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     

b1Σ+ Emissions from group V–VII diatomic molecules. b 0+ → X1 0+, X2 1 emissions of AsI and SbI

Chemiluminescence from the b 0⁺ → X₁ 0⁺ band system of AsI and of the b 0⁺ → X₁ 0⁺, X₂ 1 systems of SbI in the near-infrared spectral region has been observed in a discharge flow system. Analysis of the spectra led to the spectroscopic constants (in cm^?1) of AsI: ω_e(X₁, X₂) = 257 ± 2, ω_ex_e(X₁, X₂) = 0.82 ± 0.2, T_e(b 0⁺) = 11738 ± 5, ω_e(b 0⁺) = 271 ± 2, ω_ex_e(b 0⁺) = 0.66 ± 0.2, and of SbI: T_e(X₂ 1) = 965 ± 10, ω_e(X₁, X₂) = 206 ± 6, T_e(b 0⁺) = 12328 ± 10, ω_e(b 0⁺) = 211 ± 6. The intensity ratio of the two sub-systems b 0⁺ → X₂ 1 and b 0⁺→ X₁ 0⁺ was found to be ≈0.013 in the case of SbI and ? 0.01 for AsI.     

Influence of substrate morphology on organic layer growth: PTCDA on Ag(1 1 1)

By UV-excited photoelectron emission microscopy (UV-PEEM) we investigated the microscopic growth behavior of organic thin films using 3,4,9,10-perylene-tetracarboxylicacid dianhydride (PTCDA) on a Ag(1 1 1) single crystal substrate as example. Direct, real time observation allows to correlate the initial growth modes and the related kinetic parameters with substrate properties like terrace width, step density, and step bunches from the submonolayer range up to 5 layers or more. Above room temperature PTCDA grows in a Stranski–Krastanov fashion: after completion of the first two stable layers three-dimensional islands are formed. The nucleation density strongly depends on the temperature and the substrate morphology thus affecting the properties of the organic film.     

Determination of metal additives and bromine in recycled thermoplasts from electronic waste by TXRF analysis

A new method for analysis of metal additives in recycled thermoplasts from electronic waste was developed, based on dissolving the samples in an organic solvent and subsequent analysis of the corresponding solutions or suspensions by total-reflection X-ray fluorescence spectroscopy (TXRF). The procedure proved to be considerably less time consuming than the conventional digestion of the polymer matrix. Additives containing Ti, Zn, Br, Cd, Sn, Sb, and Pb were analyzed in a hundred randomly selected samples from recycling, which provided an overview of the range of elemental concentrations in thermoplasts utilized for consumer electronics. The results were validated independently by instrumental neutron activation analysis (INAA), subsequent regression analysis confirmed the trueness of the chosen approach.     

Square‐Planar Carbonylchlororhodium(I) Complexes Containing trans‐Spanning Diphosphine Ligands as Catalysts for the Carbonylation of Methanol

The rhodium(I) complexes trans‐[Rh(diphos)(CO)Cl] 7 (diphos=pbpb), 8 (diphos=nbpb), and 9 (diphos=cbpb) were synthesized (Scheme 4) and used as catalysts for the carbonylation of MeOH to AcOH (Scheme 1). The trans coordination imposed by the rigid C‐spacer framework of the diphos ligands pbpb, nbpb, and cbpb, demonstrated by ³¹P‐NMR and IR spectroscopy of 7 – 9 and unambiguously confirmed by single‐crystal X‐ray structure analysis of 7 , improved the thermal stability of the rhodium(I) system under carbonylation conditions and, hence, the catalytic performance of the complexes. For the catalytic carbonylation of MeOH, the active catalyst could be prepared in situ from the mixture of [Rh(CO)₂Cl]₂ and the corresponding diphos ligand pbpb, nbpb, or cbpb, giving the same results as carbonylation in the presence of the isolated complexes 7, 8 or 9 (see Table). The highest activity was observed for complex 7 (or the mixture [Rh(CO)₂Cl]₂/pbpb, the catalytic turnover number (TON) being 950 after 15 min (170°, 22 bar).     

Dyeing uric acid crystals with methylene blue

The growth of anhydrous uric acid (UA) and uric acid dihydrate (UAD) crystals from supersaturated aqueous solutions containing methylene blue, a cationic organic dye, has been investigated. Low concentrations of dye molecules were found to be included in both types of crystal matrixes during the growth process. Incorporation of dye into UA crystals occurs with high specificity, affecting primarily [001] and [201] growth sectors, while UAD crystals grown from solutions of similar dye concentration show inclusion but little specificity. The orientation of the UA-trapped species was determined from polarization data obtained from visible light microspectrometry. To achieve charge neutrality, a second anionic species must also be included with the methylene blue into UA and UAD crystal matrices. Under high pH conditions, crystallization of 1:1 stoichiometric mixtures of methylene blue and urate yields methylene blue hexahydrate (MBU.6(H2O). The crystal structure of MBU.6(H2O) reveals continuous pi-pi stacks of planes of dye cations and urate anions mediated by water molecules. This structure provides an optimal geometry for methylene blue-urate pairs and additional support for the incorporation of these dimers in uric acid single-crystal matrices. The strikingly different inclusion patterns in UA and UAD demonstrate that subtle changes in the crystal surfaces and/or growth dynamics can greatly affect recognition events.