On the Cartan–Jacobson Theorem

The well-known Cartan–Jacobson theorem claims that the Lie algebra of derivations of a Cayley algebra is central simple if the characteristic is not 2 or 3. In this paper we have studied these two cases, with the following results: if the characteristic is 2, the theorem is also true, but, if the characteristic is 3, the derivation algebra is not simple. We have also proved that in this last case, there is a unique nonzero proper seven-dimensional ideal, which is a central simple Lie algebra of type A₂, and the quotient of the derivation algebra modulo this ideal turns out to be isomorphic, as a Lie algebra, to the ideal itself. The original motivation of this work was a series of computer-aided calculations which proved the simplicity of derivation algebras of Cayley algebras in the case of characteristic not 3. These computations also proved the existence of a unique nonzero proper ideal (which turns out to be seven-dimensional) in the algebra of derivations of split Cayley algebras in characteristic 3.     

Effect of excess halide on the palladium‐catalyzed insertion‐triggered radical copolymerization of methyl acrylate and 1‐hexene

[Pd₂(μ‐Cl)₂(C₆F₅)₂(tht)₂] ( 1 ) is a very efficient initiator of the radical polymerization of methyl acrylate, but it is not active in the polymerization of methyl methacrylate or in the copolymerization with 1‐hexene. The addition of an excess of NBu₄Cl to solutions of [Pd₂(μ‐Cl)₂(C₆F₅)₂(tht)₂] ( 1 ) provides an initiator system that copolymerizes methyl acrylate and 1‐hexene by an insertion‐triggered radical mechanism. Random copolymers are obtained with 11% incorporation of 1‐hexene in moderate yields (about 35%). Studies of the decomposition products obtained after the first insertion of methyl acrylate in the Pd? C₆F₅ bond of 1 show that the addition of excess halide in the presence of monomer favors the homolytic cleavage of the Pd? C bond, and the generation of the radicals that are active species in the polymerization, versus alternative evolution pathways. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5682–5691, 2006     

Multiscale Finite Element Modeling of Arc Dynamics in a DC Plasma Torch

The dynamics of the electric arc inside a direct current non-transferred arc plasma torch are simulated using a three-dimensional, transient, equilibrium model. The fluid and electromagnetic equations are solved numerically in a fully coupled approach by a multiscale finite element method. Simulations of a torch operating with argon and argon–hydrogen under different operating conditions are presented. The model is able to predict the operation of the torch in steady and takeover modes without any further assumption on the reattachment process except for the use of an artificially high electrical conductivity near the electrodes, needed because of the equilibrium assumption. The results obtained indicate that the reattachment process in these operating modes may be driven by the movement of the arc rather than by a breakdown-like process. It is also found that, for a torch operating in these modes and using straight gas injection, the arc will tend to re-attach to the opposite side of its original attachment. This phenomenon seems to be produced by a net angular momentum on the arc due to the imbalance between magnetic and fluid drag forces.     

Inorganic-metalorganic hybrids based on copper(II)-monosubstituted Keggin polyanions and dinuclear copper(II)-oxalate complexes. Synthesis, X-ray structural characterization, and magnetic properties

Reaction of in situ generated copper(II)-monosubstituted Keggin polyoxometalates and copper(II)-bipyridine-oxalate complexes in the corresponding alkaline acetate buffer led to the formation of hybrid metal organic-inorganic compounds K(2)[{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(H(2)O)(2)(mu-ox)}(2)].14H(2)O (1), K(14)[{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(mu-ox)}](2)[SiW(11)O(39)Cu(H(2)O)].55H(2)O (2), (NH(4))(4)[{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(mu-ox)}].10H(2)O (3), and Rb(4)[{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(mu-ox)}].10H(2)O (4). Their structures have been established by single-crystal X-ray diffraction. The main structural feature of these compounds is the presence of copper(II)-monosubstituted alpha-Keggin polyoxoanions as inorganic building blocks, on which the mu-oxalatodicopper metalorganic blocks are supported. Compound 1contains the discrete hybrid polyanion [{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(H(2)O)(2)(mu-ox)}(2)](2)(-), whereas the polymeric hybrid polyanion [{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(mu-ox)}(2)](n)(4)(n)(-) gives a monodimensional character to compounds 2-4. Magnetic and EPR results are discussed with respect to the crystal structure of the compounds. DFT calculations on both the [Cu(2)(bpy)(2)(H(2)O)(4)(mu-ox)](2+) cationic complex and the metalorganic blocks have been performed in order to determine the optimized geometry and the magnetic coupling constants, respectively.     

