Rhodium- and palladium-catalyzed 1,5-substitution reactions of 2-en-4-yne acetates and carbonates with organoboronic acids

Two methods involving the rhodium-catalyzed reaction of 2-en-4-yne acetates and the palladium-catalyzed reaction of 2-en-4-yne carbonates with organoboronic acids were investigated; both afforded exclusively the (E)-configured vinylallenes. The coordinative interaction of the rhodium with the acetate group promoted the δ-elimination of Rh(I)-OAc from the alkenylrhodium intermediate II in both syn and anti modes, with the syn-elimination being the major path. DFT calculations revealed that a conformer of this intermediate (II), which can lead to the (E)-configured vinylallene product via the syn-elimination mode, is energetically the most favorable conformer. The rhodium-catalyzed procedure is not applicable to reactions involving (E)-configured enyne acetates, because the geometry of the alkenylrhodium intermediate that is derived from the corresponding (E)-enyne acetate would not allow such coordinative interaction to occur. The palladium-catalyzed method, which proceeds through formation of the σ-vinylallenylpalladium intermediate, B, is suitable for both the (E)- and (Z)-configured enyne carbonates and appears to have a wider scope for both organoboronic acids and enyne substrates. The palladium-catalyzed reaction of an enantiomerically enriched enyne carbonate proceeded with racemization.     

Raman spectroscopic study of tungsten(VI) oxosulfato complexes in WO3-K2S2O7-K2SO4 molten mixtures: stoichiometry, vibrational properties, and molecular structure

The dissolution reaction of WO3 in pure molten K2S2O7 and in molten K2S2O7-K2SO4 mixtures is studied under static equilibrium conditions in the XWO3(0) = 0-0.33 mol fraction range at temperatures up to 860 °C. High temperature Raman spectroscopy shows that the dissolution leads to formation of W(VI) oxosulfato complexes, and the spectral features are adequate for inferring the structural and vibrational properties of the complexes formed. The band characteristics observed in the W=O stretching region (band wavenumbers, intensities, and polarization characteristics) are consistent with a dioxo W(=O)2 configuration as a core unit within the oxosulfato complexes formed. A quantitative exploitation of the relative Raman intensities in the binary WO3-K2S2O7 system allows the determination of the stoichiometric coefficient, n, of the complex formation reaction WO3 + nS2O7(2-) --> C(2n-). It is found that n = 1; therefore, the reaction WO3 + S2O7(2-) > WO2(SO4)2(2-) with six-fold W coordination is proposed as fully consistent with the observed Raman features. The effects of the incremental dissolution and presence of K2SO4 in WO3-K2S2O7 melts point to a WO3 · K2S2O7 · K2SO4 stoichiometry and a corresponding complex formation reaction in the ternary molten WO3-K2S2O7-K2SO4 system according to WO3 + S2O7(2-) + SO4(2-) --> WO2(SO4)3(4-). The coordination sphere of W in WO2(SO4)2(2-) (binary system) is completed with two oxide ligands and two chelating sulfate groups. A dimeric [{WO2(SO4)2}2(μ-SO4)2](8-) configuration is proposed for the W oxosulfato complex in the ternary system, generated from inversion symmetry of aWO2(SO4)3(4-) moiety resulting in two bridging sulfates. The most characteristic Raman bands for the W(VI) oxosulfato complexes pertain to W(=O)2 stretching modes (i) at 972 (polarized) and 937 (depolarized) cm(-1) for the ν(s) and ν(as) W(=O)2 modes of WO2(SO4)2(2-), and (ii) at 933 (polarized) and 909 (depolarized) cm(-1) for the respective modes of [{WO2(SO4)2}2(μ-SO4)2](8-).     

