Curvature invariants, differential operators and local homogeneity

We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.

     

Infinitesimal obstructions to weakly mixing

Let ^t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M ⁿ , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d ^t and, for each x M, we define a smooth real function _x (t) : (1 + _i (t)), where the _i(t) are the eigenvalues of AA ^T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d^2t , restricted to v at the point _x ^-t M ⁿ.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that _x ^' (t) 0 for all x M and real t; then, if _x ^t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.     

From Weakly Coordinating to Non‐Coordinating Anions? A Simple Preparation of the Silver Salt of the Least Coordinating Anion and Its Application To Determine the Ground State Structure of the Ag(η2‐P4)2+ Cation

The unexpected but facile preparation of the silver salt of the least coordinating [(RO)₃Al‐F‐Al(OR)₃]^? anion (R=C(CF₃)₃) by reaction of Ag[Al(OR)₄] with one equivalent of PCl₃ is described. The mechanism of the formation of Ag[(RO)₃Al‐F‐Al(OR)₃] is explained based on the available experimental data as well as on quantum chemical calculations with the inclusion of entropy and COSMO solvation enthalpies. The crystal structures of (RO)₃Al←OC₄H₈, Cs⁺[(RO)₂(Me)Al‐F‐Al(Me)(OR)₂]^?, Ag(CH₂Cl₂)₃⁺[(RO)₃Al‐F‐Al(OR)₃]^? and Ag(η²‐P₄)₂⁺[(RO)₃Al‐F‐Al(OR)₃]^? are described. From the collected data it will be shown that the [(RO)₃Al‐F‐Al(OR)₃]^? anion is the least coordinating anion currently known. With respect to the fluoride ion affinity of two parent Lewis acids Al(OR)₃ of 685 kJ mol^?1, the ligand affinity (441 kJ mol^?1), the proton and copper decomposition reactions (?983 and ?297 kJ mol^?1) as well as HOMO level and HOMO–LUMO gap and in comparison with [Sb₄F₂₁]^?, [Sb(OTeF₅)₆]^?, [Al(OR)₄]^? as well as [B(R^F)₄]^? (R^F=CF₃ or C₆F₅) the [(RO)₃Al‐F‐Al(OR)₃]^? anion is among the best weakly coordinating anions (WCAs) according to each value. In contrast to most of the other cited anions, the [(RO)₃Al‐F‐Al(OR)₃] anion is available by a simple preparation in conventional inorganic laboratories. The least coordinating character of this anion was employed to clarify the question of the ground state geometry of the Ag(η²‐P₄)₂⁺ cation (D_2h, D₂ or D_2d?). In agreement with computational data and NMR spectra it could be shown that the rotation along the Ag‐(P‐P‐centroid) vector has no barrier and that the structure adopted in the solid state depends on packing effects which lead to an almost D_2h symmetric Ag(η²‐P₄)₂⁺ cation (0 to 10.6° torsion) for the more symmetrical [Al(OR)₄]^? anion, but to a D₂ symmetric Ag(η²‐P₄)₂⁺ cation with a 44° twist angle of the two AgP₂ planes for the less symmetrical [(RO)₃Al‐F‐Al(OR)₃]^? anion. This implies that silver back bonding, suggested by quantum chemical population analyses to be of importance, is only weak.     

An Uzawa-type algorithm for the coupled Stokes equations

An Uzawa-type algorithm is designed for the coupled Stokes equations discretized by the mixed finite element method. The velocity solved by the presented algorithm is weakly divergence-free, which is different from the one solved by the common Uzawa method. Besides, an optimal relaxation parameter of the presented algorithm is provided.     

From Ion‐Like Ethylzinc Aluminates to [EtZn(arene)2]+[Al(ORF)4]− Salts

Attempts to prepare previously unknown simple and very Lewis acidic [RZn]⁺[Al(OR^F)₄]^? salts from ZnR₂, AlR₃, and HO?R^F delivered the ion‐like RZn(Al(OR^F)₄) (R=Me, Et; R^F=C(CF₃)₃) with a coordinated counterion, but never the ionic compound. Increasing the steric bulk in RZn⁺ to R=CH₂CMe₃, CH₂SiMe₃, or Cp*, thus attempting to induce ionization, failed and led only to reaction mixtures including anion decomposition. However, ionization of the ion‐like EtZn(Al(OR^F)₄) compound with arenes yielded the [EtZn(arene)₂]⁺[Al(OR^F)₄]^? salts with arene=toluene, mesitylene, or o‐difluorobenzene (o‐DFB)/toluene. In contrast to the ion‐like EtZn(η³‐C₆H₆)(CHB₁₁Cl₁₁), which co‐crystallizes with one benzene molecule, the less coordinating nature of the [Al(OR^F)₄]^? anion allowed the ionization and preparation of the purely organometallic [EtZn(arene)₂]⁺ cation. These stable materials have further applications as, for example, initiators of isobutene polymerization. DFT calculations to compare the Lewis acidities of the zinc cations to those of a large number of organometallic cations were performed on the basis of fluoride ion affinity. The complexation energetics of EtZn⁺ with arenes and THF was assessed and related to the experiments.     

