Basins of Attraction of Periodic Oscillations in Suspension Bridges

We consider the dynamics of the lowest order transversal vibration mode of a suspension bridge, for which the hangers are treated as one-sided springs, according to the model of Lazer and McKeena [SIAM Review 58, 1990, 537]. We analyze in particular the multi-stability of periodic attractors and the basin of attraction structure in phase space and its dependence with the model parameters. The parameter values used in numerical simulations have been estimated from a number of bridges built in the United States and in the United Kingdom, thus taking into account realistic, yet sometimes simplified, structural, aerodynamical, and physical considerations.     

Stereoselective preparation of spirane bridged, sandwiched bisarenes

Preparation of α-oxo derivatives of spiro[4.4]nonane, spiro[4.5]decane and spiro[5.5]undecane derivatives is described. An efficient method for spiroannulation by Rh(I)-catalysed intramolecular hydroacylation provides α,α′-difunctionalised spiro[4.5]decanes. The α,α′-dioxo groups have been converted into vinyl triflates for arylation by Pd-catalysed cross-coupling reactions under Stille, Negishi or Suzuki conditions depending on relative reactivities. Stereoselective saturation of the conjugated aryl olefinic bonds by catalytic hydrogenation over Pd-carbon provides methodology for stereoselective preparation of α-aryl- and α,α′-cis,cis-diaryl spiranes, the latter with a sandwich like structure. Single crystal X-ray analyses have been used in the structural assignments.     

Synthesis,Structure and Reactivity of PH‐Phosphoraneiminato‐ and Iminophosphoraneiminato Group 4 Transition‐Metal Complexes

The versatile coordination chemistry of the well‐investigated phosphoraneiminato‐ligand R₃PN^— ( I ) was extended by the successive introduction of protons to the phosphorus atom. The position of the resulting equilibrium between the NH‐phosphanylamido‐ [R₂P‐NH^—] and the PH‐phosphoraneiminato‐form [R₂HP=N^—] is affected by the Lewis acidity of the coordinated metal fragment. Experimental studies on complexes with various substitution patterns at the group 4 metal center R₂HP=N[M] ( II ) were unambiguously confirmed by DFT‐calculations. The isolation of group 4 PH‐dihydrido‐phosphoraneiminato‐complexes RH₂P‐N[M] ( III ) is prevented by the low thermodynamic stability of the target molecules, also supported by the results of ab initio calculations. However, an access to the by then unknown transition‐metal substituted iminophosphanes RP=N[M] ( IV ) was verified for the first time. Within extensive studies on the coordination chemistry of bis(imino)phosphoranes RP(=NR′)(=NR″), several species of group 4 complexes R(R′N=)P=N[M] ( V ) were isolated and structurally characterized. In this case, investigations on the NH/PH‐tautomerism were performed exclusively on theoretical level, because the required educts are experimentally non‐accessible due to their kinetic instability.     

Synthesis and structures of new compounds based on tetrahedral rhenium chalcocyanide cluster anions [Re4Q4(CN)12]4− (Q = S or Se) and [Cu(bipy)2]2+ cations

The reactions of the rhenium chalcocyanide cluster salts K₄[Re₄Q₄(CN)₁₂]·6H₂O (Q = S or Se) with Cu²⁺ cations coordinated by the bidentate ligand 2,2′-bipyridyl (bipy) produced two new cluster compounds, [Cu(NH₃)(bipy)₂]₂[Re₄S₄(CN)₁₂]·bipy·3.25H₂O (1) and [{Cu(bipy)₂}₂Re₄Se₄(CN)₁₂]·bipy·8.5H₂O (2). The structures of these complexes were solved by X-ray diffraction. Compound 1 is ionic. Compound 2 is molecular. In the structures of both compounds, there are staking interactions between the {Cu(bipy)₂}²⁺ cationic moieties and the solvate 2,2′-bipyridyl molecules. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1875–1878, November, 2006.     

Marginal electron density and density-difference functions

Summary For visual analysis of the density reorganization and distortion, the one-dimensional cut (x, y ₀,z ₀) and the two-dimensional cut (x, y, z ₀) of the three-dimensional electron density difference function (x, y, z) are frequently employed. However, these cut functions do not satisfy any sum rules in contrast to the original difference function (x, y, z). To avoid this difficulty, the use of the marginal electron density functions _x (x) and _xy (x, y) and their difference functions _x (x) and _xy (x, y) is proposed. The marginal densities are condensation of the three-dimensional density onto a particular plane or line of our interest, and they satisfy the sum rule (i.e., the conservation of the number of electrons) exactly. Some basic properties of the marginal electron density are clarified for typical diatomic molecular orbitals. An illustrative application is given for the bonding and antibonding processes in the H₂ system.     

