Coordination and organometallic chemistry of relevance to the rhodium-based catalyst for ethylene hydroamination

The RhCl(3)·3H(2)O/PPh(3)/nBu(4)PI catalytic system for the hydroamination of ethylene by aniline is shown to be thermally stable by a recycle experiment and by a kinetic profile study. The hypothesis of the reduction under catalytic conditions to a Rh(I) species is supported by the observation of a high catalytic activity for complex [RhI(PPh(3))(2)](2). New solution equilibrium studies on [RhX(PPh(3))(2)](2) (X = Cl, I) in the presence of ligands of relevance to the catalytic reaction (PPh(3), C(2)H(4), PhNH(2), X(-), and the model Et(2)NH amine) are reported. Complex [RhCl(PPh(3))(2)](2) shows broadening of the (31)P NMR signal upon addition of PhNH(2), indicating rapid equilibrium with a less thermodynamically stable adduct. The reaction with Et(2)NH gives extensive conversion into cis-RhCl(PPh(3))(2)(NHEt(2)), which is however in equilibrium with the starting material and free Et(2)NH. Excess NHEt(2) yields a H-bonded adduct cis-RhCl(PPh(3))(2)(Et(2)NH)···NHEt(2), in equilibrium with the precursors, as shown by IR spectroscopy. The iodide analogue [RhI(PPh(3))(2)](2) shows less pronounced reactions (no change with PhNH(2), less extensive addition of Et(2)NH with formation of cis-RhI(PPh(3))(2)(NHEt(2)), less extensive reaction of the latter with additional Et(2)NH to yield cis-RhI(PPh(3))(2)(Et(2)NH)···NHEt(2). The two [RhX(PPh(3))(2)](2) compounds do not show any evidence for addition of the corresponding X(-) to yield a putative [RhX(2)(PPh(3))(2)](-) adduct. The product of C(2)H(4) addition to [RhI(PPh(3))(2)](2), trans-RhI(PPh(3))(2)(C(2)H(4)), has been characterized in solution. Treatment of the RhCl(3)·3H(2)O/PPh(3)/nBu(4)PI/PhNH(2) mixture under catalytic conditions yields mostly [RhCl(PPh(3))(2)](2), and no significant halide exchange, demonstrating that the promoting effect of iodide must take place at the level of high energy catalytic intermediates. The equilibria have also been investigated at the computational level by DFT with treatment at the full QM level including solvation effects. The calculations confirm that the bridge splitting reaction is slightly less favorable for the iodido derivative. Overall, the study confirms the active role of rhodium(I) species in ethylene hydroamination catalyzed by RhCl(3)·3H(2)O/PPh(3)/nBu(4)PI and suggest that the catalyst resting state is [RhCl(PPh(3))(2)](2) or its C(2)H(4) adduct, RhCl(PPh(3))(2)(C(2)H(4)), under high ethylene pressure.     

Two types of coordination polymers based on cluster anions [Re4Q4(CN)12] (Q = S, Se) and cations of rare-earth metals Ln: Syntheses and crystal structures

The reactions of aqueous solutions of the tetrahedral cluster anions [Re₄Q₄(CN)₁₂]⁴⁻ (Q = S, Se) with lanthanide chlorides resulted in the crystallization of the formed compounds into two main structural types [{Ln(H₂O)₄(H₂O)_2/3Cl_1/3}₃{Re₄Q₄(CN)₁₂}₂]·2H₂O (Ln = La-Gd, Q = S, Se) and K_0.5(H)_0.5[{Ln(H₂O)₄}{Re₄S₄(CN)₁₂}]·nH₂O or (H)[{Ln(H₂O)₄}{Re₄Se₄(CN)₁₂}]·nH₂O (Ln = Tb-Lu). Compounds of the first type crystallize in the hexagonal crystal system (space group Р6₃/m) and they have a three-dimensional polymeric structure; compounds of the second type crystallize in the orthorhombic crystal system (space group Cmcm) and they have a two-dimensional crystal structure due to the polymeric anion {[{Ln(H₂O)₄}{Re₄Q₄(CN)₁₂}]⁻}_∞∞.     

