Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

Charge location and fragmentation under electron impact. IV—the behaviour under electron impact of some N-methyl,N′-R-1,2,4-phosphadiazetidine-3-ones and related compounds

The ionization potentials of a series of N-methyl,N′-R-1,2,4-phosphadiazetidine-3-ones and related compounds have been determined. The nature of the highest occupied orbital of the molecules and the use of empirical rules to rationalize the variations in the ionization potentials are discussed. The changes in the fragmentation patterns are related to the different low ionization potential site(s) in each molecule. The occurrence of various rearrangement ions are discussed on a similar basis.     

Detecting proximities between quadrupolar nuclei by double-quantum NMR

A robust, easy to optimize, and efficient homonuclear correlation NMR experiment for half-integer quadrupolar nuclei in solids is described and has been experimentally tested on anhydrous Na2HPO4-(23Na, S= 3/2 nucleus) and as-synthesized AlPO4-14 (27Al, S= 5/2 nucleus), an aluminophosphate molecular sieve.     

Vierring-synthesen durch [3 + 1]-cycloaddition . Synthese von 3-imino-azetidinen aus azomethin-yliden und isonitrilen

Azomethine ylide 3 , generated by thermolysis of 3,4-diphenyl-Δ¹-1,2,3-triazoline-5,5-dimethyldicarboxylate 1 , can be trapped by isonitriles to give 3-imino-1,4-diphenylazetidine-2,2-dimethyldicarboxylates 5 . The IR, ¹H-NMR, ¹³C-NMR and mass spectral data of the new compounds are discussed.     

Reactive scattering of sodium clusters with molecular oxygen

The first reactive differential scattering study for atomic clusters is reported. Oxidation of Na _x (x8) with O₂ is investigated in a crossed beam apparatus. Sodium oxide (Na _n O,n4) and sodium dioxide (Na _n O₂,n6) are produced with a total reactive cross section from 50 to 80 Ų, depending on the cluster size. The excess energies for these reactions are estimated by an SCF type ab initio calculation and range from 0.5 to 5 eV. The large cross section may then be understood quantitatively in terms of a harpooning mechanism as a first step in the reaction path. Angular distributions have been determined for the most abundant products, showing strong forward scattering. Two different schemes are discussed for the reaction: while the dioxides Na _n O₂ may be formed by an evaporative cooling process from a highly excited collision complex, formation of Na _n O appears to originate from a direct process. In both cases the experimental data suggest that most of the exothermicity remains in the reaction products.     

Oleophilic ion-exchange resins. IV. Swelling of quaternary ammonium polymers in mixed solvents

The swelling characteristics of an oleophilic anion-exchange resin in methanol–benzene and ethanol–chloroform mixed solvent systems were compared with those of a conventional anion-exchange resin. The oleophilic resin was prepared by amination of chloromethylated polystyrene 1% DVB with N,N-dimethyldodecylamine. It showed a large shift of the swelling peak from polar to less polar solution compositions in both methanol–benzene and ethanol–chloroform systems as compared with the swelling of conventional resins. Total solvent uptake and solvent distribution between resin and solvent phases were also determined. The less polar solvent (benzene or chloroform) was sorbed preferentially by the oleophilic resin over a wide range of composition, while preference for the more polar solvent (methanol or ethanol) by the conventional resin was shown over the entire composition of the mixed solvent systems. The Newman-Krigbaum treatment of mixed solvents was applied to swelling data on the ethanol–chloroform–oleophilic resin system, where the volume of the gel network plus the solvent imbibed was relatively constant over the entire range of composition. The result suggests a strong similarity of the liquid–liquid interaction terms in this gel phase compared with those in the pure binary liquid phase.