153 research outputs found

    Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries

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    The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ symmetries; in particular we focus on the spin-rotational symmetry SU(2) in combination with point-group symmetries. With these methods one is able to block-diagonalize the Hamiltonian and thus to treat spin systems of unprecedented size. In addition it provides a spectroscopic labeling by irreducible representations that is helpful when interpreting transitions induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance (NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the reader with detailed knowledge on how to set up such a diagonalization scheme.Comment: 29 pages, many figure

    Highly efficient catalysis of the Kemp elimination in the cavity of a cubic coordination cage.

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    The hollow cavities of coordination cages can provide an environment for enzyme-like catalytic reactions of small-molecule guests. Here, we report a new example (catalysis of the Kemp elimination reaction of benzisoxazole with hydroxide to form 2-cyanophenolate) in the cavity of a water-soluble M8L12 coordination cage, with two features of particular interest. First, the rate enhancement is among the largest observed to date: at pD 8.5, the value of kcat/kuncat is 2 × 10(5), due to the accumulation of a high concentration of partially desolvated hydroxide ions around the bound guest arising from ion-pairing with the 16+ cage. Second, the catalysis is based on two orthogonal interactions: (1) hydrophobic binding of benzisoxazole in the cavity and (2) polar binding of hydroxide ions to sites on the cage surface, both of which were established by competition experiments

    Mapping the internal recognition surface of an octanuclear coordination cage using guest libraries

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    Size and shape criteria for guest binding inside the cavity of an octanuclear cubic coordination cage in water have been established using a new fluorescence displacement assay to quantify guest binding. For aliphatic cyclic ketones of increasing size (from C5 to C11), there is a linear relationship between ΔG for guest binding and the guest’s surface area: the change in ΔG for binding is 0.3 kJ mol–1 Å–2, corresponding to 5 kJ mol–1 for each additional CH2 group in the guest, in good agreement with expectations based on hydrophobic desolvation. The highest association constant is K = 1.2 × 106 M–1 for cycloundecanone, whose volume is approximately 50% of the cavity volume; for larger C12 and C13 cyclic ketones, the association constant progressively decreases as the guests become too large. For a series of C10 aliphatic ketones differing in shape but not size, ΔG for guest binding showed no correlation with surface area. These guests are close to the volume limit of the cavity (cf. Rebek’s 55% rule), so the association constant is sensitive to shape complementarity, with small changes in guest structure resulting in large changes in binding affinity. The most flexible members of this series (linear aliphatic ketones) did not bind, whereas the more preorganized cyclic ketones all have association constants of 104–105 M–1. A crystal structure of the cage·cycloundecanone complex shows that the guest carbonyl oxygen is directed into a binding pocket defined by a convergent set of CH groups, which act as weak hydrogen-bond donors, and also shows close contacts between the exterior surface of the disc-shaped guest and the interior surface of the pseudospherical cage cavity despite the slight mismatch in shape

    Seeing and believing: Observing desistance-focused practice and enduring values in the National Probation Service

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    This article focuses on the feasibility of using a desistance-focused approach in the National Probation Service (NPS) in the post-Transforming Rehabilitation (TR) context. Findings are drawn from an exploratory study undertaken in one NPS Division, which used triangulation of three data collection methods; observations of one-to-one supervision sessions, documentary analysis and practitioner focus groups. Findings show that practitioners use elements of a desistance-focussed approach, although not exclusively. Values based upon belief in the capacity to change and the need to offer support endure, despite mass organisational upheaval. The article concludes by suggesting that this 'enduring habitus' of probation could be an enabler for a desistance-focused approach but instrumentalism in policy and practice is a significant barrier

    An Interconverting Family of Coordination Cages and a meso-Helicate; Effects of Temperature, Concentration, and Solvent on the Product Distribution of a Self-Assembly Process

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    The self-assembly between a water-soluble bis-bidentate ligand L<sup>18w</sup> and Co­(II) salts in water affords three high-spin Co­(II) products: a dinuclear <i>meso</i>-helicate [Co<sub>2</sub>(L<sup>18w</sup>)<sub>3</sub>]­X<sub>4</sub>; a tetrahedral cage [Co<sub>4</sub>(L<sup>18w</sup>)<sub>6</sub>]­X<sub>8</sub>; and a dodecanuclear truncated-tetrahedral cage [Co<sub>12</sub>(L<sup>18w</sup>)<sub>18</sub>]­X<sub>24</sub> (X = BF<sub>4</sub> or ClO<sub>4</sub>). All three products were crystallized under different conditions and structurally characterized. In [Co<sub>2</sub>(L<sup>18w</sup>)<sub>3</sub>]­X<sub>4</sub> all three bridging ligands span a pair of metal ions; in the two larger products, there is a metal ion at each vertex of the Co<sub>4</sub> or Co<sub>12</sub> polyhedral cage array with a bridging ligand spanning a pair of metal ions along every edge. All three structural types are known: what is unusual here is the presence of all three from the same reaction. The assemblies <b>Co</b><sub><b>2</b></sub>, <b>Co</b><sub><b>4</b></sub>, and <b>Co</b><sub><b>12</b></sub> are in slow equilibrium (hours/days) in aqueous solution, and this can be conveniently monitored by <sup>1</sup>H NMR spectroscopy because (i) the paramagnetism of Co­(II) disperses the signals over a range of ca. 200 ppm and (ii) the different symmetries of the three species give characteristically different numbers of independent <sup>1</sup>H NMR signals, which makes identification easy. From temperature- and concentration-dependent <sup>1</sup>H NMR studies it is clear that increasing temperature and increasing dilution favors fragmentation to give a larger proportion of the smaller assemblies for entropic reasons. High concentrations and low temperature favor the larger assembly despite the unfavorable entropic and electrostatic factors associated with its formation. We suggest that this arises from the hydrophobic effect: reorganization of several smaller complexes into one larger one results in a smaller proportion of the hydrophobic ligand surface being exposed to water, with a larger proportion of the ligand surface protected in the interior of the assembly. In agreement with this, <sup>1</sup>H NMR spectra in a nonaqueous solvent (MeNO<sub>2</sub>) show formation of only [Co<sub>2</sub>(L<sup>18w</sup>)<sub>3</sub>]­X<sub>4</sub> because the driving force for reorganization into larger assemblies is now absent. Thus, we can identify the contributions of temperature, concentration, and solvent on the result of the metal/ligand self-assembly process and have determined the speciation behavior of the <b>Co</b><sub><b>2</b></sub>/<b>Co</b><sub><b>4</b></sub>/<b>Co</b><sub><b>12</b></sub> system in aqueous solution
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