Ambiphilic boryl groups in a neutral Ni(ii) complex: a new activation mode of H2

The concept of metal–ligand cooperation opens new avenues for the design of catalytic systems that may offer alternative reactivity patterns to the existing ones. Investigations of this concept with ligands bearing a boron center in their skeleton established mechanistic pathways for the activation of small molecules in which the boron atom usually performs as an electrophile. Here, we show how this electrophilic behavior can be modified by the ligand trans to the boron center, evincing its ambiphilic nature. Treatment of diphosphinoboryl (PBP) nickel–methyl complex 1 with bis(catecholato)diboron (B₂Cat₂) allows for the synthesis of nickel(ii) bis-boryl complex 3 that promotes the clean and reversible heterolytic cleavage of dihydrogen leading to the formation of dihydroborate nickel complex 4. Density functional theory analysis of this reaction revealed that the heterolytic activation of H₂ is facilitated by the cooperation of both boryl moieties and the metal atom in a concerted mechanism that involves a Ni(ii)/Ni(0)/Ni(ii) process. Contrary to 1, the boron atom from the PBP ligand in 3 behaves as a nucleophile, accepting a formally protic hydrogen, whereas the catecholboryl moiety acts as an electrophile, receiving the attack from the hydride-like fragment. This manifests the dramatic change in the electronic properties of a ligand by tuning the substituent trans to it and constitutes an unprecedented cooperative mechanism that involves two boryl ligands in the same molecule operating differently, one as a Lewis acid and the other one as a Lewis base, in cooperation with the metal. In addition, reactivity towards different nucleophiles such as amines or ammonia confirmed the electrophilic nature of the Bcat moiety, allowing the formation of aminoboranes.

A bis(boryl)nickel complex promotes the facile and reversible activation of H₂ through a cooperative mechanism that involves the metal and both boryl moieties in a concerted five-center process.     

Broad-band spectroscopy of a vanadyl porphyrin: a model electronuclear spin qudit

We explore how to encode more than a qubit in vanadyl porphyrin molecules hosting a S = 1/2 electronic spin coupled to a I = 7/2 nuclear spin. The spin Hamiltonian and its parameters, as well as the spin dynamics, have been determined via a combination of electron paramagnetic resonance, heat capacity, magnetization and on-chip magnetic spectroscopy experiments performed on single crystals. We find low temperature spin coherence times of micro-seconds and spin relaxation times longer than a second. For sufficiently strong magnetic fields (B > 0.1 T, corresponding to resonance frequencies of 9–10 GHz) these properties make vanadyl porphyrin molecules suitable qubit realizations. The presence of multiple equispaced nuclear spin levels then merely provides 8 alternatives to define the ‘1’ and ‘0’ basis states. For lower magnetic fields (B < 0.1 T), and lower frequencies (<2 GHz), we find spectroscopic signatures of a sizeable electronuclear entanglement. This effect generates a larger set of allowed transitions between different electronuclear spin states and removes their degeneracies. Under these conditions, we show that each molecule fulfills the conditions to act as a universal 4-qubit processor or, equivalently, as a d = 16 qudit. These findings widen the catalogue of chemically designed systems able to implement non-trivial quantum functionalities, such as quantum simulations and, especially, quantum error correction at the molecular level.

We show that a sizeable electronuclear entanglement of the S = 1/2 and I = 7/2 spins of a vanadyl porphyrin provides the conditions to act as a universal 4-qubit processor, and thus implement quantum error correction at the molecular level.     