掺杂对CH样品Rayleigh-Taylor不稳定性增长的影响

在神光II激光装置上进行了辐射驱动不同掺杂样品的单模Rayleigh-Taylor(RT)不稳定性实验.结果显示:与纯碳氢(CH)样品相比,掺Br的CH样品的扰动更早、更快地进入非线性区,产生二次谐波,并且掺Br比例越高,CH样品扰动进入非线性区的时间越早,相同时刻扰动的二次谐波的幅度越高.这是因为密度梯度效应抑制了二次谐波的产生,掺Br比例越高,密度梯度标长越小;同时密度梯度效应还抑制三次谐波对基模增长的负反馈,造成基模具有更大的线性增长,导致线性饱和幅值大于经典值0.1λ.     

The effect of electron correlation on the conformational space of melatonin

The pineal gland hormone melatonin regulates several physiological processes including circadian rhythm and also alleviates oxidative stress‐induced degenerative diseases. In spite of its important biological roles, no high level ab initio conformational study has been conducted to reveal its structural features. In this work, the conformational flexibility of melatonin was investigated using correlated ab initio calculations. Conformers, obtained previously at the Hartree‐Fock level (HF/6‐31G*), were fully optimized using second order Møller‐Plesset perturbation theory applying the frozen core approximation (MP2(FC)/6‐31G*). Furthermore, single‐point MP4(SDQ,FC)/6‐31G*//MP2(FC)/6‐31G* computations were performed to investigate the effect of higher order perturbation terms. The HF and MP2 conformational spaces are considerably different: the initial 128 structures converged into 102 different local minima as confirmed by frequency calculations; 28 new minima appeared and 26 previous HF local minima disappeared; no “all‐trans” C3 side chain conformations are seen at the MP2(FC) level. The MP2 global minimum conformation is stabilized by an aromatic‐side chain interaction. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008     

微波波谱方法与应用研究进展

综述了微波波谱法及其应用研究进展,阐述了微波波谱法的基本原理及仪器构造。对微波波谱法在分子结构及构象分析、弱相互作用体系的研究、分析化学、星际物质的探测等方面的应用进行了综述。并展望了微波波谱方法未来的发展趋势。     

Tetrakis(pentafluoroethyl)gallate, [Ga(C2F5)4]−, Ionic Liquids

We synthesized new imidazolium-based tunable aryl alkyl ionic liquids (TAAILs) with the weakly coordinating tetrakis(pentafluoroethyl)gallate anion, [Ga(C₂F₅)₄]⁻. Phenyl and phenyl derivatives (2-Me, 4-OMe, 2,4-F) were combined with varying alkyl chain lengths at the imidazolium core leading to TAAILs, which were investigated with regard to their viscosity, conductivity, and electrochemical window and compared to EMIM and BMIM standard cations. Remarkable low viscosities of 29 cP at 25 °C for [BMIM][Ga(C₂F₅)₄] were achieved. However, the EMIM and BMIM gallates show electrochemical instability, releasing pentafluoroethane at a voltage of 1.5 V. The 2-Me-substituted gallate-TAAILs slowly decompose over several weeks, whereas all other gallate-TAAILs showed no decomposition at all. With electrochemical windows of up to 5.15 V and low viscosities in a range of 66–162 cP, the gallate-TAAILs are promising candidates as electrolytes in electrochemical applications.     

A novel vapor phase process for aromatic ketone synthesis

The vapor phase catalytic reaction between aromatic carboxylic acid and acetic acid was investigated. Many metal oxides catalyzed the reaction between 2methylbenzoic acid (OTA) and acetic acid (AA) to produce 2methylacetophenone (OMA), and weakly acidic oxides such as Th, U, Ce, and La oxide exhibited higher yield of OMA. The OMA yield depended on the catalyst support. SiO₂, Al₂O₃, TiO₂, and ZrO₂ with a surface area of less than 200 m² g^–1 appeared to be suitable as industrial catalyst supports. CeO₂ on Al₂O₃was chosen as an industrial catalyst for the synthesis of OMA because of higher productivity, longer catalyst life, and lifting of legal restrictions on catalyst handling. This catalyst system can also be applied to the syntheses of acetophenone, nitroacetophenone, and chloroacetophenone.