidation reaction of dioxygen with a bimetallic dicobalt(II) complex bearing five- and six-coordinate sites

The di-Co(2+) complex, [Co(2+)(mu-OH)(oxapyme)Co(2+)(H(2)O)](+), contains an unsymmetrical binucleating ligand (oxapyme) which provides five- and six-coordinate metal sites when a hydroxide bridge is introduced. This complex absorbs 1 equiv of O(2) irreversibly in solution, producing an unstable di-Co(3+) oxygenated product. The oxygenated product has been studied at low temperatures, where its electronic absorption and (1)H NMR spectra were recorded. It is probable that the oxygenation reaction involves a one-site addition two-metal oxidation reaction to produce an end-on-bonded peroxide ligand at the available coordination site, giving the complex [Co(3+)(mu-OH)(oxapyme)Co(3+)(mu(1)-O(2))](+). Addition of 1 equiv of HClO(4) to this oxygenation product gives a stable peroxide complex, [Co(3+)(mu,eta(1):eta(2)-O(2))(oxapyme)Co(3+)](2+), where one of the oxygen atoms bridges the two metals and is sideways bonded to one of the metals. The formation of this stable complex involves expulsion of the OH(-) bridge. Addition of NO(2)(-) to the sideways-bonded peroxide complex leads to the formation of another stable complex, [Co(3+)(mu,eta(1):eta(1)-O(2))(oxapyme)Co(3+)(NO(2))](+), where the peroxide forms a classic di-end-on bridge to the two metals. Both of these complexes have been fully characterized. Addition of acid to this second stable dioxygen complex leads to the release of HNO(2) and the formation of the mu,eta(1):eta(2) sideways-bonded peroxide complex.