Electronic structure of neutral and monoanionic tris(benzene-1,2-dithiolato)metal complexes of molybdenum and tungsten

The reaction of 3 equiv of the ligand 2-mercapto-3,5-di-tert-butylaniline, H2[LN,S], or 3,5-di-tert-butyl-1,2-benzenedithiol, H2[LS,S], with 1 equiv of [MoO2(acac)2] or WCl6 (acac=acetonylacetate(1-)) in methanol or CCl4 afforded the diamagnetic neutral complexes [MoV(LN,S)2(L*N,S)]0 (1), [MoV(LS,S)2(L*S,S)] (2), and [WV(LS,S)2(L*S,S)] (3), where (L*N,S)- and (L*S,S)- represent monoanionic pi-radical ligands (Srad=1/2), which are the one-electron oxidized forms of the corresponding closed-shell dianions (LN,S)2- and (LS,S)2-. Complexes 1-3 are trigonal-prismatic members of the electron-transfer series [ML3]z (z=0, 1-, 2-). Reaction of 2 and 3 with [N(n-Bu)4](SH) in CH2Cl2 under anaerobic conditions afforded paramagnetic crystalline [N(n-Bu)4][MoV(LS,S)3] (4) and [N(n-Bu)4][WV(LS,S)3] (5). Complexes 1-5 have been characterized by X-ray crystallography. S K-edge X-ray absorption and infrared spectroscopy prove that a pi-radical ligand (L*S,S)- is present in neutral 2 and 3, whereas the monoanions [MV(LS,S)3]- contain only closed-shell dianionic ligands. These neutral species have previously been incorrectly described as [MVI(L)3]0 complexes with a MoVI or WVI (d0) central metal ion; they are, in fact MV (d1) (M=Mo, W) species: [MoV(LS,S)2(L*S,S)] and [WV(LS,S)2(L*S,S)] with a diamagnetic ground state St=0, which is generated by intramolecular, antiferromagnetic coupling between the MV (d1) central ion (SM=1/2) and a ligand pi radical (L*S,S)- (Srad=1/2).     

Iron complexes of new pentadentate ligands containing the 1,4,7-triazacyclononane-1,4-diacetate motif. spectroscopic, electro-, and photochemical studies

Three new pentadentate, pendent arm macrocycles containing the 1,4,7-triazacyclononane-1,4-diacetate motif have been synthesized, and their coordination chemistry with Fe(III) has been investigated. Eight new octahedral Fe(III) complexes containing chloro, azido, or mu-oxo ligands have been synthesized, five of which have been characterized by X-ray crystallography. Spectroscopic characterization of these octahedral Fe(III) complexes by UV-vis, IR, electrochemistry, EPR, magnetic susceptibility, and zero-field M?ssbauer measurements firmly establishes the high-spin state of the iron in all complexes. Electrochemistry studies of the azido-Fe(III) complexes show that they can be reversibly oxidized to the corresponding Fe(IV) species at -20 degrees C, and Fe(II), Fe(III), and Fe(IV) species show characteristic IR and UV-vis profiles. Photolysis of one of the azido complexes was studied as a function of temperature (room temperature vs 77 K) and wavelength (480, 419, and 330 nm). Photoreduction to a high-spin Fe(II) species occurs under all conditions, which is proposed to be the dominant photochemical pathway generally available to high-spin ferric azido complexes.     

Electronic structures of tris(dioxolene)chromium and tris(dithiolene)chromium complexes of the electron-transfer series [Cr(dioxolene)(3)](z) and [Cr(dithiolene)(3)](z) (z = 0, 1-, 2-, 3-). A combined experimental and density functional theoretical study

From the reaction mixture of 3,6-di-tert-butylcatechol, H2[3,6L(cat)], [CrCl3(thf)3], and NEt3 in CH3CN in the presence of air, the neutral complex [CrIII(3,6L*(sq))3] (S = 0) (1) was isolated. Reduction of 1 with [Co(Cp)2] in CH2Cl2 yielded microcrystals of [Co(Cp)2][CrIII(3,6L*(sq))2(3,6L(cat))] (S = 1/2) (2) where (3,6L*(sq)(1-) is the pi-radical monoanionic o-semiquinonate of the catecholate dianion (3,6Lcat)(2-). Electrochemistry demonstrated that both species are members of the electron-transfer series [Cr(3,6LO,O)]z (z = 0, 1-, 2-, 3-). The corresponding tris(benzo-1,2-dithiolato)chromium complex [N(n-Bu)4][CrIII(3,5L*S,S)2(3,5LS,S)] (S = 1/2) (3) has also been isolated; (3,5LS,S)(2-) represents the closed-shell dianion 3,5-di-tert-butylbenzene-1,2-dithiolate(2-), and (3,5L*S,S)(1-) is its monoanionic pi radical. Complex 3 is a member of the electron-transfer series [Cr(3,5L(S,S))3]z (z = 0, 1-, 2-, 3-). It is shown by Cr K-edge and S K-edge X-ray absorption, UV-vis, and EPR spectroscopies, as well as X-ray crystallography, of 1 and 3 that the oxidation state of the central Cr ion in each member of both electron-transfer series remains the same (+III) and that all redox processes are ligand-based. These experimental results have been corroborated by broken symmetry density functional theoretical calculations by using the B3LYP functional.     

