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.     

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.     

Local Borel summability of Euclidean 311-1311-1311-1a simple proof via differential flow equations

It is shown how the differential flow equation (or, equivalently, the continous renormalization group) method can be employed to give an astonishingly easy proof of the local Borel summability of the renormalized perturbative Euclidean massive ₄ ⁴ .Supported by NSF grant # DMS-9100383     

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.     

Low frequency Raman spectroscopic study on lamellar polymer crystals

The recently observed very low-frequencyRaman bands in polyethylene open up the possibility of determining the straight-chain stem lengths within the crystal as opposed to the full periodicity constituted by crystal core plus amorphous surface layer given by lowangle X-ray diffraction. Past works (6–10) have established the correlation with lamellar thickness but leave doubts about the possibility of making the distinction just indicated. The first objective of the present work was to examine this point on crystals where the chains are inclined to different extents with respect to the lamellar surface. The samples include single-crystals grown from solution at different temperatures and oriented bulk polyethylenes. It is concluded that the low-frequencyRaman peaks correspond to the inclined chain length as opposed to the layer thickness, hence providing a measure of a chain as opposed to a platelet property. TheRaman based length figures are only slightly below those of the appropriately inclined straight traverses across the full lamellae, hence on the basis of existing understanding non-trans chain sequences are confined to a surface region which must be much narrower than required by the usually envisaged amorphous crystalline two-phase structure. Similar studies were carried out also on single crystals of the linear polyester poly(decamethylene sebacate). These demonstrate in the first place that polymers other than polyethylene can also be amenable to suchRaman studies and secondly that in this particular instance, changes in the relative thicknesses of crystal core and surface layer could be registered. The two studies in conjunction affirm the potential of the low-frequencyRaman technique for the study of polymer crystal morphology.     

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.     

The Nitrosation of Primary Aliphatic Diazocarbonyl Compounds: Formation of α-carbonyl nitrile oxides. Preliminary communication

Aqueous nitrosation of primary α-carbonyl diazo compounds (ethyl diazoacetate, diazoacetone, diazoacetophenones) yields α-carbonyl nitrile oxides, R? CO? CNO; their formation is demonstrated by 1,3-dipolar addition reactions.