Stability of a vertically positioned heavy rotating rod

The stability boundary for a heavy, vertically positioned rotating rod is determined. Generalized constitutive equations, taking into account compressibility of the rod axis and the influence of the shear stresses are used. It is shown that by changing values of the parameters, the bifurcation pattern changes from super to sub - critical.     

Two Stereoinduction Events in One C−H Activation Step: A Route towards Terphenyl Ligands with Two Atropisomeric Axes

Herein we disclose the synthesis of original chiral scaffolds—ortho‐orientated terphenyls presenting two atropisomeric Ar–Ar axes. These unusual structures were built up by using the C?H activation approach, and remarkably, both chiral axes were controlled with excellent stereoselectivity in a single transformation. During the reaction, not only does atroposelective functionalization of a biaryl precursor occur to establish one stereogenic axis, but an unprecedented atropo‐stereoselective C?H arylation also takes place to generate the second stereogenic element. These enantiomerically pure ortho‐terphenyls show an original tridimensional structure and thus constitute a unique foundation for building up a library of enantiomerically pure bidentate ligands, such as the new ligands S/N‐Biax and diphosphine BiaxPhos.     

New manganese-scaffolded organic triple-deckers based on quinoxaline, pyrazine and pyrimidine cores

The thermolytic coupling of Ph(2)CN(2) and (t-Bu)(Ph)CN(2) with doubly cyclomanganated 2,5-diphenylpyrazine and 4,6-diphenylpyrimidine afforded substantial amounts of new triple decker compounds of either C(i) and C(2) symmetry respectively containing, in both series, two eta(3)-bonded Mn(CO)(3) fragments which intervene as scaffolds sustaining the helical non-conjugated triaryl backbone. The molecular structures of two pyrazine derivatives show a typical non-parallel stacking of the aromatic rings and the encapsulation of the central pyrazyl fragment with interplanar centroid-to-centroid distances of ca. 3.5 A. The stacking of the aromatics in the triple-decker pyrimidine derivatives has been assessed by (1)H NMR experiments at low temperature. All the triple-decker-type compounds are electroactive. Pyrimidine triple-deckers can reversibly be electrochemically reduced to the corresponding anions.     

Cation-cation "attraction": when London dispersion attraction wins over Coulomb repulsion

London forces are omnipresent in nature and relevant to molecular engineering. Proper tuning of their energetic contribution may stabilize molecular aggregates, which would be otherwise highly unstable by virtue of other overwhelming repulsive terms. The literature contains a number of such noncovalently bonded molecular aggregates, of which the "binding mode" has never been thoroughly settled. Among those are the emblematic cationic complexes of tetrakis(isonitrile)rhodium(I) studied by a number of researchers. The propensity of these complexes to spontaneously produce oligomers has been an "open case" for years. For the dimer [(PhNC)(4)Rh](2)(2+), one of the archetypes of such oligomers, density functional theory methods (DFT-D3) and wave function based spin-component-scaled second-order M?ller-Plesset perturbation theory (SCS-MP2) quantum chemical calculations indicate that when the eight isonitrile ligands arrange spatially in an optimal π-stacked fashion, the energy due to dispersion not only overcomes coulombic repulsion but also the entropy penalty of complex formation. This central role of long-range electron correlation explains such cation-cation attractive interactions. Furthermore, the present findings relativize the role of the metal-metal "d(8)-d(8)" interactions, which are present on a relatively small scale compared to the effects of the ligands; d(8)-d(8) interactions represent about 10-15% of the total dispersion contribution to the binding energy.     

