Cyanido-bridged Fe(III)-Mn(III) heterobimetallic materials built from Mn(III) Schiff base complexes and di- or tri-cyanido Fe(III) precursors

The reaction of [Fe(III)L(CN)(3)](-) (L being bpca = bis(2-pyridylcarbonyl)amidate, pcq = 8-(pyridine-2-carboxamido)quinoline) or [Fe(III)(bpb)(CN)(2)](-) (bpb = 1,2-bis(pyridine-2-carboxamido)benzenate) ferric complexes with Mn(III) salen type complexes afforded seven new bimetallic cyanido-bridged Mn(III)-Fe(III) systems: [Fe(pcq)(CN)(3)Mn(saltmen)(CH(3)OH)]·CH(3)OH (1), [Fe(bpca)(CN)(3)Mn(3-MeO-salen)(OH(2))]·CH(3)OH·H(2)O (2), [Fe(bpca)(CN)(3)Mn(salpen)] (3), [Fe(bpca)(CN)(3)Mn(saltmen)] (4), [Fe(bpca)(CN)(3)Mn(5-Me-saltmen)]·2CHCl(3) (5), [Fe(pcq)(CN)(3)Mn(5-Me-saltmen)]·2CH(3)OH·0.75H(2)O (6), and [Fe(bpb)(CN)(2)Mn(saltmen)]·2CH(3)OH (7) (with saltmen(2-) = N,N'-(1,1,2,2-tetramethylethylene)bis(salicylideneiminato) dianion, salpen(2-) = N,N'-propylenebis(salicylideneiminato) dianion, salen(2-) = N,N'-ethylenebis(salicylideneiminato) dianion). Single crystal X-ray diffraction studies were carried out for all these compounds indicating that compounds 1 and 2 are discrete dinuclear [Fe(III)-CN-Mn(III)] complexes while systems 3-7 are heterometallic chains with {-NC-Fe(III)-CN-Mn(III)} repeating units. These chains are connected through π-π and short contact interactions to form extended supramolecular networks. Investigation of the magnetic properties revealed the occurrence of antiferromagnetic Mn(III)···Fe(III) interactions in 1-4 while ferromagnetic Mn(III)···Fe(III) interactions were detected in 5-7. The nature of these Mn(III)···Fe(III) magnetic interactions mediated by a CN bridge appeared to be dependent on the Schiff base substituent. The packing is also strongly affected by the nature of the substituent and the presence of solvent molecules, resulting in additional antiferromagnetic interdinuclear/interchain interactions. Thus the crystal packing and the supramolecular interactions induce different magnetic properties for these systems. The dinuclear complexes 1 and 2, which possess a paramagnetic S(T) = 3/2 ground state, interact antiferromagnetically in their crystal packing. At high temperature, the complexes 3-7 exhibit a one-dimensional magnetic behavior, but at low temperature their magnetic properties are modulated by the supramolecular arrangement: a three-dimensional antiferromagnetic order with a metamagnetic behavior is observed for 3, 4, and 7, and Single-Chain Magnet properties are detected for 5 and 6.     

Periodic solutions of singular radially symmetric systems with superlinear growth

We prove the existence of infinitely many periodic solutions for periodically forced radially symmetric systems of second-order ODE??s, with a singularity of repulsive type, where the nonlinearity has a superlinear growth at infinity. These solutions have periods, which are large integer multiples of the period of the forcing, and rotate exactly once around the origin in their period time, while having a fast oscillating radial component. Analogous results hold in the case of an annular potential well.     

On the mechanism of the conversion of methanol to 2,2,3-trimethylbutane (triptane) over zinc iodide

Methanol is converted to a mixture of hydrocarbons by reaction with zinc iodide at 200 degrees C with one highly branched alkane, 2,2,3-trimethylbutane (triptane), being obtained in surprisingly high selectivity. Mechanistic studies implicate a two-stage process, the first involving heterogeneously catalyzed formation of a carbon-carbon-bonded species, probably ethylene, that undergoes homogeneously catalyzed sequential cationic methylation to higher hydrocarbons. The first stage can be bypassed by addition of olefins, higher alcohols, or arenes, which act as initiators. Rationales for the particular activity of zinc iodide and for the selectivity to triptane are proposed.     

Cooperation in dividing the cake

This paper defines models of cooperation among players partitioning a completely divisible good (such as a cake or a piece of land). The novelty of our approach lies in the players’ ability to form coalitions before the actual division of the good with the aim to maximize the average utility of the coalition. A social welfare function which takes into account coalitions drives the division. In addition, we derive a cooperative game which measures the performance of each coalition. This game is compared with the game in which players start cooperating only after the good has been portioned and has been allocated among the players. We show that a modified version of the game played before the division outperforms the game played after the division.     

Chamber structure and wallcrossing in the ADHM theory of curves II

This is the second part of a project concerning variation of stability and chamber structure for ADHM invariants of curves. Wallcrossing formulas for such invariants are derived using the theory of stack function Ringel-Hall algebras constructed by Joyce and the theory of generalized Donaldson-Thomas invariants of Joyce and Song. Some applications are presented, including strong rationality for local stable pair invariants of higher genus curves, and comparison with wallcrossing formulas of Kontsevich and Soibelman, and the halo formula of Denef and Moore.