The reaction of allenylsilanes with α,β-unsaturated acylsilanes: new annulation approaches to five and six-membered carbocyclic compounds

The reaction of α,β-unsaturated acylsilanes with allenylsilanes can be directed to produce either five or six-membered carbocyclic compounds.     

Intramolecular multiple scattering in electron diffraction from fluoro-methyl halides

Relative elastic differential cross sections for scattering of 1 keV electrons from CF₃H, CF₄, CF₃Cl, CH₃F and CH₃Cl molecules were measured for momentum transfer from 3 Å^?1 to 29 Å^?1. The oscillatory residuals remaining after substraction of the atomic scattering and the molecular interference contributions calculated in the independent atom model are ascribed to the influence of intramolecular multiple scattering. The data reflect the dominant contributions of the CF₃-group and show larger oscillations than obtained from triple scattering calculations according to the method of Liu and Bonham using the second Born approximation.     

Projection between basis sets: A means of defining the electronic structure of functional subunits

The general problem of the transfer of the representation of a set of orthonormal functions from one basis to a different, nonequivalent one is considered and specialized to a matrix formulation convenient for use in molecular electronic structure calculations. A procedure is suggested for treating problems where the transfer of representation breaks into a subset of most interest and one of less interest as for example the occupied and virtual orbitals of a Hartree-Fock SCF calculation. These techniques are then applied to obtain a representation of a methyl group from an SCF wave function for methane.     

Rapidly converging lattice sums for nonelectrostatic interactions

The relative energies of one-, two-, and three-dimensional Bravais lattice Lennard-Jones particles can be calculated by lattice sums. The expression of lattice sums over a Lennard-Jones potential can be manipulated into a form that converges rapidly. A formalism capable of calculating the lattice potential at arbitrary points of a completely general lattice has been developed. This method provides an alternative way to calculate the relative energies from the surface and the interior bulk sites of many chemical systems. The method is illustrated with application to hcp and fcc Lennard-Jonesium, both for the relative binding energy and for calculating the potential along the geometric diffusion pathway between tetrahedral and octahedral interstitial sites. Diffusion from the tetrahedral site to the octahedral site experiences a barrier of 752.600 in units of 4 epsilon. The reverse pathway experiences a barrier of 1035.614 in units of 4 epsilon.     

Propylene bulk phase oligomerization with bisiminepyridine iron catalysts: Mechanistic investigation of 1,2-versus 2,1-propylene insertion

Iron(II) complexes were synthesized with bisiminepyridine ligands of different steric demand. Activation with modified MAO (25 mol% isobutyl groups) generated very active catalysts for propylene oligomerization. These oligomerizations were carried out in liquid propylene in a heat flow calorimeter. The oligomers were separated by preparative gas chromatography and the dimers and trimers analyzed using analytical gas chromatography, ¹H-NMR-, and ¹³C NMR-spectroskopy. By means of the knowledge of the dimer and trimer structure, we were able to establish a mechanistic pathway for propylene insertion and obtained knowledge about the iron alkyl species involved. Analysis of the various dimers formed allowed us to determine the percentage of 1,2-versus 2,1-propylene insertions. Considering the same iron alkyl species with ligands of different steric demand, a change in the probabilities for 1,2-versus 2,1-propylene insertions can be observed. With this knowledge, the catalyst behaviour for ligands of varying steric demand can be predicted. The question of how to produce oligomers versus polymers is one of knowing how to control the ratio of the 1.2-and 2.1-insertion. One method is to alter the steric demand in the ortho position of the ligand. The more bulky the ligand, the more often a 2,1-propylene insertion happens and, therefore, the higher the molecular mass of the oligomers, i.e., polymer is formed. Another important observation is that the formation of α-olefines is favored with a higher steric demand of the catalyst. The text was submitted by the authors in English.     

Solution manifolds and submanifolds of parametrized equations and their discretization errors

Summary The paper concerns solution manifolds of nonlinear parameterdependent equations (1)F(u, )=y₀ involving a Fredholm operatorF between (infinite-dimensional) Banach spacesX=Z× andY, and a finitedimensional parameter space . Differntial-geometric ideas are used to discuss the connection between augmented equations and certain onedimensional submanifolds produced by numerical path-tracing procedures. Then, for arbitrary (finite) dimension of , estimates of the error between the solution manifold of (1) and its discretizations are developed. These estimates are shown to be applicable to rather general nonlinear boundaryvalue problems for partial differential equations.This work was in part supported by the U.S. Air Force Office of Scientific Research under Grant 80-0176, the National Science Foundation under Grant MCS-78-05299, and the Office of Naval Research under Contract N-00014-80-C-0455