Synthesis of syn-facial (Cr,Mn) benzyl complexes by the stereoselective thermolytic coupling of unsymmetric diazomethanes with cyclomanganated (η-arene)tricarbonylchromium complexes

The heat-promoted reaction of 1,3-bis(2,4,6-trimethylphenyl)imidazol-2-ylidene with cyclomanganated 2-[tricarbonyl(η⁶-phenyl)chromium]pyridine afforded, upon departure of a molecule of CO, a new stable manganese alkylidene complex in which, according to X-ray diffraction analyses, the heterocyclic ligand is anti-facial with respect to the Cr(CO)₃ moiety. Similar heat-promoted reactions of unsymmetrically substituted diazoalkanes such as (Me₃Si)(H)CN₂, (Ph)(Me)CN₂, (Ph)(t-Bu)CN₂ and (Ph)(FcCH₂CH₂)CN₂, which are precursors of more electrophilic alkylidenes, with cyclomanganated 2-[tricarbonyl(η⁶-phenyl)chromium]pyridine derivatives afforded new syn-facial heterobimetallic benzyl complexes. The stereoselectivity of these reactions depends on the steric demand of the substituents at the diazoalkane. A phenyl substituent at the diazoalkane favors the formation of syn-facial heterobimetallic benzyl complexes with the Ph group in the endo position. Combining this “phenyl directing effect” to the steric effect operated by a bulky group at the phenyldiazoalkane, like noticed with (Ph)(t-Bu)CN₂, led to total stereoselectivity. This study discloses four new X-ray structures of syn-facial Cr,Mn benzyl complexes, which all present the same short Cr-to-Mn distance of ca. 3.04 Å.     

Cobalt Nanoparticles Formed upon Reaction of Cp*Co(III) Metallacycles with Na[BHEt3] Show Catalytic Activity in the Hydrosilylation of Aryl Ketones,Aldehydes and Nitriles

The reactivity of the 2-phenylpyridine-derived [Cp*CoI(phpy-κ^C,N)] metallacycle towards Et₃SiH and hydrides was evaluated. The treatment of the same Co(III) complex with Na[BHEt₃] resulted in its decomposition into cobalt nanoparticles. The hydride-promoted decomposition of the metallacycle involves the transient formation of an elusive hydrido-cobalt(III) intermediate, the traces of which were detected by ¹H NMR spectroscopy at sub-ambient temperature. The Co nanoparticles produced from a 5 mol% and 10 mol% load of cobaltacycle and Na[BHEt₃] respectively contain Co(0) that is responsible for the hydrosilylation by Et₃SiH of arylketones into silylalkyl ethers. To minimize the residual side reduction of carbonyls by Na[BHEt₃], a mixture of 5 mol% of the latter with 5 mol% of BEt₃ was found to produce optimal hydrosilylation yields at 40 °C in 2 h. Under similar conditions, several arylnitriles were mono-hydrosilylated into N-silyl-imines in yields ranging from 68 to 100 %.     

Effect of shear on stability and nonlinear behavior of a rotating rod

Summary The nonlinear equations describing in-plane deformation of a rotating elastic rod, taking into account shear effect, are derived. It is shown that the critical rotation speed is determined from the linearized equation. The nonlinear equilibrium equations are solved numerically and the effect of shear on maximal deflection is studied.

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Der Einfluß der Schubspannungen auf die Stabilität und das nichtlineare Verhalten einer rotierenden Welle

Übersicht Die nichtlinearen Differentialgleichungen für die ebene Verformung einer rotierenden elastischen Welle mit Schubspannungseinfluß auf die Biegelinie wird hergeleitet. Wir zeigen, daß die kritische Rotationsgeschwindigkeit aus den linearen Gleichgewichtsbedingungen folgt. Die nichtlinearen Gleichungen werden numerisch gelöst und der Schubspannungseinfluß auf die Durchbiegung wird untersucht.

     

Persistent metal bis(hexafluoroacetylacetonato) complexes featuring a 2,2'-bipyridine substituted triarylamminium radical cation

Herein, we describe the preparation of a 2,2'-bipyridine derivative containing a redox-active N,N'-(4,4'-dimethoxydiphenylamino) substituent (1), which readily coordinates M(hfac)(2) salts [M = Mn (2), Ni (3), Cu (4)] to generate stable, neutral, and pseudo-octahedral coordination complexes, which have been fully characterized. Cyclic voltammetry and spectroelectrochemical measurements on complexes 2-4 indicate stable one-electron oxidation processes, and the formation of persistent radical cation complexes. The neutral complexes (M = Mn or Ni) were subject to one-electron oxidation with NOPF(6) in acetonitrile, and magnetic moments of the resulting solutions were obtained using the Evans method at different temperatures. Our experimental results suggest that the first reported ferromagnetically coupled metal-triarylamminum radical cation complex is obtained when M = Mn(2+), and antiferromagnetic coupling results when M = Ni(2+). These results are supported by results from density functional theory calculations, which indicate that a π spin polarization mechanism for magnetic exchange coupling is operative in singly oxidized complexes, 2-4.     

