Ti7Cl16 und Ti7Br16 sowie weitere Untersuchungen mit Titanhalogeniden. Al2X6 als Komplexbildner

Ti₇Cl₁₆ and Ti₇Br₁₆ and Further Investigations with Titanium Halides. Al₂X₆ as a Complex Forming Agent TiCl_3,s can be transported with Al₂Cl₆ via TiAlCl_6,g in a temperature gradient. The equilibrium of this reaction was studied by mass spectroscopy. There is no indication of the existence of a TiAl₂Cl₉ molecule as assumed in the literature. β-TiBr₃ was prepared from the elements in the presence of the transporting agent Al₂Br_6,g. The transport of TiCl₂ with Al₂Cl_6,g involves, as an important step, the disproportionation which is favoured by the reaction of Ti with the glass wall. If the disproportionation is made impossible by addition of Ti the novel compound Ti₇Cl₁₆ is obtained. Independent of Ti₇Cl₁₆, a phase TiCl_{(2 + x)} with a broad range of homogeneity exists. The compound Ti₇Br₁₆, being isostructural with Ti₇Cl₁₆, was also prepared. Results of magnetic measurements and observations on the thermal decomposition of the compounds are reported.     

Product angular distributions in the ultraviolet photodissociation of N2O

The angular distribution of products from the ultraviolet photodissociation of nitrous oxide yielding O((1)D) and N(2)(X Σ(g)(+)(1)) was investigated using classical trajectory calculations. The calculations modeled absorption only to the 2(1)A(') electronic state but used surface-hopping techniques to model nonadiabatic transitions to the ground electronic state late in the dissociation. Observed values of the anisotropy parameter β, which decrease as the product N(2) rotational quantum number j increases, could be well reproduced. The relatively low observed β values arise principally from nonaxial recoil due to the very strong bending forces present in the excited state. In the main part of the product rotational distribution near 203 nm, an unusual dynamical effect produces the decrease in β with increasing j; nonaxial recoil effects remain approximately constant while higher j product molecules arise from parent molecules that had their transition dipole moments aligned more closely along the molecular axis. In both low and high j tails of the rotational distribution, the variations in β with j are caused by changes in the extent of nonaxial recoil. In the high-j tail, additional torque present on the ground state potential energy surface following nonadiabatic transitions causes both the additional rotational excitation and the lower β values.     

Atropselective Dibrominations of a 1,1′‐Disubstituted 2,2′‐Biindolyl with Diverging Point‐to‐Axial Asymmetric Inductions. Deriving 2,2′‐Biindolyl‐3,3′‐diphosphane Ligands for Asymmetric Catalysis

On the ¹H NMR timescale, 2,2′‐biindolyls with (R)‐configured (1‐alkoxyprop)‐2‐yl, (1‐hydroxyprop)‐2‐yl, or (1‐siloxyprop)‐2‐yl substituents at C‐1 and C‐1′ are atropisomerically stable at <0 °C and interconvert at >30 °C. A 2,2′‐biindolyl (R,R)‐ 17 a of that kind and achiral (!) brominating reagents gave the atropisomerically stable 3,3′‐dibromobiindolyls (M)‐ and/or (P)‐ 18 a at best atropselectively—because of point‐to‐axial asymmetric inductions—and atropdivergently, exhibiting up to 95 % (M)‐ and as much (P)‐atropselectivity. This route to atropisomerically pure biaryls is novel and should extend to other substrates and/or different functionalizations. The dibromobiindolyls (M)‐ and (P)‐ 18 a furnished the biindolyldiphosphanes (M)‐ and (P)‐ 14 without atropisomerization. These syntheses did not require the resolution of a racemic mixture, which distinguishes them from virtually all biaryldiphosphane syntheses known to date. (M)‐ and (P)‐ 14 acted as ligands in catalytic asymmetric allylations and hydrogenations. Remarkably, the β‐ketoester rac‐ 25 c was hydrogenated trans‐selectively with 98 % ee; this included a dynamic kinetic resolution.     

Calculation of the frequencies and intensities in the infrared and raman spectra of cyclopropenone

By using the values of the vibrational frequencies of normal and deuterated cyclopropenone (II-d₀ , II-d₂ ) and ¹⁶ O-and ¹⁸ O-substituted dimethylcyclopropenone (III) as -well as the infrared and Raman intensities of II a consistent set of force constants has been derived for the cyclopropenone skeleton. The derived values show that the zwitterionic form makes a substantial contribution to the electronic ground state of the molecule. The combined frequency and intensity calculation - simulation of the infrared and the Raman spectrum - is shown to be a good method for making a proper assignment of calculated and observed vibrations and deriving realistic sets of force constants.     

A mass conservative well‐balanced reconstruction at wet/dry interfaces for the Godunov‐type shallow water model

This paper presents a novel mass conservative, positivity preserving wetting and drying treatment for Godunov‐type shallow water models with second‐order bed elevation discretization. The novel method allows to compute water depths equal to machine accuracy without any restrictions on the time step or any threshold that defines whether the finite volume cell is considered to be wet or dry. The resulting scheme is second‐order accurate in space and keeps the C‐property condition at fully flooded area and also at the wet/dry interface. For the time integration, a second‐order accurate Runge–Kutta method is used. The method is tested in two well‐known computational benchmarks for which an analytical solution can be derived, a C‐property benchmark and in an additional example where the experimental results are reproduced. Overall, the presented scheme shows very good agreement with the reference solutions. The method can also be used in the discontinuous Galerkin method. Copyright © 2016 John Wiley & Sons, Ltd.     

Small Periodic Solutions Generated by Sublinear Terms

The paper is concerned with Hopf bifurcations in systems of autonomous ordinary differential equations with a parameter. The principal distinction between usual theorems on Hopf bifurcations and our results is that here the linearized equation is degenerate and independent of the parameter. We present sufficient conditions for a parameter value to be a bifurcation point and analyze properties of small cycles arising in the vicinity of the equilibrium. Sublinear nonlinearities play the main role in the results obtained.     

A linearized Eulerian sound propagation model for studies of complex meteorological effects

Outdoor sound propagation is significantly affected by the topography (including ground characteristics) and the state of the atmosphere. The atmosphere on its part is also influenced by the topography. A sound propagation model and a flow model based on a numerical integration of the linearized Euler equations have been developed to take these interactions into account. The output of the flow model enables the calculation of the sound propagation in a three-dimensionally inhomogeneous atmosphere. Rigid, partly reflective, or fully absorptive ground can be considered. The linearized Eulerian (LE) sound propagation model has been validated by means of four different scenarios. Calculations of sound fields above rigid and grass-covered ground including a homogeneous atmosphere deviate from analytic solutions by < or = 1 dB in most parts of the computed domain. Calculations of sound propagation including wind and temperature gradients above rigid ground agree well with measured scale model data. Calculations of sound propagation over a screen including ground of finite impedance show little deviations to measured scale model data which are probably caused by an insufficient representation of the complex ground impedance. Further calculations included the effect of wind on shading by a screen. The results agree well with the measured scale model data.