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

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