Measurements and Utilization of Consistent Gibbs Energies of Transfer of Single Ions: Towards a Unified Redox Potential Scale for All Solvents

Utilizing the “ideal” ionic liquid salt bridge to measure Gibbs energies of transfer of silver ions between the solvents water, acetonitrile, propylene carbonate and dimethylformamide results in a consistent data set with a precision of 0.6 kJ mol⁻¹ over 87 measurements in 10 half-cells. This forms the basis for a coherent experimental thermodynamic framework of ion solvation chemistry. In addition, we define the solvent independent - and the values that account for the electronating potential of any redox system similar to the value of a medium that accounts for its protonating potential. This scale is thermodynamically well-defined enabling a straightforward comparison of the redox potentials (reducities) of all media with respect to the aqueous redox potential scale, hence unifying all conventional solvents′ redox potential scales. Thus, using the Gibbs energy of transfer of the silver ion published herein, one can convert and unify all hitherto published redox potentials measured, for example, against ferrocene, to the scale.     

Synthese und Struktur von (PPh4)3[Re2NCl10]

Synthesis and Crystal Structure of (PPh₄)₃[Re₂NCl₁₀] The rhenium(V) nitrido complex (PPh₄)₃[Re₂NCl₁₀] ( 1 ) is obtained from the reaction of (PPh₄)[ReNCl₄] with 1, 3‐dioxan‐(2‐ylmethyl)diphenyl phosphine in CH₂Cl₂/CH₃CN in form of orange red crystals with the composition 1 ·2CH₂Cl₂ crystallizing in the triclinic space group P1¯ with a = 1210.7(2), b = 1232.5(1), c = 2756.3(5) pm, α = 99.68(1)°, β = 100.24(1)°, γ = 98.59(1)° and Z = 2. The crystal structure contains two symmetry independent, centrosymmetrical complex anions [Re₂NCl₁₀]^3‐ with a symmetrical nitrido bridge Re=N=Re and distances Re(1) ‐ N(1) = 181.34(5) and Re(2) ‐ N(2) = 181.51(4) pm.     

Synthese und Kristallstruktur von [ReNCl(NPPh2C6H4)]2 · [Ph3PNH2]Cl · CH3CN,einem rheniumorganischen Nitrido-Phosphaniminato-Komplex

Synthesis and Crystal Structure of [ReNCl(NPPh₂C₆H₄)]₂ · [Ph₃PNH₂]Cl · CH₃CN, a Rhenium Organic Nitrido Phosphoraneiminato Complex The title compound is synthesized by the reaction of ReNCl₄ with Me₃SiNPPh₃ in boiling acetonitrile, forming colourless crystals, which are characterized by an X-ray structure determination. Space group P1 , Z = 2, 4 037 observed unique reflections, R = 0.043. Lattice dimensions at 19°C: a = 1 005.5; b = 1 695.2; c = 1 744.7 pm, α = 105.86°; β = 101.49°; γ = 104.45°. The structure consists of dimeric molecules [ReNCl(NPPh₂C₆H₄)]₂, triphenylphosphorane ammoniumchloride and included acetonitrile molecules. In the nitrido phosphoraneiminato complex the rhenium atoms are μ₂-bridged via the N-Atoms of the phosphoraneiminato ligands. Because of this bridging and a Re? Re bond, one terminal nitrido ligand, one terminal chloro ligand, and a Re? C bond of an -C-atom of one phenylene group of Re-atoms attain co-ordination number six.     

Der erste Polyiodokomplex – Triethylsulfoniumtriiodomercurat(II)-tris(diiod), (Et3S)[Hg2I6]1/2 · 3 I2

The First Polyiodo Complex – Triethylsulfoniumtriiodomercurate(II)-tris(diiodine), (Et₃S)[Hg₂I₆]_1/2 · 3 I₂ After Raman spectroscopic investigation of the system HgI₂/Et₃SI_x, x = 3, 5, 7, triethylsulfoniumtriiodomercuratetris(diiodine), (Et₃S)[Hg₂I₆]_1/2 · 3 I₂ was synthesized by reacting of HgI₂ and liquid Et₃SI₇. The compound crystallizes at room temperature triclinically in the space group P1 with a = 879.4(7), b = 1 209.1(5), c = 1 291.5(5) pm, α = 96.16(3)°, β = 103.82(6)°, γ = 99.05(5)° and Z = 2. The crystal structure is composed of disordered Et₃S⁺ cations, the centrosymmetric complex anion [HgI_2/2I₂]₂^2? and three connecting iodine molecules I₂.