Random-phase-approximation-based correlation energy functionals: benchmark results for atoms

The random phase approximation for the correlation energy functional of the density functional theory has recently attracted renewed interest. Formulated in terms of the Kohn-Sham orbitals and eigenvalues, it promises to resolve some of the fundamental limitations of the local density and generalized gradient approximations, as, for instance, their inability to account for dispersion forces. First results for atoms, however, indicate that the random phase approximation overestimates correlation effects as much as the orbital-dependent functional obtained by a second order perturbation expansion on the basis of the Kohn-Sham Hamiltonian. In this contribution, three simple extensions of the random phase approximation are examined; (a) its augmentation by a local density approximation for short-range correlation, (b) its combination with the second order exchange term, and (c) its combination with a partial resummation of the perturbation series including the second order exchange. It is found that the ground state and correlation energies as well as the ionization potentials resulting from the extensions (a) and (c) for closed subshell atoms are clearly superior to those obtained with the unmodified random phase approximation. Quite some effort is made to ensure highly converged data, so that the results may serve as benchmark data. The numerical techniques developed in this context, in particular, for the inherent frequency integration, should also be useful for applications of random phase approximation-type functionals to more complex systems.     

Modelling and Flatness‐Based Control of a Carriage Actuated by Pneumatic Muscles

Pneumatic muscles are innovative tension actuators consisting of textile‐fibre reinforced vulcanised rubber tubing and connection flanges at both ends. They offer several advantages as compared to pneumatic cylinders: significantly less weight, no moving parts within the muscle, and higher maximum force. The main drawback is given by their non‐linear characteristics demanding for sophisticated non‐linear feedback control schemes. This contribution presents a non‐linear control concept for a carriage driven by two pneumatic muscles in parallel connection. First, the modelling of the muscle driven carriage is described in detail. For the resulting non‐linear model the differential flatness property is proven and utilised for a decoupled position and pressure trajectory control. Experimental results from an implementation of this flatness‐based control scheme at a test rig demonstrate the high tracking performance and point out the potential of this new actuator. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimization of Nonlinear Mechanical Systems under Constraints with the Particle Swarm Method

In recent years, stochastic optimization methods have gained increasing attention in parameter optimization of mechanical systems. Most popular techniques are Evolutionary Computation and the Simulating Annealing algorithm, which are applied more frequently to mechanical problems due to the increasing computing resources available now. Since theses methods do not require any gradient information, they are well suited for non‐smooth or discontinuous optimization tasks occurring in nonlinear multibody systems. In addition to these techniques, Kennedy and Eberhart [5] introduced the Particle Swarm Optimization method (PSO) based on the simulation of bird flocking. In this work, the efficiency of an extended PSO algorithm has been compared with an Evolutionary Strategy (ES) [6] and an Adapted Simulated Annealing method (ASA) [4]. In order to solve optimization tasks with both equality and inequality constraints the PSO algorithm has been extended by the Augmented Lagrangian Multiplier Method [2]. The proposed method shows often superior results and is quite simple to implement. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Automatic differentiation of numerical integration algorithms

Automatic differentiation (AD) is a technique for automatically augmenting computer programs with statements for the computation of derivatives. This article discusses the application of automatic differentiation to numerical integration algorithms for ordinary differential equations (ODEs), in particular, the ramifications of the fact that AD is applied not only to the solution of such an algorithm, but to the solution procedure itself. This subtle issue can lead to surprising results when AD tools are applied to variable-stepsize, variable-order ODE integrators. The computation of the final time step plays a special role in determining the computed derivatives. We investigate these issues using various integrators and suggest constructive approaches for obtaining the desired derivatives.

     

Impact Analysis using Modal Reduction

In impact analysis, high frequency wave phenomena and plastic deformation are important effects. For numerical impact analysis including these effects, different models are presented based on modally reduced linear finite element models and nonlinear finite elements. The numerical results are verified by experimental investigations using Laser-Doppler-Vibrometers. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Eigenvalues of Half‐Linear Boundary Value Problems

We consider the half‐linear boundary value problem where and the weight function q is assumed to change sign. We prove the existence of two sequences , of eigenvalues and derive asymptotic estimates for as .