Symbolic Computation of Newton Sum Rules for the Zeros of Polynomial Eigenfunctions of Linear Differential Operators

A symbolic algorithm based on the generalized Lucas polynomials of first kind is used in order to compute the Newton sum rules for the zeros of polynomial eigenfunctions of linear differential operators with polynomial coefficients.     

Evidence for negative cross correlations in vibrational dephasing in liquids: isotropic raman-line shift and width phenomena in isotopic mixtures of N2 and O2

To experimentally confirm the hypothesis of negative cross terms between different dephasing mechanisms, potentially leading to a broadening of the isotropic Raman line upon isotopic dilution, we present a detailed study on the concentration dependencies of all of the line shifts and widths in the four isotopic mixtures of type (15N14N)(x)-(14N2)(1-x), (15N2)(x)-(14N2)(1-x), (15N2)(x)-(15N14N)(1-x), and (16O2)(x)-(18O2)(1-x) near the normal boiling point of nitrogen at T = 77.35 K. A quite disparate behavior of the nitrogen oscillators compared to the oxygen oscillators was observed in respect to a change of their isotopic baths.     

Purification of carbon nanotubes grown by thermal CVD

We show the results of a set of purifications on carbon nanotubes (CNT) by acid and basic treatments. CNTs were obtained by thermal decomposition of camphor at 850 °C in a CVD growth system, by means of a growth process catalyzed by iron clusters originating from the addition of ferrocene in the precursors mixture. The purification procedures involved HNO₃, H₂SO₄, HSO₃Cl and NaOH for different process temperatures.As-grown CNTs showed a consistent presence of metal catalyst (about 6 wt%), evidenced by TGA. The purification treatments led to a certain amount of opening of the CNT tips, with a consequent loss of metal catalyst encapsulated in tips. This is also confirmed by BET analysis, which showed an increase of the surface area density of CNT after the purification.FT-IR and XPS revealed the presence of carboxylic groups on the CNT surface chemically modified by the harsh environment of the purification process.Among the various treatments that have been tested, the 1:3 solution of nitric and sulphuric acid was the most effective in modifying the CNT surface and inducing the formation of functional groups.     

Bounds and monotonicity for the generalized Robin problem

We consider the principal eigenvalue λ ₁^Ω(α) corresponding to Δu = λ (α) u in W, \frac?u?v = au \Omega, \frac{\partial u}{\partial v} = \alpha u on ∂Ω, with α a fixed real, and W ì Rⁿ\Omega \subset {\mathcal{R}}^n a C ^0,1 bounded domain. If α > 0 and small, we derive bounds for λ ₁^Ω(α) in terms of a Stekloff-type eigenvalue; while for α > 0 large we study the behavior of its growth in terms of maximum curvature. We analyze how domain monotonicity of the principal eigenvalue depends on the geometry of the domain, and prove that domains which exhibit domain monotonicity for every α are calibrable. We conjecture that a domain has the domain monotonicity property for some α if and only if it is calibrable.     

Photo-induced pyridine substitution in cis-[Ru(bpy)(2)(py)(2)]Cl(2): a snapshot by time-resolved X-ray solution scattering

Determination of transient structures in light-induced processes is a challenging goal for time-resolved techniques. Such techniques are becoming successful in detecting ultrafast structural changes in molecules and do not require the presence of probe-like groups. Here, we demonstrate that TR-WAXS (Time-Resolved Wide Angle X-ray Scattering) can be successfully employed to study the photochemistry of cis-[Ru(bpy)(2)(py)(2)]Cl(2), a mononuclear ruthenium complex of interest in the field of photoactivatable anticancer agents. TR-WAXS is able to detect the release of a pyridine ligand and the coordination of a solvent molecule on a faster timescale than 800 ns of laser excitation. The direct measurement of the photodissociation of pyridine is a major advance in the field of time-resolved techniques allowing detection, for the first time, of the release of a multiatomic ligand formed by low Z atoms. These data demonstrate that TR-WAXS is a powerful technique for studying rapid ligand substitution processes involving photoactive metal complexes of biological interest.     