Conservation laws in classical mechanics for quasi-coordinates

Noether's theorem and Noether's inverse theorem for mechanical systems with gauge-variant Lagrangians under symmetric infinitesimal transformations and whose motion is described by quasi-coordinates are established. The existence of first integrals depends on the existence of solutions of the system of partial differential equations — the so-called Killing equations. Non-holonomic mechanical systems are analysed separately and their special properties are pointed out. By use of this theory, the transformation which corresponds to Ko Valevskaya first integral in rigid-body dynamics is found. Also, the nature of the energy integral in non-holonomic mechanics is shown and a few new first integrals for non-conservative problems are obtained. Finally, these integrals are used in constructing Lyapunov's function and in the stability analyses of nonautonomous systems. The theory is based on the concept of a mechanical system, but the results obtained can be applied to all problems in mathematical physics admitting a Lagrangian function.     

A novel bis tridentate bipyridine carboxamide ligand and its complexation to copper(II): synthesis, structure, and magnetism

A new bis tridentate ligand 2,2'-bipyridine-3,3'-[2-pyridinecarboxamide] H(2)L(1) which can bind transition metal ions has been synthesized via the condensation of 3,3'-diamino-2,2'-bipyridine together with 2-pyridine carbonyl chloride. Two copper(II) coordination compounds have been prepared and characterized: [Cu(2)(L(1))(hfac)(2)].3CH(3)CN.H(2)O (1) and [Cu(2)(L(1))Cl(2)].CH(3)CN (2). The single-crystal X-ray structures reveal that complex 1 crystallizes in the triclinic space group P1, with the unit cell parameters a = 12.7185(6) A, b = 17.3792(9) A, c = 19.4696(8) A, alpha = 110.827(2) degrees, beta = 99.890(3) degrees, gamma = 97.966(3) degrees, V = 3868.3(3) A3, Z = 4, R = 0.0321 and R(w) = 0.0826. Complex 2 crystallizes in the monoclinic space group P2(1)/n with the unit cell parameters a = 12.8622(12) A, b = 9.6100(10) A, c = 19.897(2) A, beta = 102.027(3) degrees, V = 2405.3(4) A(3), Z = 4, R = 0.0409 and R(w) = 0.1005. In both complexes the ligand is in the dianionic form and coordinates the divalent Cu(II) ions via one amido and two pyridine nitrogen donor atoms. In 1, the coordination geometry around both Cu(II) ions is best described as distorted trigonal bipyramidal where the remaining two coordination sites are satisfied by hexafluoroacetylacetonate counterions. In 2 both Cu(II )ions adopt a (4 + 1) distorted square pyramidal geometry. One copper forms a longer apical bond to an adjacent carbonyl oxygen atom, whereas the second copper is chelated to a neighboring Cu-Cl chloride ion to afford a mu-Cl-bridged dimerized [Cu(2)(L(1))Cl(2)](2) complex. The magnetic susceptibility data for 1 (2 -270 K), reveal the occurrence of weak antiferromagnetic interactions between the Cu(II) ions. In contrast, variable-temperature magnetic susceptibility measurements for 2 reveal more complex magnetic properties, with the presence of a weak antiferromagnetic exchange (J = -10.1 K) between the copper ions in each dinuclear copper complex and a stronger ferromagnetic exchange interaction (J = 32.9 K) between the Cu(II) ions of the Cu(mu-Cl)(2)Cu dimeric bridging units.