Organometallic–inorganic charge transfer salts containing a cationic iron mixed sandwich and polyoxomolybdate anions: Syntheses,X-ray molecular structures and spectroscopic properties

Two new organometallic–inorganic charge transfer salts formulated as [(η⁵-Cp)Fe(η⁶-MeO-p-C₆H₄–NHNH₂)]₂[Mo₆O₁₉], 1, and [(η⁵-Cp)Fe(η⁶-MeO-p-C₆H₄–NHNH₂)]₄[β-Mo₈O₂₆], 2, were prepared through a metathesis reaction between the organometallic hydrazine precursor [(η⁵-Cp)Fe(η⁶-MeO-p-C₆H₄–NHNH₂)]⁺PF₆^? and either [n-Bu₄N]₂[Mo₆O₁₉] or [n-Bu₄N]₄[α-Mo₈O₂₆] in acetonitrile. In the second case, the [α-Mo₈O₂₆]^4? anion transforms into the [β-Mo₈O₂₆]^4? isomer. These organometallic–inorganic hybrids were characterized by spectroscopic techniques (IR, ¹H NMR and UV–vis). In addition, the UV–vis diffuse reflectance spectra of 1 and 2 in solid state exhibit a band at λ_max = 475 and 470 nm, respectively, not observed in DMSO solution, which have been attributed to a charge transfer transition. On the other hand, the solid state structure of 2, solved by X-ray diffraction analysis shows the formation of hydrogen bonds between the protons of the –NHNH₂ and C–H groups with the terminal oxo groups of the β-octamolybdate anions [β-Mo₈O₂₆]^4?. Finally, hybrid 3, formulated as [(η⁵-Cp)Fe(η⁶-C₆H₅OMe)]₄[β-Mo₈O₂₆] was prepared in EtOH under solvothermal conditions. The single crystal X-ray structure shows the elimination of the –NHNH₂ group from the organometallic mixed sandwich reducing its associative ability toward the oxo groups of the counterion only to the electrostatic interactions and to the very weak CH?O hydrogen bonds.     

Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction–diffusion problem

A semilinear reaction–diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter e²{\varepsilon^2} , is considered. It can have multiple solutions. The numerical computation of solutions having interior transition layers is analysed. It is demonstrated that the accurate computation of such solutions is exceptionally difficult. To address this difficulty, we propose an artificial-diffusion stabilization. For both standard and stabilised finite difference methods on suitable Shishkin meshes, we prove existence and investigate the accuracy of computed solutions by constructing discrete sub- and super-solutions. Convergence results are deduced that depend on the relative sizes of e{\varepsilon} and N, where N is the number of mesh intervals. Numerical experiments are given in support of these theoretical results. Practical issues in using Newton’s method to compute a discrete solution are discussed.     

Attracting cycles for the relaxed Newton’s method

We study the relaxed Newton’s method applied to polynomials. In particular, we give a technique such that for any n≥2, we may construct a polynomial so that when the method is applied to a polynomial, the resulting rational function has an attracting cycle of period n. We show that when we use the method to extract radicals, the set consisting of the points at which the method fails to converge to the roots of the polynomial p(z)=z^m−c (this set includes the Julia set) has zero Lebesgue measure. Consequently, iterate sequences under the relaxed Newton’s method converge to the roots of the preceding polynomial with probability one.     

Electron-deficient and polycenter bonds in the high-pressure γ-B28 phase of boron

The peculiar bonding situation in γ boron is characterized on the basis of an experimental electron-density distribution which is obtained by multipole refinement against low-temperature single-crystal x-ray diffraction data. A topological analysis of the electron-density distribution reveals one-electron-two-center bonds connecting neighboring icosahedral B(12) clusters. A unique polar-covalent two-electron-three-center bond between a pair of atoms of an icosahedral cluster and one atom of the interstitial B(12) dumbbell explains the observed charge separation in this high-pressure high-temperature polymorph of boron.     

