Ab initio SCF Calculation of the Fluoronium Ion: Geometry,electronic structure and vibrational constants

An ab initio SCF calculation of 42 points of the energy hypersurface of the fluoronium ion is presented using a contracted F(5s/3p), H(2s) gaussian basis set. In its equilibrium structure a bond length of 1.812 a.u. and a HFH bond angle of 127.2° are predicted. The calculated vibrational frequencies for H₂F⁺, HDF⁺, and D₂F⁺ are in good agreement with the experimental data.     

An adaptive kernel-split quadrature method for parameter-dependent layer potentials

Advances in Computational Mathematics - It is well known in the literature that standard hierarchical matrix ( ${\mathscr{H}}$ -matrix)-based methods, although very efficient for asymptotically...     

Densest packings of eleven congruent circles in a circle

In 1969 Pirl provided the densest packings ofn equal circles in a circle forn 10. We will prove the optimality for the packings that were conjectured forn=11. The proof is based on elementary combinatorial and analytical techniques.     

Selective mixed coupling of carboxylic acids (II). — photolysis of unsymmetrical diacylperoxides with alkenyl-, halo-, keto-, carboxyl-groups and a chiral α-carbon. Comparison with the mixed kolbe electrolysis

Alkenoyl and functionalized alkanoyl dodecanoyl peroxides are prepared in 70 to 97 % yield and photolyzed at ?78° C. Thereby 4- to 10-alkenoyl and 4-alkanoyl peroxides afford good yields (56 – 68 %) of unsymmetrical coupling products. Similarly α- to σ-haloalkanoyl, cholanoyl or 3- and 4-carboxyalkanoyl peroxides can be coupled (40 – 70 %). The α-chiral diacyl peroxide ls undergoes the photochemical coupling reaction with 80 % retention of its configuration. The photolysis of diacyl peroxides at ?78° C proves to be a favorable supplement of the Kolbe-electrolysis in cases, where the electrolysis fails or produces low yields.     

High-Resolution,Higher-Order UV/VIS Derivative Spectrophotometry

Derivative spectrophotometry has gained increasing importance in the past two years and is currently experiencing vigorous development. Following and introduction the present article provides a review of this extremely effective method. In particular, the advantages of higher-order derivative spectrophotometry (HODS method, n > 2) are discussed on the basis of practical examples from a wide range of analytical fields. The results are achieved with the aid of a newly developed analog computer unit, whereby for the first time readily reproducible, low-noise, on-line spectra can be obtained up to the 7th order and even, in favorable cases, up to the 9th order. In practice it has proved valuable to work with spectra of the 3rd to 5th order; but even higher derivations could be profitable for the separation of strongly superposed signals or for “fingerprinting”.     

Isolierung von (−)-Dunnion aus Calceolaria integrifolia MURR. (Scrophulariaceae)

Isolation of (?)-dunnione from the leaves of Calceolaria integrifolia, MURR . (fam. Scrophulariaceae) From the leaves of Calceolaria integrifolia, a plant often used in horticulture. partially racemic (?)-dunnione (1) has been isolated. This seems to be the first record of its occurrence outside the family Gesneriaceae, where it previously has been found in two species as the (+)-enantiomer.     

Hexacyanopalladium(IV)-säure und Hexacyanopalladate(IV)

The preparation and the properties of the hexacyanopalladium(IV) acid (H₃O)₂[Pd(CN)₆] and of a number of metal hexacyanopalladates(IV) are described. UV, IR and Raman spectra are reported, force constants have been calculated and the bonding properties are discussed. K₂[Pd(CN)₆] crystallizes in a hexagonal lattice; a = 7.42, c = 6.65 Å, Z = 1.