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.     

Performance of the diffusive gradients in thin films technique for measuring Ca and Mg in freshwater

Measurements of the major cations Ca and Mg by the technique of diffusive gradients in thin films (DGTs) were systematically evaluated. The concentration in solution was calculated using Fick’s first law of diffusion from the directly measured flux to the DGT device. A selective cation exchange resin (Bio-Rad Chelex^®100), which has been used extensively with DGT for trace metals, such as Cd²⁺, Cu²⁺ and Ni²⁺, was used for this work.

Elution of Ca and Mg from the resin with 1 M HNO₃ was very reproducible. Measurements of Ca and Mg concentrations in synthetic solutions agreed well with the theoretical predictions. The negative response on uptake caused by lowered pH was investigated. Uptake was found to decline below pH 5. The capacity of the DGT device for Ca and Mg was also investigated to establish maximum deployment times for given concentrations.

Experiments with filtered and modified lake water show that DGT can be used to measure Ca and Mg when trace metals are present in the solution. An in situ deployment of DGT combined with an ultrafiltration study suggest that the Mg concentration measured by DGT is similar to the concentration found in the fraction <1 kDa.     

Synthesis and Photochemical Behaviour of 2-Amino-1,3-Cyclohexadienes

The reaction of the 4,4-dialkylated 2-cyclohexenones 1 or 2 with a twofold excess of a secondary amine 3 affords the 2-amino-1,3-cyclohexadienes 4 and 5 , respectively. Irradiation (λ ≧ 300 nm) of the morpholino derivative 4a yields a mixture of the isomeric 3-morpholino-6-methyl-1,3,5-heptatrienes 6 and 7 , while 5 gives only one corresponding product 8 . The reaction of enone 1 with an equimolar amount of pyrrolidine ( 3c ) affords the bis-enamine 9 which is converted to the unsaturated diketone 10 by oxidative hydrolysis.     

A matrix isolation study of the C(s) symmetric OCNO(X 2A') radical

Here we report the first experimental detection of the C(s) symmetric nitroformyl radical, OCNO(X 2A') in a nitrogen-carbon dioxide matrix at 10 K using a Fourier transform infrared spectrometer (FTIR). The nu1 vibrational frequency was observed at 2113 cm(-1). This assignment was confirmed by follow-up experiments using isotopically labeled reactant molecules (15N, 18O, 13C). To synthesize this radical, we irradiated solid nitrogen-carbon dioxide ice mixtures with energetic electrons at 10 K. Suprathermal nitrogen atoms in their electronic ground and/or first electronically excited state were generated via the radiation induced degradation of molecular nitrogen; these atoms could then react with carbon dioxide to eventually yield the nitroformyl radical. We also investigated the kinetics of the formation of the nitroformyl radical and support the arguments with computations on the doublet and quartet OCNO potential energy surfaces (PESs).     

Asymmetric lithiation of 2-alkynyl aryl sulfides—Enantio- and diastereoselective formation of allenyl aryl sulfides and their application in nickel-catalyzed cross-coupling reactions

The enantio- and diastereoselective synthesis of allenyl aryl sulfides by asymmetric lithiation of 2-alkynyl (2-hetero)aryl sulfides is described. A dynamic thermodynamic resolution by selective crystallization of the intermediate lithium complexes derived from deprotonation, applying a bis(oxazoline) ligand, was achieved to give enantioselectivities up to 85% ee. Subsequent stereospecific nickel-catalyzed cross-coupling reactions with arylzinc reagents established a versatile access to threefold carbon-substituted allenes.     

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