First Bis(σ)-borane Complexes of Group 6 Transition Metals: Experimental and Theoretical Studies

A series of bis(σ)-borane complexes of Group 6 transition metals were prepared by direct dihydroborane coordination to the metal center. Reaction of [M(CO)₃(PCy₃)₂] and two dihydroboranes [DurBH₂] and [(Me₃Si)₂NBH₂] (Dur=2,3,5,6-Me₄C₆H) yielded bis(σ)-borane complexes fac-[M(CO)₃(PCy₃){η²-(H₂BR)}] (R=Dur; 1 : M=Cr, 2 : M=W; R=N(SiMe₃)₂; 3 : M=Cr, 4 : M=W). In the case of molybdenum, we have isolated an arene complex ( 5 ) with [DurBH₂] in which the Dur group acts as a η⁶-bound ligand, and with [(Me₃Si)₂NBH₂] a similar bis(σ)-borane complex was isolated, cis,trans-[Mo(CO)₂(PCy₃)₂{η²-(H₂BN(SiMe₃)₂}] ( 6 ), with a different pattern of auxiliary ligands. The complexes were investigated by multinuclear NMR spectroscopy, mass spectrometry, X-ray diffraction analysis, and computational methods. Quantum theory of atoms in molecules (QTAIM) calculations demonstrated that the borane complexes may be described as pure bis(σ)-borane complexes rather than elongated or stretched examples given that the calculations do not show the presence of a ring-critical point (RCP) at the ring formed by the interactions of the B−H with metal center.     

Preparation and Characterization of a π-Conjugated Donor–Acceptor System Containing the Strongly Electron-Accepting Tetraphenylborolyl Unit

A novel thiophene-bridged donor–acceptor system was synthesized with a carbazole as donor and a borole as acceptor unit. The borole group was successfully installed via the tin–boron exchange reaction of 1,1-dimethyl-2,3,4,5-tetraphenylstannole with 9-(5-(dibromoboryl)thiophen-2-yl)carbazole. The effect of the borole on the optoelectronic properties of the donor–acceptor system was explored by spectroscopic (UV/Vis and fluorescence spectroscopy), electrochemical (cyclic voltammetry) and theoretical (TD-DFT) methods as well as by modifying its structure. The corresponding donor–acceptor compound bearing the widely employed dimesitylboryl acceptor group was also synthesized for comparison.     

Synthesis and Characterization of Liquid-Crystalline Tetraoxapentacene Derivatives Exhibiting Aggregation-Induced Emission

A series of new tetrakis(dialkoxyphenyl) dicyanotetraoxapentacene derivatives ( 1 a – c ) were prepared by reaction of the appropriate terphenyl diols with tetrafluoroterephthalonitrile in good yields. Compounds 1 b and 1 c , which bear hexyloxy and decyloxy side chains, exhibited columnar hexagonal mesophases, as shown by polarized optical microscopy, variable-temperature powder X-ray diffraction, and differential scanning calorimetry. Single-crystal X-ray diffraction of methoxy-substituted 1 a revealed that the dicyanotetraoxapentacene core is highly planar, consistent with the notion that these molecules are able to stack in columnar mesophases. A detailed photophysical characterization showed that these compounds exhibit aggregation-induced emission in solution, emission in nonpolar solvents, weak emission in polar solvents, and strong emission in the solid state both as powder and in thin films. These observations are consistent with a weakly emissive charge-transfer state in polar solvents and a more highly emissive locally excited state in nonpolar solvents.     

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This paper presents a framework for incorporating arbitrary implicit multistep schemes into the lattice Boltzmann method. While the temporal discretization of the lattice Boltzmann equation is usually derived using a second-order trapezoidal rule, it appears natural to augment the time discretization by using multistep methods. The effect of incorporating multistep methods into the lattice Boltzmann method is studied in terms of accuracy and stability. Numerical tests for the third-order accurate Adams-Moulton method and the second-order backward differentiation formula show that the temporal order of the method can be increased when the stability properties of multistep methods are considered in accordance with the second Dahlquist barrier.     

The degenerate C. Neumann system I: symmetry reduction and convexity

The C. Neumann system describes a particle on the sphere S ⁿ under the influence of a potential that is a quadratic form. We study the case that the quadratic form has ℓ +1 distinct eigenvalues with multiplicity. Each group of m _σ equal eigenvalues gives rise to an O(m _σ )-symmetry in configuration space. The combined symmetry group G is a direct product of ℓ + 1 such factors, and its cotangent lift has an Ad*-equivariant momentum mapping. Regular reduction leads to the Rosochatius system on S ^ℓ , which has the same form as the Neumann system albeit for an additional effective potential.     

Generating Hyperbolic Singularities in Semitoric Systems Via Hopf Bifurcations

Let \((M,\Omega )\) be a connected symplectic 4-manifold and let \(F=(J,H) :M\rightarrow \mathbb {R}^2\) be a completely integrable system on M with only non-degenerate singularities. Assume that F does not have singularities with hyperbolic blocks and that \(p_1,\ldots ,p_n\) are the focus–focus singularities of F. For each subset \(S=\{i_1,\ldots ,i_j\}\), we will show how to modify F locally around any \(p_i, i \in S\), in order to create a new integrable system \(\widetilde{F}=(J, \widetilde{H}) :M \rightarrow \mathbb {R}^2\) such that its classical spectrum \(\widetilde{F}(M)\) contains j smooth curves of singular values corresponding to non-degenerate transversally hyperbolic singularities of \(\widetilde{F}\). Moreover the focus–focus singularities of \(\widetilde{F}\) are precisely \(p_i\), \(i \in \{1,\ldots ,n\} \setminus S\). The proof is based on Eliasson’s linearization theorem for non-degenerate singularities, and properties of the Hamiltonian Hopf bifurcation.