Spectral Diffusion of Single Molecules in a Hierarchical Energy Landscape

Spectral diffusion as a result of both the transitions between different molecular conformers and the ′′molecular softness′′ of quasi‐free perylene diimides on a SiO₂ surface is investigated by means of single‐molecule spectroscopy, which reveals the time dependence of both the fluorescence spectra and the three‐dimensional orientation. Spectral wavelengths of all single emitters cover a wide energy range of about 0.27 eV, which is due to different types of conformers with large differences in optical transition energy. Time‐dependent spectral trajectories of single emitters within this wavelength manifold are evaluated with a model transcribed from the analysis of spatial diffusion. Spectral diffusion processes are closely correlated with fluorescence emission and excitation power. The overall analysis of spectral diffusion reveals, similar to proteins, a hierarchy of energy barriers in a broad energy landscape.     

Reverse inequalities for zonoids and their application

We prove inequalities for mixed volumes of zonoids with isotropic generating measures. A special case is an inequality for zonoids that is reverse to the generalized Urysohn inequality, between mean width and another intrinsic volume; here the equality case characterizes parallelepipeds. We apply this to a question from stochastic geometry. It is known that among the stationary Poisson hyperplane processes of given positive intensity in n-dimensional Euclidean space, the ones with rotation invariant distribution are characterized by the fact that they yield, for k∈{2,…,n}, the maximal intensity of the intersection process of order k. We show that, if the kth intersection density is measured in an affine-invariant way, the processes of hyperplanes with only n fixed directions are characterized by a corresponding minimum property.     

Graph problems arising from parameter identification of discrete dynamical systems

This paper focuses on combinatorial feasibility and optimization problems that arise in the context of parameter identification of discrete dynamical systems. Given a candidate parametric model for a physical system and a set of experimental observations, the objective of parameter identification is to provide estimates of the parameter values for which the model can reproduce the experiments. To this end, we define a finite graph corresponding to the model, to each arc of which a set of parameters is associated. Paths in this graph are regarded as feasible only if the sets of parameters corresponding to the arcs of the path have nonempty intersection. We study feasibility and optimization problems on such feasible paths, focusing on computational complexity. We show that, under certain restrictions on the sets of parameters, some of the problems become tractable, whereas others are NP-hard. In a similar vein, we define and study some graph problems for experimental design, whose goal is to support the scientist in optimally designing new experiments.     

Small faces in stationary Poisson hyperplane tessellations

We consider the tessellation induced by a stationary Poisson hyperplane process in d‐dimensional Euclidean space. Under a suitable assumption on the directional distribution, and measuring the k‐faces of the tessellation by a suitable size functional, we determine a limit distribution for the shape of the typical k‐face, under the condition of given size and this tending to zero. The limit distribution is concentrated on simplices. This extends a result of Gilles Bonnet.     

Spin-orbit interaction in molecular photoelectron spectra An intermediate coupling approach

A new and general semiempirical method for calculating ionization energies of molecules containing heavy atoms is presented. The extended Hückel hamiltonian is amended with a phenomenological one-electron spin-orbit interaction operator, and ionization energies are equated to orbital energies according to Koopmans' theorem. Calculations are presented for molecules with Br and I as heavy atoms. The systems considered are the hydrogen halides, diatomic halogens and interhalogens, haloacetylenes, halomethanes, and boron trihalides. Good agreement with the observed spin-orbit splitting is obtained. New assignments are proposed for the trihalides considered.     

BEEM-π calculations for a series of pyridines and their 14N N.Q.R.

The ⁵⁷Fe Mössbauer spectrum of a powdered sample of phthalocyanine-iron(II) in an applied magnetic field of 3·0 teslas has been measured as a function of temperature in the range 4·2 K to 100 K. Measurements have also been made at 4·2 K with 6·0 teslas applied, and on a single crystal specimen at 4·2 K with 3·0 teslas applied. Independent computer fits to the three measurements taken at 4·2 K were found to be consistent with one another, and showed that detailed information concerning magnetic anisotropy can be obtained even from powdered samples of paramagnets by Mössbauer spectroscopy. Although the asymmetry parameter in the electric field gradient tensor was found to be small, there was a significant departure from tetragonal symmetry in the magnetic properties of the molecule. The magnetic hyperfine field at the ⁵⁷Fe nucleus was found to be positive in all directions, indicating that all three electronic g values are significantly greater than 2·0.