Mixed-metal cluster chemistry. 26 . Proclivity for “all-terminal” or “plane-of-bridging-carbonyls” ligand disposition in tungsten-triiridium clusters

Reaction of WH(CO)₃(η-C₅Me₅) with IrCl(CO)₂(4-H₂NC₆H₄Me) affords WIr₃(μ-CO)₃(CO)₈(η-C₅Me₅) in low yield. A structural study reveals a WIr₂-centred plane of bridging carbonyls, in contrast to the crystal structure of WIr₃(CO)₁₁(η-C₅H₅) (all-terminal carbonyl distribution). DFT calculations reveal an increasing proclivity to adopt an all-terminal CO disposition for clusters MIr₃(CO)₁₁(η-C₅H₅) in the gas phase on proceeding from M=Cr to Mo and then W, consistent with structural studies in the solid state for which the tungsten-containing cluster is the only all-terminal example. Increasing electron donation from the ligands in the tungsten system (either from phosphine substitution or cyclopentadienyl permethylation) suffices to impose a plane of bridging carbonyls in the ground state structure. ¹³C NMR fluxionality studies reveal that CO exchange mechanism(s) for WIr₃(CO)₁₁(η-C₅H₅) and the related tetrahedral cluster W₂Ir₂(CO)₁₀(η-C₅H₅)₂ are very fast and involve all carbonyls on the clusters. DFT calculations on MIr₃(CO)₁₁(η-C₅H₅) (M=Cr, Mo) substantiate a ‘merry-go-round’ mechanism for carbonyl scrambling in these systems, a result which is consistent with the scrambling behaviour seen in the NMR fluxionality studies on the W-containing congener.     

A density functional theory study of the gas-phase elimination reactions of 4-arylideneimino-1,2,4-triazol-3(2H )-ones and their 3(2H )-thione analogues

Theoretical studies on the thermolysis in the gas phase of 4-arylideneimino-1,2,4-triazol-3(2H)-ones and 4-arylideneimino-1,2,4-triazol-3(2H)-thiones were carried out using density functional theory methods, at the B3LYP/6-31G(d) and B3LYP/6-311+G(2d,p) levels of theory. The proposed reaction mechanism occurs in one step, leading to the formation of 3-hydroxy-(2H)-1,2,4-triazole or 3-mercapto-(2H)-1,2,4-triazole and a 4-substituted benzonitrile, via a six-membered cyclic transition state. The progress of the reactions was followed by means of the Wiberg bond indices. The results indicate that the transition states have character intermediate between reactants and products, and the calculated synchronicities show that the reactions are slightly asynchronous, in the case of triazolones, and show a higher asynchronicity in the case of triazolthiones. The bond-breaking processes are slightly more advanced than the bond-forming ones, indicating a small bond deficiency in the transition states. Kinetic and activation parameters for the reactions studied have been calculated and compared with available experimental data.From the Proceedings of the 28th Congreso deQuímicos Teóricos de Expresión Latina (QUITEL 2002)     

DFT法研究离子液中EMIM~ 催化丁烯双键异构反应机理(II)

用密度泛函理论(DFT)在B3LYP/6鄄31G(d,p)的计算水平上研究了离子液中1鄄乙基鄄3鄄甲基咪唑阳离子(EMIM )的4鄄H和5鄄H原子催化丁烯双键异构反应的可能途径,优化了反应体系的平衡态和过渡态的几何构型,分析了反应过程中键参数的变化,通过振动分析对平衡态和过渡态进行了验证.计算结果表明,离子液中的EMIM 首先通过4鄄H和5鄄H原子吸附丁烯,进而催化丁烯的双键异构反应,EMIM 的4鄄H和5鄄H催化1鄄丁烯异构为2鄄丁烯的正反应活化能分别为204.2和207.3kJ·mol-1,逆反应活化能约为220.9和223.8kJ·mol-1,反应为基元反应.     

