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

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

Photoinduced energy- and electron-transfer from a photoactive coordination cage to bound guests.

In a coordination cage which contains an array of twelve naphthyl chromophores surrounding a central cavity, photoinduced energy or electron-transfer can occur from the chromophore array to the bound guest in supramolecular host/guest complexes

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

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

Binding of chemical warfare agent simulants as guests in a coordination cage: contributions to binding and a fluorescence-based response.

Cubic coordination cages act as competent hosts for several alkyl phosphonates used as chemical warfare agent simulants; a range of cage/guest structures have been determined, contributions to guest binding analysed, and a fluorescent response to guest binding demonstrated

Stimuli-Responsive Reversible Assembly of 2D and 3D Metallosupramolecular Architectures

The discovery of interconvertible platinum coordination modes, which reveals and masks cis coordinating groups upon addition of acid and base, respectively, has been exploited to facilitate stimuli-responsive assembly and disassembly of both two- and three-dimensional metallosupramolecular architectures. Treatment of a binclear platinum complex with acid along with ditopic and tritopic donor ligands generated a molecular square and a trigonal prism, respectively, in good to high yield. These complexes were unambiguously identified using electrospray mass spectrometry, H-1 NMR spectroscopy, and X-ray crystallography. Both assemblies can be disassembled into their constituent parts simply by treatment with base, and the prism can be cycled between the assembled and disassembled states by the alternate addition of acid and base.</p

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

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

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

The self-assembly between a water-soluble bis-bidentate ligand L^18w and Co­(II) salts in water affords three high-spin Co­(II) products: a dinuclear <i>meso</i>-helicate [Co₂(L^18w)₃]­X₄; a tetrahedral cage [Co₄(L^18w)₆]­X₈; and a dodecanuclear truncated-tetrahedral cage [Co₁₂(L^18w)₁₈]­X₂₄ (X = BF₄ or ClO₄). All three products were crystallized under different conditions and structurally characterized. In [Co₂(L^18w)₃]­X₄ 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 Co₄ or Co₁₂ 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>_<b>2</b>, <b>Co</b>_<b>4</b>, and <b>Co</b>_<b>12</b> are in slow equilibrium (hours/days) in aqueous solution, and this can be conveniently monitored by ¹H 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 ¹H NMR signals, which makes identification easy. From temperature- and concentration-dependent ¹H 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, ¹H NMR spectra in a nonaqueous solvent (MeNO₂) show formation of only [Co₂(L^18w)₃]­X₄ 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>_<b>2</b>/<b>Co</b>_<b>4</b>/<b>Co</b>_<b>12</b> system in aqueous solution