NMR and theoretical investigations on the structures and dynamics of octahedral bis(chelate)dichloro V(III) compounds isolated by an unusual reduction of non-oxo V(IV) species

Reaction of the non-oxo V(IV) species [V(IV)Cl(2)(L(OO))(2)] [L(OO) = acetylacetonate (acac(-)) or benzoylacetonate (bzac(-))] with a chelate nitrogen-donor ligand L(NN) in acetonitrile leads to the reduction of V(IV) to V(III) and the formation of the mononuclear V(III) compounds of the general formula [V(III)Cl(2)(L(OO))(L(NN))] (L(OO) and L(NN) are acac(-) and bipy for 1; acac- and 5,5'-me(2)bipy for 2; acac(-) and 4,4'-tb(2)bipy for 3; acac(-) and phen for 4; bzac(-) and bipy for 5; bzac(-) and phen for 6). The reduction of the V(IV) complexes was monitored by GC-MS and (1)H NMR spectroscopy. Both one- and two-dimensional (2D COSY and 2D EXSY) (1)H NMR techniques were used to assign the observed (1)H NMR resonances of 1-6 in CD(2)Cl(2) or CDCl(3) solution. It appeared that in solution these V(III) complexes form two isomers which are in equilibrium: cis-[V(III)Cl(2)(L(OO))(L(NN))] <==> trans-[V(III)Cl(2)(L(OO))(L(NN))]. 2D EXSY cross-peaks were clearly observed between bipy- and acac-hydrogen atoms of the two geometrical isomers of 1-3 as well as between bipy and acac(-) protons of the cis isomer, indicating a dynamic process that corresponds to cis-trans isomerization and a cis-cis racemization. The thermodynamic and kinetic parameters of the equilibrium between these two isomers were calculated for compounds 1 and 2 by using variable temperature (VT) NMR data. Both cis-trans isomerization and cis-cis racemization processes probably proceed with an intramolecular twist mechanism involving a trigonal prismatic transition state. Density functional calculations (DFT) also indicated such a rearrangement mechanism.     

Template synthesis and single-molecule magnetism properties of a complex with spin S = 16 and a [Mn8O8]8+ saddle-like core

The compound [CeIVMnIII8O8(O2CMe)12(H2O)4].4H2O (1.4H2O) has been obtained from a template synthesis involving the reaction of the chain polymer {[MnIII(OH)(O2CMe)2] .(MeCO2H).(H2O)}n (3) with Ce(IV). Compound 1 contains a MnIII8 loop inside which is held the Ce(IV) ion by the bridging oxide ions. Magnetization and magnetic susceptibility studies establish that 1 has an S = 16 spin ground state, the largest yet for a Mn cluster, and displays the slow magnetization relaxation and hysteresis behavior of a single-molecule magnet (SMM). It is thus the highest spin Mn SMM discovered to date.     

Finitary Spacetime Sheaves of Quantum Causal Sets: Curving Quantum Causality

A locally finite, causal, and quantal substitute for a locally Minkowskian principal fiber bundle of modules of Cartan differential forms over a bounded region X of a curved C -smooth spacetime manifold M with structure group G that of orthochronous Lorentz transformations L ⁺ := SO(1,3), is presented. is usually regarded as the kinematical structure of classical Lorentzian gravity when the latter is viewed as a Yang-Mills type of gauge theory of a sl(2, {})-valued connection 1-form . The mathematical structure employed to model this replacement of is a principal finitary spacetime sheaf of quantum causal sets with structure group G _n, which is a finitary version of the continuous group G of local symmetries of General Relativity, and a finitary Lie algebra g _n-valued connection 1-form on it, which is a section of its subsheaf . is physically interpreted as the dynamical field of a locally finite quantum causality, whereas its associated curvature as some sort of finitary and causal Lorentzian quantum gravity.     

An Elementary Proof of Pólya-Vinogradov's Inequality, II

Let be a primitive character mod k, k > 2. In [1], the following elementary estimate

Novel disposable microfabricated antimony-film electrodes for adsorptive stripping analysis of trace Ni(II)

This work describes a novel type of antimony electrode for adsorptive stripping voltammetry (AdSV). The electrode was microfabricated by coating a silicon chip with a thin antimony-film by means of sputtering and the active area of the electrode was defined by photolithography. The resulting antimony-film electrodes (SbFEs) were characterized by optical and electrochemical techniques. The sensors were tested for the detection of low concentrations of Ni(II) by AdSV in the presence of dimethylglyoxime. Well-formed stripping peaks and a linear dependence of the stripping peak current on the Ni(II) concentration were observed on the microfabricated SbFEs while comparative measurements attempted with electroplated SbFEs were unsuccessful. Utilizing thin-film technology for the formation of the antimony-film extends the scope of these devices as mercury-free sensors in AdSV.     

