Amalgamated free products of weakly rigid factors and calculation of their symmetry groups

We consider amalgamated free product II₁ factors M = M _1*B M _2*B … and use “deformation/rigidity” and “intertwining” techniques to prove that any relatively rigid von Neumann subalgebra Q ⊂ M can be unitarily conjugated into one of the M _i ’s. We apply this to the case where the M _i ’s are w-rigid II₁ factors, with B equal to either C, to a Cartan subalgebra A in M _i , or to a regular hyperfinite II₁ subfactor R in M _i , to obtain the following type of unique decomposition results, àla Bass–Serre: If M = (N _1 * CN_2*C …) ^t , for some t > 0 and some other similar inclusions of algebras C ⊂ N _i then, after a permutation of indices, (B ⊂ M _i ) is inner conjugate to (C ⊂ N _i ) ^t , for all i. Taking B = C and , with {t _i } _i⩾1 = S a given countable subgroup of R ₊ ^*, we obtain continuously many non-stably isomorphic factors M with fundamental group equal to S. For B = A, we obtain a new class of factors M with unique Cartan subalgebra decomposition, with a large subclass satisfying and Out(M) abelian and calculable. Taking B = R, we get examples of factors with , Out(M) = K, for any given separable compact abelian group K.     

Short proofs of the universality of certain diagonal quadratic forms

In a paper of Kim, Chan, and Rhagavan, the universal ternary classical quadratic forms over quadratic fields of positive discriminant were discovered. Here a proof of the universality of some of these quadratic forms is given using a technique of Liouville. Another quadratic form over the field of discriminant 8 is shown universal by a different elementary approach. Received: 30 October 2007     

Solution phase synthesis of a diverse library of highly substituted isoxazoles

The iodocyclization of O-methyloximes of 2-alkyn-1-ones affords 4-iodoisoxazoles, which undergo various palladium-catalyzed reactions to yield 3,4,5-trisubstituted isoxazoles. The palladium-catalyzed processes have been adapted to parallel synthesis utilizing commercially available boronic acid, acetylene, styrene, and amine sublibraries. Accordingly, a diverse 51-member library of 3,4,5-trisubstituted isoxazoles has been generated.     

Molecular structure and dynamics in the low temperature (orthorhombic) phase of NH3BH3

Variable temperature 2H NMR experiments on the orthorhombic phase of selectively deuterated NH3BH3 spanning the static to fast exchange limits of the borane and amine motions are reported. New values of the electric field gradient (EFG) tensor parameters have been obtained from the static 2H spectra of V(zz) = 1.652 (+/-0.082) x 10(21) V/m(2) and eta = 0.00 +/- 0.05 for the borane hydrogens and V(zz) = 2.883 (+/-0.144) x 10(21) V/m(2) and eta = 0.00 +/- 0.05 for the amine hydrogens. The molecular symmetry inferred from the observation of equal EFG tensors for the three borane hydrogens and likewise for the three amine hydrogens is in sharp contrast with the C(s) symmetry derived from diffraction studies. The origin of the apparent discrepancy has been investigated using molecular dynamics methods in combination with electronic structure calculations of NMR parameters, bond lengths, and bond angles. The computation of parameters from a statistical ensemble rather than from a single set of atomic Cartesian coordinates gives values that are in close quantitative agreement with the 2H NMR electric field gradient tensor measurements and are more consistent with the molecular symmetry revealed by the NMR spectra.     

Copper complexes of anionic nitrogen ligands in the amidation and imidation of aryl halides