Unusual volumetric and hydration behavior of the catanionic system sodium undecenoate: sodecyltrimethylammonium bromide

Following the studies on the effect of double bonds in the surfactant hydrophobic tail on the formation of mixed surfactant aggregates, we studied the viscosity and density of the system Sodium 10-undecenoate (SUD)–decyltrimethylammonium bromide (DTAB)–water. We found that the partial molar volume (pmv) and intrinsic viscosity of both, micellised and unmicellised mixtures, are non-ideal, dependent on the mixture composition and related to structural changes in micelles. These phenomena are caused by the presence of the double bond at the distal extreme of the SUD molecule, which has some affinity with water by formation of hydrogen bonds. In particular, as far as we know, this is the first report on non-ideal behavior of the pmv in mixed micelles.     

The aqueous cationic system sodium undecenoate-dodecyltrimethylammonium bromide at low concentration

The aqueous sodium undecenoate (SUD) –dodecyltrimethylammonium bromide (DTAB) catanionic system was studied at low concentration. The system did not precipitate, even at a 1:1 SUD:DTAB proportion, but showed the formation of a coacervate in a range of surfactant mixture compositions. Micelles have a preferential composition of 0.37 mole fraction of SUD. This behavior is attributed to the presence of the double bond at the distal extreme of the SUD molecule, which can form hydrogen bonds with water. Consequently, the –CH=CH₂ group is situated at the interface between the hydrocarbon micelle core and water, reducing the interfacial free energy. Structural computations demonstrate that the mentioned SUD proportion produces complete coverage of the micelle surface by the double bonds.     

Hexaruthenium carbonyl cluster complexes with basal edge-bridged square pyramidal metallic skeleton: efficient synthesis of 2-imidopyridine derivatives and determination of their reactive sites in carbonyl substitution reactions

The reactions of [Ru(3)(CO)(12)] with half equivalent of 2-amino-6-methylpyridine (H(2)ampy) or 2-aminopyridine (H(2)apy) in refluxing xylene give the hexanuclear products [Ru(6)(mu(3)-H)(2)(mu(5)-eta(2)-L)(mu-CO)(2)(CO)(14)] (L = ampy, 1; apy, 2). These reactions represent the first high-yield syntheses of hexanuclear complexes with a basal edge-bridged square pyramidal metallic skeleton. Five metal atoms of these complexes are bridged by the N-donor ligand in such a way that the edge-bridging metal atom is attached to the pyridine nitrogen, while the basal atoms of the square pyramid are capped by an imido fragment that arises from the activation of both N-H bonds of the NH(2) group. The reactive sites of these complexes in CO substitution reactions have been determined by studying the reactivity of 1 with triphenylphosphine. Two kinetically controlled monosubstitutions take place on the edge-bridging metal atom in positions cis to the pyridine nitrogen, leading to a mixture of two isomers of formula [Ru(6)(mu(3)-H)(2)(mu(5)-eta(2)-ampy)(mu-CO)(2)(CO)(13)(PPh(3))] (3 and 4). On heating at 80 degrees C, these monosubstituted isomers are transformed, via a dissociative pathway, into the product of thermodynamic control (5), which has the PPh(3) ligand on the apical Ru atom. The di- and trisubstituted derivatives [Ru(6)(mu(3)-H)(2)(mu(5)-eta(2)-ampy)(mu-CO)(2)(CO)(12)(PPh(3))(2)] (6) and [Ru(6)(mu(3)-H)(2)(mu(5)-eta(2)-ampy)(mu-CO)(2)(CO)(11)(PPh(3))(3)] (7) are stepwise formed from 3-5 and PPh(3). Compound 6 has the PPh(3) ligands on the edge-bridging and apical Ru atoms, and compound 7 has an additional PPh(3) ligand on an unbridged basal Ru atom. The compound [Ru(6)(mu(3)-H)(2)(mu(5)-eta(2)-ampy)(mu-CO)(2)(CO)(12)(mu-dppm)] (8), in which a basal and the apical Ru atoms are spanned by the dppm ligand, has been isolated from the reaction of 1 with bis(diphenylphosphino)methane.