Mechanism of the mild functionalization of arenes by diboron reagents catalyzed by iridium complexes. Intermediacy and chemistry of bipyridine-ligated iridium trisboryl complexes

This paper describes mechanistic studies on the functionalization of arenes with the diboron reagent B(2)pin(2) (bis-pinacolato diborane(4)) catalyzed by the combination of 4,4'-di-tert-butylbipyridine (dtbpy) and olefin-ligated iridium halide or olefin-ligated iridium alkoxide complexes. This work identifies the catalyst resting state as [Ir(dtbpy)(COE)(Bpin)(3)] (COE = cyclooctene, Bpin = 4,4,5,5-tetramethyl-1,3,2-dioxaborolanyl). [Ir(dtbpy)(COE)(Bpin)(3)] was prepared by independent synthesis in high yield from [Ir(COD)(OMe)](2), dtbpy, COE, and HBpin. This complex is formed in low yield from [Ir(COD)(OMe)](2), dtbpy, COE, and B(2)pin(2). Kinetic studies show that this complex reacts with arenes after reversible dissociation of COE. An alternative mechanism in which the arene reacts with the Ir(I) complex [Ir(dtbpy)Bpin] after dissociation of COE and reductive elimination of B(2)pin(2) does not occur to a measurable extent. The reaction of [Ir(dtbpy)(COE)(Bpin)(3)] with arenes and the catalytic reaction of B(2)pin(2) with arenes catalyzed by [Ir(COD)(OMe)](2) and dtbpy occur faster with electron-poor arenes than with electron-rich arenes. However, both the stoichiometric and catalytic reactions also occur faster with the electron-rich heteroarenes thiophene and furan than with arenes, perhaps because eta(2)-heteroarene complexes are more stable than the eta(2)-arene complexes and the eta(2)-heteroarene or arene complexes are intermediates that precede oxidative addition. Kinetic studies on the catalytic reaction show that [Ir(dtbpy)(COE)(Bpin)(3)] enters the catalytic cycle by dissociation of COE, and a comparison of the kinetic isotope effects of the catalytic and stoichiometric reactions shows that the reactive intermediate [Ir(dtbpy)(Bpin)(3)] cleaves the arene C-H bond. The barriers for ligand exchange and C-H activation allow an experimental assessment of several conclusions drawn from computational work. Most generally, our results corroborate the conclusion that C-H bond cleavage is turnover-limiting, but the experimental barrier for this bond cleavage is much lower than the calculated barrier.     

Grand canonical ensemble approach to electrochemical thermodynamics,kinetics, and model Hamiltonians

The unique feature of electrochemistry is the ability to control reaction thermodynamics and kinetics by the application of electrode potential. Recently, theoretical methods and computational approaches within the grand canonical ensemble (GCE) have enabled to explicitly include and control the electrode potential in first principles calculations. In this review, recent advances and future promises of GCE density functional theory and rate theory are discussed. Particular focus is devoted to considering how the GCE methods either by themselves or combined with model Hamiltonians can be used to address intricate phenomena such as solvent/electrolyte effects and nuclear quantum effects to provide a detailed understanding of electrochemical reactions and interfaces.     

On Generating Discrete Orthogonal Bivariate Polynomials

In this paper we present an algorithm for recursively generating orthogonal bivariate polynomials on a discrete set S ². For this purpose we employ commuting pairs of real symmetric matrices H, K ^n×n to obtain, in a certain sense, a two dimensional Hermitian Lanczos method. The resulting algorithm relies on a recurrence having a slowly growing length. Practical implementation issues an applications are considered. The method can be generalized to compute orthogonal polynomials depending on an arbitrary number of variables.     

Wave equation for generalized Zener model containing complex order fractional derivatives

We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. The initial boundary value problem for such materials is formulated and solution is presented in the form of convolution. Two specific examples are analyzed.     

How Fear of Future Outcomes Affects Social Dynamics

Journal of Statistical Physics - Mutualistic relationships among the different species are ubiquitous in nature. To prevent mutualism from slipping into antagonism, a host often invokes a...     

Prediction of elastic strain recovery of a formed steel sheet considering stiffness degradation

The aim of this work is to show first, how the springback of a steel sheet drawn part is affected by the stiffness degradation, as it results from the damage evolved during forming process, and second, to build a respective modeling approach to take this degradation into account. For the consideration of the orthotropic elastic properties degradation we develop an approach, based on the Mori-Tanaka theory, where damage is considered by inclusion of ellipsoidal cavities. The respective void shape evolution is proposed to be identified with the measurements of elastic modulus in two perpendicular directions during the uniaxial tensile test of a flat specimen at different loading stages. The proposed approach is coupled with the Gurson-Tvergaard-Needleman (GTN) plastic potential, though it could be substituted by almost any other continuum damage model. At the end the presented approach is experimentally validated by a simple springback test, developed by authors. A very good agreement between by calculation predicted and measured springback amount is observed.     

Integration of self-consistent polycrystal plasticity with dislocation density based hardening laws within an implicit finite element framework: Application to low-symmetry metals

We present an implementation of the viscoplastic self-consistent (VPSC) polycrystalline model in an implicit finite element (FE) framework, which accounts for a dislocation-based hardening law for multiple slip and twinning modes at the micro-scale grain level. The model is applied to simulate the macro-scale mechanical response of a highly anisotropic low-symmetry (orthorhombic) crystal structure. In this approach, a finite element integration point represents a polycrystalline material point and the meso-scale mechanical response is obtained by the mean-field VPSC homogenization scheme. We demonstrate the accuracy of the FE-VPSC model by analyzing the mechanical response and microstructure evolution of α-uranium samples under simple compression/tension and four-point bending tests. Predictions of the FE-VPSC simulations compare favorably with experimental measurements of geometrical changes and microstructure evolution. Specifically, the model captures accurately the tension–compression asymmetry of the material associated with twinning, as well as the rigidity of the material response along the hard-to-deform crystallographic orientations.     

Shear stress analysis in engineering beams using deplanation field of special 2-D finite elements

This paper deals with the 2-D finite element shear stress analysis in beams, loaded by bending with shear and St. Venant’s torsion. The properties of these finite elements, like stiffness matrices as well as load vectors, are derived on the basis of their axial nodal displacements, e.g. by warping field. Proposed finite elements enable stress analysis independently of both cross-sectional member shape and material properties. Stiffness matrices and load vectors are derived for several finite element types. Material is assumed to be isotropic and linear elastic. For justification of the proposed stress analysis procedure, some examples are presented.