Produktintegration mit nicht-äquidistanten Stützstellen

Summary For the numerical evaluation of , 0<<1 andx smooth, product integration rules are applied. It is known that high-order rules, e.g. Gauss-Legendre quadrature, become normal-order rules in this case. In this paper it is shown that the high order is preserved by a nonequidistant spacing. Furthermore, the leading error terms of this product integration method and numerical examples are given.

     

An average-of-configuration method for using Kohn-Sham density functional theory in modeling ligand-field theory

The Amsterdam Density Functional (ADF) package has been used to constrain Kohn-Sham DFT in such a fashion that a transition from KS-DFT to ligand-field theory in the form of the parametrical d(q)() model is completely well-defined. A relationship is established between the strong-field approximation of the parametrical d(2) model for the tetrahedral complexes VCl(4)(-) and VBr(4)(-) and certain fixed-orbital ADF-computed energies. In this way values for all the parameters of the d(2)() model may be computed, thus allowing the ADF results to be expressed in terms of a KS-DFT energy matrix that can be diagonalized. This means that the KS-DFT deficiency with regard to computation of nondiagonal elements has been overcome and the KS-DFT eigenenergies have become available through the KS-DFT mimicking of the ligand-field plus repulsion model. By using mutually orthogonal strong-field energy matrices, the mimicking has been further elucidated. The computed values for the empirical parameters of VCl(4)(-) and VBr(4)(-) are in good agreement with experimental data. The spectrochemical and the nephelauxetic series have been computed by including the remaining halide complexes and the quantitatively special position of F(-)() among the halides corroborated for both series.     

Phase-fixed double-group 3-Γ symbols. IV. Real 3-Γ symbols and coupling coefficients for the group hierarchies T* ⊃ C 3 * and T* ⊃ C 2 *

We present sets of real 3- symbols which correspond to explicitly given irreducible matrix representations for the two double group hierarchies T* C ₃ ^* and T* C ₂ ^* . They fit into the formalism exposed in a previous paper [1] on the general theory of 3- symbols and coupling coefficients and illustrate much of the discussion in a subsequent one [2] treating the particular properties of the double groups.     

1,4-dimethyl-3,6-dioxo-1,2,4,5-tetrazin-1-IUM-5(4h)-id,a new six-membered heterocyclic betaine

The preparation, the spectroscopic characterization, the crystal structure and chemical reactions of the new six-membered heterocyclic betaine2 are reported; 2 is a representative of a possibly large group of yet unkonwn betaines of the general structure 8.     

Oral malodor,assessed by closed-loop,gas chromatography,and ion-trap technology

A method is described for the analysis of volatile organic compounds in saliva and tongue coating samples. The techniue is based on an off-line preconcentration step by means of a closed-loop trapping system followed by gas chromatography-ion trap detection. With the closed-loop technique, the volatile organic compounds(VOCs) are released from the matrix and trapped on an adsorbent without interference of water. The VOCs are released from the adsorbent into the gas chromatograph by thermdesorption. After separation, identification of the compounds is performed by ion trap technology. By this technique 82 compounds could be demonstrated in saliva and tongue coating samples. The technique is also used to demonstrate the formation of volatile bacterial fermentation compounds when a protein substrate is added to tongue coating samples. It is considered a very promising tool in further research on oral malodor.     

Ab initioSTO-3G optimization of planar,perpendicular, and twisted molecular structures of biphenyl

The complete molecular structure of biphenyl, characterized by 12 independent parameters, has been derived by ab initio gradient techniques using a STO -3G basis set for coplanar, perpendicular, and minimum energy conformations with the constraint of planar phenyl ring units and a C₂ symmetry axis along the CC interring bond. The minimum torsional angle obtained was ? = 38.63° with torsional energy barriers of 8.59 and 10.04 kJ/mol for ? = 0° and ? = 90°, respectively.     

Die Brauchbarkeit von PbClF und PbBrF zur Fluorbestimmung in technischen Fluoriden

Zusammenfassung PbClF und PbBrF werden bezüglich ihrer Fällungsbedingungen und Eignung zur Fluoridbestimmung verglichen.Für reine Lösungen sind bei Einhaltung bestimmter Fällungsbedingungen beide Methoden gleich gut geeignet. Bei der Fällung aus silicathaltigen Probelösungen, wie sie bei der Fluorbestimmung in technischen Fluoriden anfallen, liefert die PbClF-Fällung positive Fehler, während man über PbBrF sehr gute Werte erhält.Eine Arbeitsvorschrift für die Fluorbestimmung in Aluminiumfluorid und Kyrolith nach der Bleibromidfluoridmethode ist angegeben.

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Summary PbClF and PbBrF have been compared with respect to their precipitation conditions and their suitability for the determination of fluoride.For pure solutions, if certain precipitation conditions are adhered to, both methods are equally well suitable. When precipitating from silicate-containing sample solutions, as they are obtained when fluorine is determined in technical fluorides, the PbClF precipitations yields positive errors, while very good values are obtained with PbBrF.A working procedure is given for the determination of fluorine in aluminium fluoride and cryolite by the lead bromide fluoride method.

     

Refined ab initio 6-31G split-valence basis set optimization of the molecular structures of biphenyl in twisted,planar, and perpendicular conformations

Improved full ab initio optimizations of the molecular structure of biphenyl in twisted minimum energy, coplanar, and perpendicular conformations by use of Poles's GAUSSIAN 82 program have been performed in the 6-31G basis set. These lead to geometries and energies of much higher reliability than our earlier STO-3G results. The torsional angle Φ_min obtained now is 45.41° in close agreement with the recent experimental value of 44.4° ± 1.2°. Calculated CC distances may be converted to experimental ED r_g-values by means of independently determined linear regression correlations with very high statistical confidence, although they agree better with experimental x ray data for coplanar biphenyl without this correction. Calculated intramolecular angles are very similar for both STO-3G and 6-31G basis sets. The calculated torsional energy barrier towards Φ = 90° (ΔE⁹⁰) is 6.76 kJ/mol in close agreement with the experimental-31G value of 6.5 ± 2.0 kJ/mol. For coplanar biphenyl with D_2h-symmetry the calculated torsional energy barrier ΔE⁰ is 13.26 kJ/mol which is surprisingly much higher than the experimental value of 6.0 ± 2.1 kJ/mol. This discrepancy could not be resolved by optimizations assumed for two kinds of distortions of planarity of orthohydrogens from the molecular plane of the coplanar carbon atoms. But for the twisted minimum energy conformation asymmetric bending of ortho-H atoms lead to a torsional angle Φ_min = 44.74° together with a dihedral angle towards ortho-H of 1.22°, and consequently even to an increase of torsional energy barriers to ΔE⁰ = 13.51 and ΔE⁹⁰ = 6.91 kJ/mol.