Scaling by Binormalization

We present an iterative algorithm (BIN) for scaling all the rows and columns of a real symmetric matrix to unit 2-norm. We study the theoretical convergence properties and its relation to optimal conditioning. Numerical experiments show that BIN requires 2–4 matrix–vector multiplications to obtain an adequate scaling, and in many cases significantly reduces the condition number, more than other scaling algorithms. We present generalizations to complex, nonsymmetric and rectangular matrices.     

Homoconjugated ketones with extended unsaturation: Wavelength-selective,regioselective, diastereoselective,and enantiospecific photochemical transformations of methyl 7-oxospiro[5.5]undeca-1,3-and -2,4,-diene-2-carboxylate

The title molecules were shown to photorearrange with remarkable selectivity. Wavelength variation steers the rearrangement modes, of which the [1,2]-acyl shift was found to be largely regioselective, diastereoselective, and enantiospecific. Chemical intercorrelation of products and mechanistic studies were carried out all along. The potential significance of these photochemical processes in selective synthetic schemes is discussed.     

Current distribution on a three-dimensional,bond-diluted,random-resistor network at the percolation threshold

Current and logarithm-current distributions on a three-dimensional random-bond percolation cubic network were studied at the percolation threshold by computer simulations. Predictions of a hierarchical model that combine fractal structure and randomness agree with our numerical simulations. In the thermodynamic limit the logarithm-current distribution exhibits ann(ln(i))i ^1/3 dependence below some characteristic currenti _c. This distribution may scale with lni/lnL, but the data are insufficient to make this a definite conclusion. Due to the small range of lnL considered, a study of the moments does not reveal this behavior and a study of the distribution itself is required.     

Tellurium in organic synthesis : V. X-ray structure of 8-ethoxy-4-cyclooctenyltellurium trichloride and its relevance to the TeO2-oxidation of alkenes

The molecular structure of 8-ethoxy-4-cyclooctenyltellurium trichloride has been determined from three-dimensional X-ray diffraction data. The crystal belongs to the monoclinic system, space group P2₁/n, with four formula units in a cell of dimensions: a 7.712(1), b 13.406(3), c 13.820(2) Å and β 95.18(1)°. The structure was solved by the conventional heavy atom method, and refined by the least-squares procedure to R = 0.025 for 2199 reflections.The compound is formed from the corresponding β-chloroalkyltellurium tri-chloride, obtained from TeCl₄ and cis, cis-1,5-cyclooctadiene, by an unusually mild solvolytic substitution reaction in ethanol. Similar β-chloroalkyltellurium compounds are postulated as intermediates in the TeO₂ oxidation of alkenes to alkanediol diacetates and alkanediol monoacetates in HOAc containing a lithium halide, LiX. Oxidation of cis-2-butene and trans-2-butene with TeO₂/HOAc/LiBr gave a high preference for cis-stereochemistry in the products while 1-decene showed no stereospecificity.     

Zirconium-mediated metathesis of imines: a study of the scope, longevity, and mechanism of a complicated catalytic system

By kinetically stabilizing imidozirconocene complexes through the use of a sterically demanding ligand, or by generating a more thermodynamically stable resting state with addition of diphenylacetylene, we have developed transition metal-catalyzed imine metathesis reactions that are mechanistically analogous to olefin metathesis reactions catalyzed by metal carbene complexes. When 5 mol % of Cp*Cp(THF)Zr=N(t)Bu is used as the catalyst precursor in the metathesis reaction between PhCH=NPh and p-TolCH=N-p-Tol, a 1:1:1:1 equilibrium mixture with the two mixed imines p-TolCH=NPh and PhCH=N-p-Tol is generated in C(6)D(6) at 105 degrees C. The catalyst was still active after 20 days with an estimated 847 turnovers (t(1/2) 170 m; TON = 1.77 h(-1)). When the azametallacyclobutene Cp(2)Zr(N(Tol)C(Ph)=C(Ph)) is used as the catalyst precursor under similar reaction conditions, a total of 410 turnovers are obtained after 4 days (t(1/2) 170 m; TON = 4.3 h(-1)). An extensive kinetic and equilibrium analysis of the metallacyclobutene-catalyzed metathesis of PhCH=N-p-Tol and p-F-C(6)H(4)CH=N-p-F-C(6)H(4) was carried out by monitoring the concentrations of imines and observable metal-containing intermediates over time. Numerical integration methods were used to fit these data to a detailed mechanism involving coordinatively unsaturated (16-electron) imido complexes as critical intermediates. Examination of the scope of reaction between different organic imines revealed characteristic selectivity that appears to be unique to the zirconium-mediated system. Several zirconocene complexes that could generate the catalytically active "CpCp'Zr=NAr" (Cp' = Cp or Cp*) species in situ were found to be effective agents in the metathetical exchange between different N-aryl imines. N-Alkyl aldimines were found to be completely unreactive toward metathesis with N-aryl aldimines, and metathesis reactions involving the two N-alkyl imines TolCH=NPr and PhCH=NMe gave slow or erratic results, depending on the catalyst used. Metathesis was observed between N-aryl ketimines and N-aryl aldimines, but for N-aryl ketimine substrates, the catalyst resting state consists of zirconocene enamido complexes, generated by the formal C-H activation of the alpha position of the ketimine substrates.     

A mechanistic investigation of the carbon-carbon bond cleavage of aryl and alkyl cyanides using a cationic RhIII silyl complex

Cationic Rh(III) complex [Cp(PMe(3))Rh(SiPh(3))(CH(2)Cl(2))]BAr(4)' (1) activates the carbon-carbon bond of aryl and alkyl cyanides (R-CN, where R = Ph, (4-(CF(3))C(6)H(4)), (4-(OMe)C(6)H(4)), Me, (i)Pr, (t)Bu) to produce complexes of the general formula [Cp*(PMe(3))Rh(R)(CNSiPh(3))]BAr(4)'. With the exception of the (t)BuCN case, every reaction proceeds at room temperature (t(1/2) < 1 h for aryl cyanides, t(1/2) < 14 h for alkyl cyanides). A general mechanism is presented on the basis of (1) an X-ray crystal structure determination of an intermediate isolated from the reaction involving 4-methoxybenzonitrile and (2) kinetic studies performed on the C-C bond cleavage of para-substituted aryl cyanides. Initial formation of an eta(1)-nitrile species is observed, followed by conversion to an eta(2)-iminoacyl intermediate, which was observed to undergo migration of R (aryl or alkyl) to rhodium to form the product [Cp*(PMe(3))Rh(R)(CNSiPh(3))]BAr(4)'.