Strong Direct Magnetic Coupling in a Dinuclear CoII Tetrazine Radical Single‐Molecule Magnet

The ligand‐centered radical complex [(CoTPMA)₂‐μ‐bmtz^.?](O₃SCF₃)₃ ? CH₃CN (bmtz=3,6‐bis(2′‐pyrimidyl)‐1,2,4,5‐tetrazine, TPMA=tris‐(2‐pyridylmethyl)amine) has been synthesized from the neutral bmtz precursor. Single‐crystal X‐ray diffraction studies have confirmed the presence of the ligand‐centered radical. The Co^II complex exhibits slow paramagnetic relaxation in an applied DC field with a barrier to spin reversal of 39 K. This behavior is a result of strong antiferromagnetic metal–radical coupling combined with positive axial and strong rhombic anisotropic contributions from the Co^II ions.     

Diimidazo[4,5-b:4′,5′-e]pyridine: synthesis and nucleophilic aromatic substitution reaction

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Interwoven hydrogen‐bonded network assembly and supramolecular isomerism of meso‐5,10,15,20‐tetrakis(4‐carboxyphenyl)porphyrin as its dimethylformamide solvate

Molecules of the title compound, porphyrin‐5⁴,10⁴,15⁴,20⁴‐tetrabenzoic acid, C₄₈H₃₀N₄O₈, lie on sites of 2/m symmetry in the space group Cmca. The crystals consist of doubly interwoven two‐dimensional supramolecular arrays sustained by multiple (COOH)₂ cyclic dimeric hydrogen bonds, each molecule of the porphyrintetrabenzoic acid coordinating to four neighbouring species. This structure, which encloses substantial spaces occupied by disordered dimethylformamide solvent molecules, represents yet another supramolecular isomer of this porphyrin.     

Weak–Strong Uniqueness of Dissipative Measure-Valued Solutions for Polyconvex Elastodynamics

For the equations of elastodynamics with polyconvex stored energy, and some related simpler systems, we define a notion of a dissipative measure-valued solution and show that such a solution agrees with a classical solution with the same initial data, when such a classical solution exists. As an application of the method we give a short proof of strong convergence in the continuum limit of a lattice approximation of one dimensional elastodynamics in the presence of a classical solution. Also, for a system of conservation laws endowed with a positive and convex entropy, we show that dissipative measure-valued solutions attain their initial data in a strong sense after time averaging.     

A mathematical programming approach for sequential clustering of dynamic networks

A common analysis performed on dynamic networks is community structure detection, achallenging problem that aims to track the temporal evolution of network modules. Anemerging area in this field is evolutionary clustering, where thecommunity structure of a network snapshot is identified by taking into account both itscurrent state as well as previous time points. Based on this concept, we have developed amixed integer non-linear programming (MINLP) model, SeqMod, that sequentially clusterseach snapshot of a dynamic network. The modularity metric is used to determine the qualityof community structure of the current snapshot and the historical cost is accounted for byoptimising the number of node pairs co-clustered at the previous time point that remain soin the current snapshot partition. Our method is tested on social networks of interactionsamong high school students, college students and members of the Brazilian Congress. Weshow that, for an adequate parameter setting, our algorithm detects the classes that thesestudents belong more accurately than partitioning each time step individually or bypartitioning the aggregated snapshots. Our method also detects drastic discontinuities ininteraction patterns across network snapshots. Finally, we present comparative resultswith similar community detection methods for time-dependent networks from the literature.Overall, we illustrate the applicability of mathematical programming as a flexible,adaptable and systematic approach for these community detection problems.     

Highly anisotropic orbitally dependent superexchange in cyano-bridged clusters containing Mn(III) and Mn(II) ions.

We study the orbitally dependent magnetic exchange in cyanide-based clusters as a source of the barrier for reversal magnetization. We consider the Mn(III)-CN-Mn(II) dimer and linear Mn(II)-NC-Mn(III)-CN-Mn(II) trimer containing octahedrally coordinated Mn(III) and Mn(II) ions with special emphasis on the magnetic manifestations of the orbital degeneracy of the Mn(III) ion. The kinetic exchange mechanism involves the electron transfer from the single occupied t(2) orbitals of the Mn(II) ion [6A1(t2(3)e2) ground state] to the singly occupied t(2) orbitals of the Mn(III) ion [3T1(t2(4)) ground state] resulting in the charge-transfer 5T2(t2(2)e2)Mn(III) - 2T2(t2(5))Mn(II) state of the pair. The deduced effective exchange Hamiltonian that takes into account orbital degeneracy leads to an essentially non-Heisenberg energy pattern. The energy levels are shown to be dependent on both spin and orbital quantum numbers, thus providing direct information about the magnetic anisotropy of the system. Along with the magnetic exchange, the model includes an axial component of the crystal field and spin-orbit coupling operating within the ground 3T1(t2(4)) cubic term of the Mn(III) ion. We have shown that under certain conditions both named interactions lead to the occurrence of the barrier for the reversal of magnetization, which significantly increases when passing from the dimer to the trimer. This provides a possible way for raising the magnetic barrier in the family of cyano-bridged manganese clusters.     

Cycle generating equations

Equations generating directed cycles in at most countable sets are considered. Such equations are the balance relations for recurrent continuous parameter Markov processes that in term of algebraic topology generate the 1-cycles. Connections of cycle generating equations with the recurrent behavior of Markov processes are given     

A Novel Synthesis of Salvadoricine Schiff Bases

Treatment of the readily available l-methylpyrano[3,4-b]indol-3-one with primary aromatic amines leads directly to the formation of Schiff bases of the indole alkaloid Salvadoricine (2-acetyl-3-methyl-indole).