Stereochemically non-rigid helical mercury(II) complexes

Reactions of the 1: 2 condensate (L) of benzil dihydrazone and 2-acetylpyridine with Hg(ClO4)(2) center dot xH(2)O and HgI2 yield yellow [HgL2](ClO4)(2) (1) and HgLI2 (2), respectively. Homoleptic 1 is a 8-coordinate double helical complex with a Hg(II)N-8 core crystallising in the space group Pbca with cell dimensions: a = 16.2250(3), b = 20.9563(7), c = 31.9886(11) angstrom. Complex 2 is a 4-coordinate single helical complex having a Hg(II)N2I2 core crystallising in the space group P2(1)/n with cell dimensions a = 9.8011(3), b = 17.6736(6), c = 16.7123(6) angstrom and b = 95.760(3). In complex 1, the N-donor ligand L uses all of its binding sites to act as tetradentate. On the other hand, it acts as a bidentate N-donor ligand in 2 giving rise to a dangling part. From variable temperature H-1 NMR studies both the complexes are found to be stereochemically non-rigid in solution. In the case of 2, the solution process involves wrapping up of the dangling part of L around the metal. (C) 2008 Elsevier B.V. All rights reserved.

Planning rigid body motions using elastic curves

This paper tackles the problem of computing smooth, optimal trajectories on the Euclidean group of motions SE(3). The problem is formulated as an optimal control problem where the cost function to be minimized is equal to the integral of the classical curvature squared. This problem is analogous to the elastic problem from differential geometry and thus the resulting rigid body motions will trace elastic curves. An application of the Maximum Principle to this optimal control problem shifts the emphasis to the language of symplectic geometry and to the associated Hamiltonian formalism. This results in a system of first order differential equations that yield coordinate free necessary conditions for optimality for these curves. From these necessary conditions we identify an integrable case and these particular set of curves are solved analytically. These analytic solutions provide interpolating curves between an initial given position and orientation and a desired position and orientation that would be useful in motion planning for systems such as robotic manipulators and autonomous-oriented vehicles.

Dimetallic complexes of macrocycles with two rigid dibenzofuran units as receptors for detection of anionic substrates

The hexaazamacrocycles [28](DBF)2N6 {cyclo[bis(4,6-dimethyldibenzo[b,d]furaniminoethyleneiminoethylene]} and [32](DBF)2N6 {cyclo[bis(4,6-dimethyldibenzo[b,d]furaniminopropyleneiminopropylene]} form stable dinuclear copper(II) complexes suitable to behave as receptors for several anionic substrates. These two receptors were used to study the binding interactions with several substrates, such as imidazole (Him) and some carboxylates [benzoate (bz−), oxalate (ox2−), malonate (mal2−), phthalate (ph2−), isophthalate (iph2−), and terephthalate (tph2−)] by spectrophotometric titrations and EPR spectroscopy in MeOH (or H2O):DMSO (1:1 v/v) solution. The largest association constant was found for ox2− with Cu2[32](DBF)2N64+, whereas for the aromatic dicarboxylate anions the binding constants follow the trend ph2− > iph2− > tph2−, i.e. decrease with the increase of the distance of the two binding sites of the substrate. On the other hand, the large blue shift of 68 nm observed by addition of Him to Cu2[32](DBF)2N64+ points out for the formation of the bridged CuimCu cascade complex, indicating this receptor as a potential sensor for the detection and determination of imidazole in solution. The X-band EPR spectra of the Cu2[28](DBF)2N64+ and Cu2[32](DBF)2N6]4+ complexes and the cascade complexes with the substrates, performed in H2O:DMSO (1:1 v/v) at 5 to 15 K, showed that the CuCu distance is slightly larger than the one found in crystal state and that this distance increases when the substrate is accommodated between the two copper centres. The crystal structure of [Cu2[28](DBF)2N6(ph)2]·CH3OH was determined by X-ray diffraction and revealed the two copper centres bridged by two ph2− anions at a Cu···Cu distance of 5.419(1) Å. Each copper centre is surrounded by three carboxylate oxygen atoms from two phthalate anions and three contiguous nitrogen atoms of the macrocycle in a pseudo octahedral coordination environment.