1-D coordination polymers consisting of a high-spin Mn17 octahedral unit

The reaction of [Mn(O₂CMe)₂] · 4H₂O with pdH₂ (1,3-propanediol) or mpdH₂ (2-methyl-1,3-propanediol) in the presence of NaN₃ in MeCN/py (py = pyridine) results in the formation of two new one-dimensional coordination polymers composed of a [Mn^III₆Mn^II₁₁(μ₄-O)₈(μ₃-N₃)₄]²⁵⁺ octahedral unit. The peripheral ligation is completed by pd^2? (or mpd^2?), acetate, pyridine and μ-1,3-N₃^? ligands. The latter bridges each Mn₁₇ unit to its neighboring one, resulting in the formation of the two 1-D coordination polymers. Variable-temperature dc magnetic susceptibility studies indicate the existence of predominantly ferromagnetic interactions and a resulting giant ground state spin within the Mn₁₇ units and intermolecular antiferromagnetic exchange interactions between the neighboring Mn₁₇ units that result in diamagnetic ground spin states for both polymeric compounds.     

Combining azide, carboxylate, and 2-pyridyloximate ligands in transition-metal chemistry: ferromagnetic Ni(II)5 clusters with a bowtie skeleton

The combined use of the anion of phenyl(2-pyridyl)ketone oxime (ppko(-)) and azides (N(3)(-)) in nickel(II) carboxylate chemistry has afforded two new Ni(II)(5) clusters, [Ni(5)(O(2)CR')(2)(N(3))(4)(ppko)(4)(MeOH)(4)] [R' = H (1), Me (2)]. The structurally unprecedented {Ni(5)(μ-N(3))(2)(μ(3)-N(3))(2)}(6+) cores of the two clusters are almost identical and contain the five Ni(II) atoms in a bowtie topology. Two N(3)(-) ions are end-on doubly bridging and the other two ions end-on triply bridging. The end-on μ(3)-N(3)(-) groups link the central Ni(II) atoms with the two peripheral metal ions on either side of the molecule, while the Ni···Ni bases of the triangles are each bridged by one end-on μ-N(3)(-) group. Variable-temperature, solid-state direct- (dc) and alternating-current (ac) magnetic susceptibility, and magnetization studies at 2.0 K were carried out on both complexes. The data indicate an overall ferromagnetic behavior and an S = 5 ground state for both compounds. The ac susceptibility studies on 1 reveal nonzero, frequency-dependent out-of-phase (χ(M)") signals at temperatures below ~3.5 K; complex 2 reveals no χ(M)" signals. However, single-crystal magnetization versus dc field scans at variable temperatures and variable sweep rates down to 0.04 K on 1 reveal no noticeable hysteresis loops, except very minor ones at 0.04 K assignable to weak intermolecular interactions propagated by nonclassical hydrogen bonds.     

Flow synthesis of tricyclic spiropiperidines as building blocks for the histrionicotoxin family of alkaloids

A domino cyclization reaction of the bis-unsaturated ketone 3 with hydroxylamine proceeds with good yield and high stereoselectivity, in a flow reactor system. The tricyclic spiropiperidine products 5 and 2 obtained are valuable building blocks for the synthesis of analogues of the histrionicotoxin alkaloids.     

Equilibria for networks with malicious users

We consider the problem of characterizing user equilibria and optimal solutions for selfish routing in a given network. We extend the known models by considering malicious behavior. While selfish users follow a strategy that minimizes their individual cost, a malicious user will use his flow through the network in an effort to cause the maximum possible damage to the overall cost. We define a generalized model, present characterizations of flows at equilibrium and prove bounds for the ratio of the social cost of a flow at equilibrium over the cost when centralized coordination among users is allowed. An extended abstract of this work appeared in the Proceedings of the 14th Annual International Symposium on Algorithms and Computation (ISAAC) 2003. G. Karakostas’ research was supported by an NSERC Discovery research grant and MITACS. Part of this research was done when Viglas was a postdoctoral fellow at the University of Toronto, Canada.