Higher order bad loci

Zero-schemes on smooth complex projective varieties, forcing all elements of ample and free linear systems to be reducible, are studied. Relationships among the minimal length of such zero-schemes, the positivity of the line bundle associated with the linear system, and the dimension of the variety are established. Bad linear spaces are also investigated.     

Scattering of Magnetic Edge States

We consider a charged particle following the boundary of a two dimensional domain because a homogeneous magnetic field is applied. We develop the basic scattering theory for the corresponding quantum mechanical edge states. The scattering operator attains a limit for large magnetic fields which preserves Landau bands. We interpret the corresponding scattering phases in terms of classical trajectories. Communicated by Yosi Avron submitted 23/02/05, accepted 3/05/05     

DFT computational study of the mechanism of allyl halides carbonylation catalyzed by nickel tetracarbonyl

A theoretical investigation at the DFT(B3LYP) level on the carbonylation reaction of allyl bromide catalyzed by nickel tetra-carbonyl Ni(CO)(4) is discussed. The computational results show the following: (i) Three main steps characterize the catalytic cycle: (a) an oxidative addition step, (b) a carbonylation step, and (c) a reductive elimination step where the acyl product is obtained and the catalyst is regenerated. (ii) Both Ni(CO)(3) and Ni(CO)(4) complexes can behave as "active" catalytic species. (iii) The oxidative addition leads to the formation of either eta(3) or eta(1)-allyl nickel complexes, which are involved in a fast equilibrium. (iv) The carbonylation occurs much more easily on the eta(1) than on the eta(3) intermediates.     

Effect of core size on the partition of organic solutes in the monolayer of water-soluble nanoparticles: an ESR investigation

ESR spectroscopy has been used to study the interaction of para-pentylbenzyl hydroxyalkyl nitroxide with the monolayer of water-soluble protected gold clusters having a core diameter ranging from 1.6 to 5.3 nm. The solubilization of the nitroxide probe in the more hydrophobic environment of the monolayer strongly depends on the size of the gold core. In particular, the partition equilibrium constant increases as the nanoparticle diameter decreases. These results have been attributed to the different packing of the chains in the monolayer resulting from the different radius of curvature of the investigated nanoparticles. This represents, to the best of our knowledge, the first report demonstrating that the core size of metallic nanoparticles affects the solvating properties of the protective organic monolayer.     

Synthesis and characterization of hybrid borosiloxane gels as precursors for Si–B–O–C fibers

The sol–gel method has been used for the synthesis of borosilicate gels from mixtures of methyltriethoxysilane (MTES) and dimethyldiethoxysilane (DMDES) and boric acid. The use of boric acid, B(OH)₃ allows the hydrolysis and condensation of hybrid silicon alkoxides without further addition of water or catalyst. The use of difunctional silicon units, –(CH₃)₂SiO– promote the formation, during the sol–gel process, of linear oligomers which facilitate fiber drawing before gelation. Gel characterization performed by FT-IR, XRD, TG-DTA and DCS analysis indicates the formation of a mixed network with incorporation of the boron units via =B-O-Si≡ bridges. The formation of borosiloxane bonds seems favored by the presence of DMDES. SiBOC glasses were obtained after pyrolysis of the borosilicate gels in argon atmosphere at 1000 °C. TG-DTA study indicates that the ceramic yield decreases by increasing the amount of DMDES. Gel fibers were successfully prepared from convenient partially-aged solutions by hand drawing. Pyrolysis of the obtained gel fibers under argon atmosphere at 1000 °C open the possibility to produce SiBOC homogeneous glass fibers with diameter as low as 10 μm.     

Rank-1 approximation to the van der Waals interaction

We present and discuss a variational single-product approximation to the van der Waals dispersion interaction leading to a simple formula for C ₆ that seems capable to give more than 99% of the ‘exact’ value. The formula is derived from Hylleraas’ variational principle in the tensor product space of the interacting molecules and therefore enjoys bounding properties. The formula has been tested by computing the C ₆ dispersion constants of H–H, and, at Full CI level, of the following systems: He–He, He–Li, Li–Li, LiH–LiH, HF–HF. Connections with the London formula are discussed. Contribution to the Fernando Bernardi Memorial Issue.     

Determination of the substituent effect on the O-H bond dissociation enthalpies of phenolic antioxidants by the EPR radical equilibration technique

The bond dissociation enthalpies (BDE) of several phenols containing electron-withdrawing substituents in the para position have been determined by means of the EPR radical equilibration technique. It has been found that CN, NO(2), CHO, COOR, and COOH induce an increase of the BDE value of the O-H bond, thus producing a worsening of the antioxidant activity of phenols, while Cl, Ph, and CH[double bond]CHPh show an opposite effect. The contributions of these substituents for the calculation of the BDE values in polysubstituted phenols by using the group additivity rule have also been derived. It is shown that this rule provides quite reliable predictions of bond strengths, so that the method can be conveniently used to estimate new data on substituted phenols.     

Effects of temperature on the triplet behavior of the styrylphenanthrene isomers

The properties of the triplet state of five styrylphenanthrene (StPh) trans isomers were studied in 2-methyltetrahydrofuran (MTHF) as a function of temperature. At room temperature the T-T absorption was observed only for 4- and 9-StPh, while under these conditions 1-, 2-, and 3-StPh have too low a quantum yield of triplet formation (Φ_T <0.02); their T-T absorption spectra were obtained at low temperature. Φ_T of 1- and 2-StPh increases more than tenfold on going from 293 to 77 K, and the triplet lifetime (τ_T) increases by four orders of magnitude and approaches values of 5–40 ms at 77 K. The change in τ_T is explained in terms of an equilibrium between trans and perpendicular (perp) conformations of the lowest triplet state in fluid solution and temperature and viscosity effects on the trans → perp rotation. Evidence is presented for the existence of two conformeric trans triplet states of 3-StPh at 77 K. Semi-empirical calculations were performed to obtain the energy of the triplet state, the wavelengths of several T-T absorption maxima (λ_T), and the oscillator strength. The calculated λ_T values coincide with those measured in n-hexane.     

Reactions of Substituted Boryl Radicals with Nitroalkanes. EPR, Kinetic, and Product Studies

The radical-initiated reaction of amine-boranes and phosphine-boranes, LBH(3) (L = R(3)N, R(3)P) with aliphatic nitro compounds has been investigated in order to explore the possibility of reducing tertiary nitroalkanes to the corresponding hydrocarbons. In all the examined cases boroxy nitroxides, RN(O(*))OBLH(2), resulting from the addition of ligated boryl radicals, LBH(2)(*), to an oxygen atom of the nitro group were detected and characterized by EPR spectroscopy. This reaction occurs at room temperature with a rate constant of 1.5 x 10(7) M(-)(1) s(-)(1) for LBH(2)(*) = Me(3)NBH(2)(*) and RNO(2) = Me(3)CNO(2). The boroxy nitroxides from tertiary nitroalkanes decay by a fragmentation reaction occurring with cleavage of the nitrogen-oxygen bond, rather than of the carbon-nitrogen bond as would be required for the reduction to the corresponding alkane to take place. The Arrhenius parameters for this fragmentation have been determined in few cases.