Copper(I) imidate and amidate complexes of chelating N,N-donor ligands, which are proposed intermediates in copper-catalyzed amidations of aryl halides, have been synthesized and characterized by X-ray diffraction and detailed solution-phase methods. In some cases, the complexes adopt neutral, three-coordinate trigonal planar structures in the solid state, but in other cases they adopt an ionic form consisting of an L 2Cu (+) cation and a CuX 2 (-) anion. A tetraalkylammonium salt of the CuX 2 (-) anion in which X = phthalimidate was also isolated. Conductivity measurements and (1)H NMR spectra of mixtures of two complexes all indicate that the complexes exist predominantly in the ionic form in DMSO and DMF solutions. One complex was sufficiently soluble for conductance measurements in less polar solvents and was shown to adopt some degree of the ionic form in THF and predominantly the neutral form in benzene. The complexes containing dative nitrogen ligands reacted with iodoarenes and bromoarenes to form products from C-N coupling, but the ammonium salt of [Cu(phth) 2] (-) did not. Similar selectivities for stoichiometric and catalytic reactions with two different iodoarenes and faster rates for the stoichiometric reactions implied that the isolated amidate and imidate complexes are intermediates in the reactions of amides and imides with haloarenes catalyzed by copper complexes containing dative N,N ligands. These amidates and imidates reacted much more slowly with chloroarenes, including chloroarenes that possess more favorable reduction potentials than some bromoarenes and that are known to undergo fast dissociation of chloride from the chloroarene radical anion. The reaction of o-(allyloxy)iodobenzene with [(phen) 2Cu][Cu(pyrr) 2] results in formation of the C-N coupled product in high yield and no detectable amount of the 3-methyl-2,3-dihydrobenzofuran or 3-methylene-2,3-dihydrobenzofuran products that would be expected from a reaction that generated free radicals. These data and computed reaction barriers argue against mechanisms in which the haloarene reacts with a two-coordinate anionic copper species and mechanisms that start with electron transfer to generate a free iodoarene radical anion. Instead, these data are more consistent with mechanisms involving cleavage of the carbon-halogen bond within the coordination sphere of the metal.     

N‐Heterocyclic Carbenes as Promotors for the Rearrangement of Phosphaketenes to Phosphaheteroallenes: A Case Study for OCP to OPC Constitutional Isomerism

The concept of isomerism is essential to chemistry and allows defining molecules with an identical composition but different connectivity (bonds) between their atoms (constitutional isomers) and/or a different arrangement in space (stereoisomers). The reaction of phosphanyl ketenes, (NHP)?P=C=O (NHP=N‐heterocyclic phosphenium) with N‐heterocyclic carbenes (NHCs) leads to phosphaheteroallenes (NHP)?O?P=C=NHC in which the PCO unit has been isomerized to OPC. Based on the isolation of several intermediates and DFT calculations, a mechanism for this fundamental isomerisation process is proposed.     

Diversity through isosterism: the case of boron-substituted 1,2-dihydro-1,2-azaborines

The first general synthesis of boron-substituted 1,2-dihydro-1,2-azaborines is described. The versatile 1,2-dihydro-1,2-azaborine precursor 4 is synthesized through a ring-closing metathesis-oxidation sequence. Treatment of 4 with a wide range of anionic nucleophiles furnishes the desired adducts 5 in good yields. The scope includes hydrogen- and a variety of carbon- and heteroatom-based nucleophiles. Furthermore, the boron-containing isostere (7) of the potent hypolipidemic agent, methyl 2-ethylphenoxyacetate (8), is readily prepared through our method.     

A computational study on the interaction of the nitric oxide ions NO+ and NO- with the side groups of the aromatic amino acids

The interaction of the nitric oxide ions NO+ and NO- with benzene (C6H6) and the aromatic R-groups of the amino acids phenylalanine (Phe), tyrosine (Tyr), histidine (His), and tryptophan (Trp) have been examined using the DFT method B3LYP and the conventional electron correlation method MP2. In particular, the structures and complexation energies of the resulting half-sandwich Ar...NO+/- and sandwich [Ar...NO...Ar]+/- complexes have been considered. For the Ar...NO+ complexes, the presence of an electron rich heteroatom within or attached to the ring is found to not preclude the cation...pi bound complex from being the most stable. Furthermore, unlike the anionic complexes, the pi...cation...pi ([Ar...NO...Ar]+) complexes do not correspond to a "doubling" of the parent half-sandwich.     

Conjugated polymer nanoparticles for biochemical protein kinase assay

Sensitive and reliable monitoring of kinase activity was reported by using highly efficient fluorescence resonance energy transfer of conjugated polymer nanoparticles (CPNs) to a rhodamine labelled peptide substrate.