Comparison of experimental time-of-flight spectra of the HF products from the F+H2 reaction with exact quantum mechanical calculations

High resolution HF product time-of-flight spectra measured for the reactive scattering of F atoms from n-H2(p-H2) molecules at collision energies between 69 and 81 meV are compared with exact coupled-channel quantum mechanical calculations based on the Stark-Werner ab initio ground state potential energy surface. Excellent agreement between the experimental and computed rotational distributions is found for the HF product vibrational states v'=1 and v'=2. For the v'=3 vibrational state the agreement, however, is less satisfactory, especially for the reaction with p-H2. The results for v'=1 and v'=2 confirm that the reaction dynamics for these product states is accurately described by the ground electronic state 1 (2)A' potential energy surface. The deviations for HF(v'=3, j' > or =2) are attributed to an enhancement of the reaction resulting from the 25% fraction of excited ((2)P(12)) fluorine atoms in the reactant beam.     

Pyramids in the complex projective plane

We study the critical points of the diameter functional on the n-fold Cartesian product of the complex projective plane C P ² with the Fubini-Study metric. Such critical points arise in the calculation of a metric invariant called the filling radius, and are akin to the critical points of the distance function. We study a special family of such critical points, P _kC P ¹C P ², k=1,2... We show that P _k is a local minimum of by verifying the positivity of the Hessian of (a smooth approximation to) at P _k. For this purpose, we use Shirokov's law of cosines and the holonomy of the normal bundle of C P ¹C P ². We also exhibit a critical point of , given by a subset which is not contained in any totally geodesic submanifold of C P ².     

Facile syntheses of unsolvated UI3 and tetramethylcyclopentadienyl uranium halides

In the course of comparing the reaction chemistry of (C5Me5)3U, 1, and its slightly less crowded analogue (C5Me4H)3U, 2, new syntheses of UI3, (C5Me4H)3U, (C5Me4H)3UCl, 3, and (C5Me5)3UCl, 4, have been developed. Additionally, (C5Me4H)3UI, 5, and (C5Me4H)2UCl2, 6, have been identified for the first time. A facile synthesis of unsolvated UI3 is reported that proceeds in high yield with inexpensive equipment from iodine and hot uranium turnings. Both UI3 and UI3(THF)4 react with KC5Me4H in toluene to make unsolvated (C5Me4H)3U in higher yield than in previous reports that involve reduction of tetravalent (C5Me4H)3UCl, 3. A more atom-efficient synthesis of complex 3 is also reported that proceeds from reduction of t-BuCl, PhCl, or HgCl2 by 2. Similarly, (C5Me4H)3U reacts with PhI or HgI2 to generate (C5Me4H)3UI. These studies also provided a basis to improve the synthesis of (C5Me5)3UCl from 1 by employing t-BuCl or HgCl2 as the halide source. Like (C5Me5)3UCl, the (C5Me4H)3UCl complex reacts with HgCl2 to form (C5Me4H)2 and (C5Me4H)2UCl2, 6, but unlike (C5Me5)3UX (X = Cl or I), the less substituted (C5Me4H)3UX complexes do not reduce t-BuCl or PhX. The synthesis of 6 from (C5Me4H)MgCl x THF and UCl4 is also included.     

Ate complexes of Ge(II) and Sn(II) with bidentate ligands [LiE(OCH2CH2NMe2)3]2 (E=Ge, Sn): synthesis and structure

The reaction of equimolar quantities of LiOCH₂CH₂NMe₂ and E¹⁴(OCH₂CH₂NMe₂)₂ (E¹⁴=Ge, Sn) in ether yielded new ate complexes [LiE¹⁴(OCH₂CH₂NMe₂)₃]₂ (E¹⁴=Ge (1), Sn (2)) with bidentate ligands. The compounds 1 and 2 are white crystalline substances which are highly soluble in THF and pyridine and very sensitive to the traces of oxygen and moisture. The structures of these compounds are studied by X-ray diffraction analysis. The ate complexes 1 and 2 are powerful nucleophiles and may be employed as ligands (neutral) in the coordination chemistry of the transition metals. The electronegative O-substituents at the divalent E¹⁴ atoms render them less oxidizable than alkyl- or aryl-substituted derivatives, and the bidentate ligands, owing to intramolecular donor-acceptor interactions, make them more thermodynamically stable compared to monodentate ligands.     

Polysila analogs of aromatic hydrocarbon ions: Structures and energies of Si3H3+, Si4H,and Si5H5−

Silicon analogs of aromatic monocyclic ions, (SiH) ( 4 ), (SiH) ( 5 ), and (SiH) ( 6 ) have been studied ab initio at MP 2(full)/6-31G *. The D_3h structure of Si₃H₃⁺ is the global minimum, whereas other two ions are nonplanar. The D_2d structure of (SiH) is less folded than the carbon analog and possesses a higher stabilization energy. Stabilization energies for the monocharged ions are diminished with respect to the corresponding carbons © 1993 John Wiley & Sons, Inc.     

Cross-metathesis reaction of vinyl sulfones and sulfoxides

Cross-metathesis reactions of α,β-unsaturated sulfones and sulfoxides in the presence of molybdenum and ruthenium pre-catalysts were tested. A selective metahesis reaction was achieved between functionalized terminal olefins and vinyl sulfones by using the ‘second generation’ ruthenium catalysts 1c-h while the highly active Schrock catalyst 1b was found to be functional group incompatible with vinyl sulfones. The cross-metathesis products were isolated in good yields with an excellent (E)-selectivity. Both the molybdenum and ruthenium-based complexes were, however, incompatible with α,β- and β,γ-unsaturated sulfoxides.     

The Tricyclooctanone Approach to the Total Synthesis of Steroids. The Cyclization of the A-CD Unit

The first steps of a novel approach to the total synthesis of 9, 11-dehydroestrone via tricyclo[3.3.0.0^2,8]octan-3-one (2) are described. One route involves a tandem-type transformation of the key intermediate 3 (A-CD unit) consisting of cyclopropane cleavage and ring B closure to afford C, 18-bisnor-13 α, 17 α-estradiol derivatives. E.g. the 3-methoxy-9 ζ-hydroxy-17 α-methanesulfonyloxy derivative (-)- 6 has been synthesized in 8 steps and 10% overall yield from 1,3-cyclohexadiene. As an alternative, the A-CD type intermediate 4b has been prepared and could be used for a ring C enlargement prior to cyclization.     

A finite volume cell‐centered Lagrangian hydrodynamics approach for solids in general unstructured grids

A finite volume cell‐centered Lagrangian hydrodynamics approach, formulated in Cartesian frame, is presented for solving elasto‐plastic response of solids in general unstructured grids. Because solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum, and energy conservation laws. The total stress is split into deviatoric shear stress and dilatational components. The dilatational response of the material is modeled using the Mie‐Grüneisen equation of state. A predicted trial elastic deviatoric stress state is evolved assuming a pure elastic deformation in accordance with the hypo‐elastic stress‐strain relation. The evolution equations are advanced in time by constructing vertex velocity and corner traction force vectors using multi‐dimensional Riemann solutions erected at mesh vertices. Conservation of momentum and total energy along with the increase in entropy principle are invoked for computing these quantities at the vertices. Final state of deviatoric stress is effected via radial return algorithm based on the J‐2 von Mises yield condition. The scheme presented in this work is second‐order accurate both in space and time. The suitability of the scheme is evinced by solving one‐ and two‐dimensional benchmark problems both in structured grids and in unstructured grids with polygonal cells. Copyright © 2013 John Wiley & Sons, Ltd.