CnBδ(δ=0, ±1; n =1～6)团簇的结构、稳定性和光谱

采用密度泛函理论(DFT)的B3LYP方法,在6-31G*和6-311＋G(3df)水平上对C_nB(n=1～6)团簇及其阴离子和阳离子的几何构型和电子结构进行了优化和振动频率计算.得到了C_nB(n=1～6)团簇的电离能,绝热电子亲合势以及C_nB^δ(δ=0,±1)团簇的能隙.结果表明C_nB^－(n=1～6)团簇的基态构型均为线形,这与等电子的C_n簇合物的结构是一致的; C_nB(n=1～6)团簇的基态构型中,除C₂B为不对称的三角形,C₆B为具有C_2v对称性的环状结构外,其余均为线形结构.阳离子团簇中n=2、3、6的基态结构具有C_2v对称性外,其它几个均为线形结构.从几何参数和振动频率上发现,采用密度泛函B3LYP方法在6-311＋G(3df)和6-31G*两种基组上计算得到的键长参数和振动频率非常接近,说明B3LYP方法在计算C_nB簇合物结构参数上对于基组的选择是不太敏感的.通过对C_nB(n=1～6)的光电子能谱性质的研究发现,C₄B容易获得一个电子形成阴离子团簇,但失去一个电子是很困难的,这与实验上观测到的结果非常吻合.     

The density and minimal gap of visible points in some planar quasicrystals

It has previously been observed that the limiting gap distribution of the directions to visible points of planar quasicrystals may vanish near zero, that is, there exist planar quasicrystals with a positive limiting minimal normalised gap between the angles of visible points. The exact values of these limiting minimal normalised gaps have not been determined. In this paper we give explicit formulas for the densities of visible points for planar quasicrystals from several families, which include the Ammann–Beenker point set and the vertex sets of some rhombic Penrose tilings. Combining these results with a known characterisation of the limiting minimal gap in terms of a probability measure on an associated homogeneous space of quasicrystals, we give explicit values of the limiting minimal normalised gap between the angles of visible points for several families of planar quasicrystals, in particular, for the Ammann–Beenker point set and for the vertex sets of some rhombic Penrose tilings. We also compare our results with numerical observations.     

Mosco approximation of integrands and integral functionals

It is shown that, given a lower semicontinuous convex integrandf satisfying a suitable integrability condition, there exists a sequence of Lipschitz simple integrands which Mosco converges tof and such that the sequence of conjugate integrands Mosco converges tof ^*. Moreover, this sequence can be chosen so that the sequence of associated integral functionals, respectively defined onL ¹(X) andL (X ^*), Mosco converges as well.We wish to thank Professor Erik J. Balder for interesting remarks on the first version of this work.     

DFT法研究分子筛催化trans-2-丁烯的双键异构

利用一个3T簇模型模拟分子筛催化剂的酸性位, 采用密度泛函理论(DFT)的 B3LYP/6-31G(d, p)方法, 研究了分子筛催化1-丁烯双键异构为trans-2-丁烯的反应机理. 对反应各驻点进行了全优化, 经过零点能校正后, 得到了反应的活化能. 研究表明, 反应分三步进行：物理吸附→化学反应→物理脱附. 分子筛的酸性位OH基团首先吸附1-丁烯的双键形成了π配位复合物, 然后按协同反应机理发生双键异构反应, 生成吸附态的trans-2-丁烯, 最后脱附成产物. 计算得到的表观活化能为57.1 kJ•mol^-1, 与实验结果接近.     

On hydrogen-bonded complexes: the case of (HF)2

The hydrogen fluoride dimer (HF)₂ is the most completely characterized hydrogen bonded species incorporating a donor molecule and an acceptor molecule. We provide a summary of experimental and theoretical information pertinent to the fundamental and harmonic vibrational frequencies, equilibrium geometry and dissociation energiesD _e andD ₀ as well as a brief critical discussion including some new results on the potential function and current best estimates of experimental quantities.     

An application of correlation energy density functionals to atoms and molecules

Four density functionals — including that recently introduced by Perdew ((1986) Phys Rev B33: 8822)—are tested for first-row atoms, hydrides and dimers. Calculated contributions of the correlation energy to the ionization potentials and electron affinities of atoms and to the dissociation energies of molecules are compared with empirical values which were reevaluated for this purpose. An improvement over Hartree-Fock is found in all cases if the self-interaction or the gradient correction are included in the density functional, although there is a rather large variation in the accuracy of the predictions.     

Volumetric properties of ethanol–water mixtures under high temperatures and pressures

The densities of ethanol and ethanol–water mixtures were measured with a vibrating tube densimeter at 25.0, 50.0 and 75.0 °C in the pressure range from 0.10 to 40.00 MPa. Densities were correlated using an empirical model. Partial molar volumes, excess molar volumes, isothermal compressibilities, cubic expansion coefficients and internal pressures were calculated from obtained densities. This study reports the dependence of densities, partial molar volumes, excess molar volumes, isothermal compressibilities, cubic expansion coefficients and internal pressures on composition, temperature and pressure.