A novel method for the synthesis of polystyrene-graft-silica particles using random copolymers based on styrene and triethoxyvinylsilane

In the present research, random copolymers based on triethoxyvinylsilane (TEVS) and styrene (St) are synthesized and structurally characterized. According to the reactivity ratios of the monomers determined by infrared analysis; St tends to form blocks whilst TEVS is expected to be incorporated as isolated units. A sample of poly(styrene-co-triethoxyvinylsilane) synthesized at low conversion using a monomer feeding ratio St:TEVS of 2:3 was used as macrosilane in the synthesis of polystyrene-g-silica particles. The grafting reaction was confirmed by infrared spectroscopy, thermogravimetric analysis and by the evaluation of the morphological characteristics of the hybrid particles.     

Photoinduced protonation and mechanical motion in the cyclodextrin cavity: Synthesis,structure and spectral properties of 4-(2-napthyl)pyridine and their pseudorotaxane complexes

The spontaneous and photoinduced protonation of 4-(2-naphthyl)pyridine (1) in solutions and in complexes with β-cyclodextrin (β-CD) and 2-hydroxypropyl-β-cyclodextrin (HP-β-CD) were studied by absorption and fluorescence spectroscopy. The structure and stability of the complexes (log K = 1.5–2.3) of 1, its protonated form 2, and quaternized derivative, 1-methyl-4-(2-naphthyl)pyridinium perchlorate (3), with β-CD and HP-β-CD were studied by ¹H NMR. It was shown that irrespective of the solution pH, compound 1 resides in the cyclodextrin cavity. HP-β-CD better binds the neutral form of 1 than β-CD, while naphthylpyridinium salts have approximately equal binding affinity to both cyclodextrins. The structures of salt 3 and pseudorotaxane complex 1@β-CD were determined by X-ray diffraction analysis. According to spectral data, pK_a of 1 in water is 5.12, which promotes protonation of nitrogen both in the ground state and in the excited state. As a consequence, the fluorescence spectrum exhibits only the protonated form with a lifetime of 15 ns. The addition of HP-β-CD to a solution of 1 results in inclusion complex 1@HP-β-CD; simultaneously pK_a of 1 decreases to 4.62 and non-protonated form fluorescence (NFF) of 1 with a lifetime of 1.25 ns appears. Thus, the residence of 1 in the HP-β-CD cavity hampers its protonation in the excited state. From comparison of the initial regions of fluorescence of 1 in solution and in the HP-β-CD complex after pulse excitation, a mechanism for appearance of short-lived NFF of 1 was proposed. Quantum chemical simulation of the protonation and complexation of 1 in the presence of water was performed. On the basis of results, reversible photoinduced mechanical motion of 1 in the HP-β-CD cavity was suggested.     

The Universal Multiplicative Envelope of the Free Malcev Superalgebra on One Odd Generator

A base of the universal multiplicative envelope for the free Malcev superalgebra on one odd generator is constructed. Some corollaries for central skew-symmetric elements in free Malcev and free alternative algebras are obtained. In particular, the Malcev Grassmann algebra is constructed.     

Harmonic vibration of prismatic shells in zero approximation of Vekua's hierarchical models

In this article elastic cusped symmetric prismatic shells (i.e., plates of variable thickness with cusped edges) in the zero approximation of I.Vekua's hierarchical models is considered. The well-posedness of the boundary value problems (BVPs) under the reasonable boundary conditions at the cusped edge and given displacements at the non-cusped edge is studied in the case of harmonic vibration. The approach works also for non-symmetric prismatic shells word for word. The classical and weak setting of the BVPs in the case of the zero approximation of hierarchical models is considered. Appropriate weighted functional spaces are introduced. Uniqueness and existence results for the variational problem are proved. The structure of the constructed weighted space is described and its connection with weighted Sobolev spaces is established. Moreover, some sufficient conditions for a linear functional arising in the right-hand side of the variational equation to be bounded are given.