Rigid ferrocenophane and its metal complexes with transition and alkaline-earth metal ions

The rigid [6]ferrocenophane, L-1, was synthesised by condensation of 1,1'-ferrocene dicarbaldehyde with trans-1,2-diaminocyclohexane in high dilution at r.t. followed by reduction. When other experimental conditions were employed, the [6,6,6]ferrocenephane (L-2) was also obtained. Both compounds were characterised by single crystal X-ray crystallography. The protonation of L-1 and its metal complexation were evaluated by the effect on the electron-transfer process of the ferrocene (fc) unit of L-1 using cyclic voltammetry (CV) and square wave voltammetry (SWV) in anhydrous CH3CN solution and in 0.1 M (Bu4NPF6)-Bu-n as the supporting electrolyte. The electrochemical process of L-1 between 300 and 900 mV is complicated by amine oxidation. On the other hand, an anodic shift from the fc/fc(+) wave of L-1 of 249, 225, 81 and 61 mV was observed by formation of Zn2+, Ni2+, Pd2+ and Cu2+ complexes, respectively. Whereas Mg2+ and Ca2+ only have with L-1 weak interactions and they promote the acid-base equilibrium of L-1. This reveals that L-1 is an interesting molecular redox sensor for detection of Zn2+ and Ni2+, although the kinetics of the Zn2+ complex formation is much faster than that of the Ni2+ one. The X-ray crystal structure of [(PdLCl2)-Cl-1] was determined and showed a square-planar environment with Pd(II) and Fe(II) centres separated by 3.781(1) angstrom. The experimental anodic shifts were elucidated by DFT calculations on the [(MLCl2)-Cl-1] series and they are related to the nature of the HOMO of these complexes and a four-electron, two-orbital interaction.

Peptidomimetic design of unusual turns by incorporating flexible and rigid omega-amino acids simultaneously

The tripeptides Boc-Gly-Aib-m-ABA-OMe (I), Boc-beta Ala-Aib-m-ABA-OMe (II) and Boc-gamma Abu-Aib-rn-ABA-OMe (III) (Aib: alpha-aminoisobutyric acid, beta Ala: beta-alanine, gamma Abu: gamma-aminobutyric acid, m-ABA: meta-aminobenzoic acid) with homologated amino acids at the N-terminus, the rigid gamma-amino acid m-ABA at the C-terminus and the helicogenic Aib at the central position have been chosen to create unusual turns. Single crystal X-ray diffraction studies, solvent dependent NMR titrations and 2D NMR analysis reveal that peptides II and III adopt unusual turns of 11- and 12-membered rings stabilized by modified 4 -> 1 type intramolecular hydrogen bonds. Solution phase studies indicate that peptide I exists in the beta-turn conformation stabilized by 10-membered intramolecular hydrogen bonding.

Rigid body trajectories in different 6D spaces

The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

Padé approximants for the acoustical properties of rigid frame porous media with pore size distributions

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with fixed cross-sectional shape, but of variable pore size distribution. The lowand high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coefficients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade´ approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned

Padé approximants for the acoustical characteristics of rigid frame porous media

In this paper it is shown that a number of theoretical models of the acoustical properties of rigid frame porous media, especially those involving ratios of Bessel functions of complex argument, can be accurately approximated and greatly simplified by the use of Padé approximation techniques. In the case of the model of Attenborough [J. Acoust. Soc. Am. 81, 93–102 (1987)] rational approximations are produced for the characteristic impedance, propagation constant, dynamic compressibility, and dynamic density, as a function of frequency and the material parameters. The model proposed by Stinson and Champoux