Abelian groups determined by subgroup lattices of direct powers

In this short note, we showthat the class of abelian groups determined by the subgroup lattice of their direct n-powers is exactly the class of the abelian groups which share the n-root property. As applications we answer in the negative a (semi)conjecture of Pálfy and solve a more general problem. Received: 24 February 2005     

[CrF(O2CtBu)2]9: Synthesis and Characterization of a Regular Homometallic Ring with an Odd Number of Metal Centers and Electrons

The first regular homometallic ring containing an odd number of metal centers is reported. The ring was synthesized by means of amine‐templated self‐assembly. Extensive physical characterization studies, including magnetic measurements, powder inelastic neutron scattering (INS), and DFT calculations, show that the molecule has a near perfect match to the expected behavior for a frustrated system with the lowest energy pair of S=1/2 spin states separated by only 0.1 meV (0.8 cm^?1).     

Targeting molecular quantum memory with embedded error correction

The implementation of a quantum computer requires both to protect information from environmental noise and to implement quantum operations efficiently. Achieving this by a fully fault-tolerant platform, in which quantum gates are implemented within quantum-error corrected units, poses stringent requirements on the coherence and control of such hardware. A more feasible architecture could consist of connected memories, that support error-correction by enhancing coherence, and processing units, that ensure fast manipulations. We present here a supramolecular {Cr₇Ni}–Cu system which could form the elementary unit of this platform, where the electronic spin 1/2 of {Cr₇Ni} provides the processor and the naturally isolated nuclear spin 3/2 of the Cu ion is used to encode a logical unit with embedded quantum error-correction. We demonstrate by realistic simulations that microwave pulses allow us to rapidly implement gates on the processor and to swap information between the processor and the quantum memory. By combining the storage into the Cu nuclear spin with quantum error correction, information can be protected for times much longer than the processor coherence.

The implementation of a quantum computer requires protecting of information from noise and the ability to perform quantum gates. We present a molecular architecture providing both these ingredients, via an electronic spin 1/2 processor and a nuclear spin 3/2 memory.     

Synthesis, structure, and dynamic properties of hybrid organic-inorganic rotaxanes

The synthesis and characterization of a series of hybrid organic-inorganic [2]rotaxanes is described. The ring components are heterometallic octa- ([Cr(7)MF(8)(O(2)C(t)Bu)(16)]; M = Co, Ni, Fe, Mn, Cu, Zn, and Cd) nuclear cages in which the metal centers are bridged by fluoride and pivalate ((t)BuCO(2)(-)) anions; the thread components feature dialkylammonium units that template the formation of the heterometallic rings about the axle to form the interlocked structures in up to 92% yield in conventional macrocyclization or one-pot 'stoppering-plus-macrocyclization' strategies. The presence in the reaction mixture of additives (secondary or tertiary amines or quaternary ammonium salts), and the nature of the stoppering groups (3,5-(t)Bu(2)C(6)H(3)CO(2)- or (t)BuCONH-), can have a significant effect on the rotaxane yield. The X-ray crystal structures of 11 different [2]rotaxanes, a pseudorotaxane, and a two-station molecular shuttle show two distinct types of intercomponent hydrogen bond motifs between the ammonium groups of the organic thread and the fluoride groups of the inorganic ring. The different hydrogen bonding motifs account for the very different rates of dynamics observed for the heterometallic ring on the thread (shuttling slow; rotation fast).     

Studies of a molecular hourglass: synthesis and magnetic characterisation of a cyclic dodecanuclear {Cr10Cu2} complex

The synthesis, structure, EPR, and magnetic studies of two dodecanuclear heterometallic cyclic clusters are reported. The compounds have the general formula [R(2)NH(2)](2)[Cr(10)Cu(2)F(14)(O(2)CCMe(3))(22)] (R=Me, 1 or iPr, 2). Both structures contain an array of metal centers which describe an approximate "hourglass", with an ammonium cation in the center of each half of the figure. The chromium sites are all six-coordinate, with the two copper sites five-coordinate. The majority of metal-metal edges are bridged by a single fluoride and two pivalate ligands, while two Cr--Cu edges are bridged by a single fluoride and a single pivalate. Magnetic studies show that 1 and 2 exhibit similar (but not identical) behavior, which can be attributed to ten antiferromagnetic and two ferromagnetic exchange interactions around the ring which gives an S=0 ground state. Quantum Monte Carlo calculations have been used to quantify the exchange interactions by successfully simulating the susceptibility for the full temperature range and thus clarifying the distinction between 1 and 2. EPR spectroscopy shows signals due to excited states, and a variable-temperature study has provided an estimate of the energy gap between the first excited state (S=1) and second excited state (S=2) for 1 that is consistent with the value obtained using the QMC method.