The roles of ligands proton affinity, π-back donation and metal fragment hardness on the Au–N bond in N-donor heterocycles gold(III) complexes

A DFT study on the Au–N interaction for some groups of N-donor heterocycles L {L = pyridines (py), pyrimidines (pm), imidazoles (im), pyrazoles (pz) and isoxazoles (io)} in neutral AuX₃L complexes {AuX₃ = AuBr₃, AuCl₃, trans-AuCl(CN)₂, Au(CN)₃} is reported. Linear relationships between the AuX₃ Mulliken charge in AuX₃L and the computed proton affinity (PA) of the heterocycle were found for all the considered ligands. The different slopes found on changing the N-donor species represent a measure of the π-acidity of these nitrogen ligands once coordinated to the metal centre, by the consequence a π-acceptor ability scale has been derived. The π-acceptor ability of the 5-membered N-donor ligands resulted in all the cases greater than that of the 6-membered N-heterocycles. The proton affinity average value corresponding to a zero charge of the AuX₃ and L fragments in the AuX₃L species has been estimated. This parameter represents the minimum PA value for the formation of a bond between the N-heterocycles and gold(III) and it does not depend on the electronic features of the coordinated ligands. The sensitivity of the AuX₃ fragments towards ligands PA variations follows the order Au(CN)₃ < trans-AuCl(CN)₂ < AuCl₃ < AuBr₃ and this last result has been explained on the basis of the metal fragments relative hardness.     

Micro‐Raman investigations on inclusions of unusual habit in a commercial tanzanite gemstone

The vibrational properties of submillimetre size inclusions of unusual habit in a commercial tanzanite gemstone were investigated by confocal Raman microspectroscopy with the aim of probing both their chemical composition and crystal structure. Highly contrasted Raman spectra were recorded in confocal conditions from several inclusions incorporated at different depths, ranging between a few microns to some tens of microns beneath the gemstone surface. The observed spectral features were identified as specific markers of hematite (α‐Fe₂O₃). Their unambiguous assignment has been inferred by comparing our experimental findings with the literature data recorded either in single crystals of hematite or in other iron oxides and oxyhydroxides. Our results rule out the presence of any pseudomorphic variety of hematite in the investigated gemstone, while confocal micro‐Raman spectroscopy definitively proved itself as a very reliable, relatively costless and noninvasive tool for unambiguous identification of subsurface regions of gemstones. Copyright © 2011 John Wiley & Sons, Ltd.     

REPRINT OF: A quasiseparable approach to five-diagonal CMV and Fiedler matrices

Recent work in the characterization of structured matrices in terms of characteristic polynomials of principal submatrices is furthered in this paper. Some classical classes of matrices with quasiseparable structure include tridiagonal (related to real orthogonal polynomials) and banded matrices, unitary Hessenberg matrices (related to Szegö polynomials), and semiseparable matrices, as well as others. Hence working with the class of quasiseparable matrices provides new results which generalize and unify classical results.Previous work has focused on characterizing (H,1)-quasiseparable matrices, matrices with order-one quasiseparable structure that are also upper Hessenberg. In this paper, the authors introduce the concept of a twist transformation, and use such transformations to explain the relationship between (H,1)-quasiseparable matrices and the subclass of (1,1)-quasiseparable matrices (without the upper Hessenberg restriction) which are related to the same systems of polynomials. These results generalize the discoveries of Cantero, Fiedler, Kimura, Moral and Velázquez of five-diagonal matrices related to Horner and Szegö polynomials in the context of quasiseparable matrices.     

Deactivation processes of homogeneous Pd catalysts using in situ time resolved spectroscopic techniques

UV-Vis, combined with ED-XAFS shows, for the first time, the evolution of inactive Pd dimers and trimers, that are a possible first stage in the deactivation process of important palladium catalysed reactions, leading to larger palladium clusters and eventually palladium black.     

[2‐(2‐{Bis[2‐(1H‐imidazol‐2‐ylmethyleneamino)ethyl]amino}ethyliminomethyl)imidazolido]cobalt(III) bis(tetrafluoridoborate) monohydrate

The title compound, [Co(C₁₈H₂₃N₁₀)](BF₄)₂·H₂O, is the result of complexing a Co cation (initially in a Co^II state) with tris[2‐(1H‐imidazol‐2‐ylmethyleneamino)ethyl]amine (L), obtained by a condensation process involving imidazole‐2‐carbaldehyde and tris(2‐aminoethyl)amine. Both the Co cation and the ligand were modified in the synthesis process, the cation via oxidation to Co^III, and the ligand via deprotonation to convert it into the 2‐(2‐{bis[2‐(1H‐imidazol‐2‐ylmethyleneamino)ethyl]amino}ethyliminomethyl)imidazolide anion (L⁻). The ligand chelates the metal centre in a hexadentate fashion, forming a slightly distorted octahedral CoN₆ chromophore. Packing is governed by N—H...N hydrogen bonds defining zigzag chains. A similar structure in the literature is discussed, and the wrong assignment of the oxidation state, given therein to the Co cation, is corrected.     

Shock-fitting method for two-dimensional inviscid,steady supersonic flows in ducts

Summary A numerical technique to solve the Euler equations for two-dimensional, steady, inviscid, supersonic flows in ducts is presented. The technique is second-order accurate and is based on the-scheme plus shock-fitting method. Many cases have been tested. The method used and the results obtained demonstrate the versatility of the technique specially if confronted with analogous methods that use shock-capturing techniques.

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Sommario Viene presentato un metodo numerico per l'integrazione delle equazioni di Eulero per flussi supersonici, bidimensionali, stazionari, non-viscosi in condotti. La tecnica, che possiede una accuratezza del secondo ordine, è basata sui metodi del-scheme e dello shock-fitting. Molti sono stati i casi provati. Il metodo usato ed i risultati ottenuti dimostrano la versatilità della tecnica, specialmente se confrontata con metodi analoghi che fanno uso di tecniche shock-capturing.

     

The Three-Component Defocusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions

We present a rigorous theory of the inverse scattering transform (IST) for the three-component defocusing nonlinear Schrödinger (NLS) equation with initial conditions approaching constant values with the same amplitude as \({x\to\pm\infty}\). The theory combines and extends to a problem with non-zero boundary conditions three fundamental ideas: (i) the tensor approach used by Beals, Deift and Tomei for the n-th order scattering problem, (ii) the triangular decompositions of the scattering matrix used by Novikov, Manakov, Pitaevski and Zakharov for the N-wave interaction equations, and (iii) a generalization of the cross product via the Hodge star duality, which, to the best of our knowledge, is used in the context of the IST for the first time in this work. The combination of the first two ideas allows us to rigorously obtain a fundamental set of analytic eigenfunctions. The third idea allows us to establish the symmetries of the eigenfunctions and scattering data. The results are used to characterize the discrete spectrum and to obtain exact soliton solutions, which describe generalizations of the so-called dark-bright solitons of the two-component NLS equation.     

Approximate reconstruction of bandlimited functions for the integrate and fire sampler

In this paper we study the reconstruction of a bandlimited signal from samples generated by the integrate and fire model. This sampler allows us to trade complexity in the reconstruction algorithms for simple hardware implementations, and is specially convenient in situations where the sampling device is limited in terms of power, area and bandwidth. Although perfect reconstruction for this sampler is impossible, we give a general approximate reconstruction procedure and bound the corresponding error. We also show the performance of the proposed algorithm through numerical simulations.