New Class of Chiral Diphosphine Ligands for Highly Efficient Transition Metal-Catalyzed Stereoselective Reactions: The Bis(diphenylphosphino) Five-membered Biheteroaryls

The synthesis and application of three examples of a new class of chiral (C(2)) atropisomeric diphosphines characterized by two interconnected five-membered heteroaromatic rings, with hindered rotation around the interanular bond, are described. Optically pure (+)- and (-)-2,2'-bis(diphenylphosphino)-4,4',6,6'-tetramethyl-3,3'-bibenzo[b]thiophene (tetraMe-bitianp) (1a) and the parent unsubstituted system (+)- and (-)-bitianp (1b) were synthesized. They were found to be optically stable at 100 degrees C and were successfully employed as ligands in the Ru(II)-catalyzed hydrogenation of alpha- and beta-oxo esters to the corresponding alpha- and beta-hydroxy esters and in the hydrogenation of olefinic substrates. The optical and chemical yields were comparable with those reported for the same Ru(II)-binap-catalyzed reactions carried out under the same experimental conditions. The 2,2'-bis(diphenylphosphino)-3,3'-bibenzo[b]furan (1c), the oxygenated analogue of bitianp, was found to be configurationally unstable at room temperature. Complete structural X-ray elucidation of the Pd complexes of 1a-c is reported. The advantages of these biheteroaromatic ligands over the classical biaryl systems are discussed.     

[Re5(μ-H)4(CO)20]− and [Re5(μ-H)5(CO)20], Two Isolobal Analogues of Cyclopentane

The first five-membered rings of metal atoms connected by M–M or M-H-M bonds only have been obtained by a Re₂+Re₃ condensation in which a polyhydride acts as a bridging bidentate ligand toward a coordinatively unsaturated fragment (see scheme below). In spite of the octahedral coordination of the Re centers, the Re₅ rings display conformations (twisted and envelope) comparable with those observed for organic five-membered rings of tetrahedral carbon atoms.     

Hydrido-Carbonyl Rhenium Clusters with a Square Geometry of the Metal Core. Synthesis and X-Ray Characterization of the Novel [Re4(μ-H)3(CO)16]− Anion

Three and tetranuclear ring clusters have been obtained by treatment of [Re₂(CO)₈(THF)₂] with carbonyl-rhenates containing two terminal hydrides. The reaction with [ReH₂(CO)₄]^- provided a selective route to the previously known [Re₃(-H)₂(CO)₁₂]^- triangular cluster anion 1. The reaction with [Re₂H₂(-H)(CO)₈]^- gave the novel [Re₄(-H)₃(CO)₁₆]^- anion 2, containing a rare example of a puckered-square metal cluster. Protonation of 1 is known to afford the neutral [Re₃(-H)₃(CO)₁₂] species 3. Analogously the reaction of 2 with a strong acid afforded the previously known square metal clusters [Re₄(-H)₄(CO)₁₆] 4. The reaction could not be reversed by treatment with bases. Photolysis of 4 gave the unsaturated complex [Re₂(-H)₂(CO)₈] 5: this is the reverse of the dimerization reaction, that in THF at room temperature produces 4 from 5. Thermal treatment (reflux in cyclohexane for 24 h) left 4 almost unchanged. A single crystal X-ray analysis of [NEt₄]2 showed a s/e/s/s (e=eclipsed, s=staggered) conformation of the Re(CO)₄ units, leading to a puckered geometry of the ring, at variance with the square-planar geometry of 4 (all eclipsed). Two of the three hydrides of 2 have been located as bridging the Re–Re edges from inside the metal ring, as previously observed in 4. Density functional computations indicated a puckered conformation as the most stable for both 2 and 4, with very low activation energies for ring inversion (6.6 and 2.2 kcal·mol^-1, respectively), but ruled out solid state fluxionality for 4, whose observed planar geometry must be attributed to packing stabilization.