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.     

Cogenerators for convex spaces

We give cogenerators for the categories of convex (= finitely superconvex), finitely positively convex, and absolute convex (= finitely totally convex) spaces introduced by Pumplün and Röhrl.Dedicated to our academic teacher Dieter Pumplün on the occasion of his sixtieth birthday.     

On the dissolution processes of Na2I+ and Na3I2+ with the association of water molecules: mechanistic and energetic details

The sequential association energies for one through six water molecules clustering to Na(2)I(+), as well as one and two water molecules clustering to Na(3)I(2)(+), are measured. The association energies show a pairwise behavior, indicating a symmetric association of water molecules to the linear Na(2)I(+) and Na(3)I(2)(+) ions. This pairwise behavior is well reproduced by Density Functional Theory (DFT) calculations. DFT calculations also suggest that a significant separation of charge for the Na-I ion pair occurs when four or more water molecules cluster to a single sodium center. Two different solvent-separated ion pairs have been identified with the DFT calculations. Experiments also show that the dissolution processes, loss of a neutral NaI unit, occurs when six or more water molecules have been added to Na(2)I(+) cluster. However, one or two water molecules are able to detach an NaI unit from the Na(3)I(2)(+) cluster. The difference in solubility of the Na(2)I(+) and Na(3)I(2)(+) ions is due to the difference in the energies required to lose an NaI unit from these two species. The experiment also confirms that the loss of a neutral NaI unit, instead of an Na(+) ion, occurs during the dissolution processes of Na(3)I(2)(+). The microsolvation schemes proposed to explain our experimental observations are supported by DFT and phase space theory (PST) calculations.     

Intact size-selected Au(n) clusters on a TiO2(110)-(1 x 1) surface at room temperature

Experiments in which mass-selected gold clusters were deposited on a surface have found that the catalytic properties depend strongly on cluster size. However, these experiments have not established definitively that the clusters maintain their size after deposition. We report here work in which we deposit low kinetic energy, mass-selected Aun+ (n = 1-8) clusters on a rutile TiO2(1 x 1) surface and use ultrahigh vacuum scanning tunneling microscopy (UHV-STM) to determine their size and shape.     

Conformation and luminescence of isolated molecular semiconductor molecules

In this article, we describe, for the first time, direct comparisons of the detailed structures of two small molecule organic semiconductors, oligo(phenylenvinylene) (OPV) molecules with chains of five and six phenyl rings (5R-OC(8)H(17) and 6R-OC(8)H(17)), respectively, and their luminescence properties on a single molecule level. Our data originate from a combination of two powerful diagnostic tools in physical chemistry: ion mobility and single molecule fluorescence spectroscopy. These techniques enable us to precisely determine the shapes of isolated molecules in the gas phase and to correlate these structures to the emission from single molecules supported on bare glass substrates. The principal structural uncertainty in OPVs is the (possible) presence and location of cis-vinylene linkages (cis-defects) in the oligomer. The results show that the structures observed in the gas phase are strongly correlated to the categories of molecules observed in the single molecule polarization anisotropy measurements with nearly identical distributions for the two OPV molecules studied. Each category is also characterized by the luminescence efficiency of the molecules in each class, providing a direct correlation between the luminescence efficiency and the shape of the molecule. This combination of techniques provides a level of information far beyond that obtained via any other analytical technique.     

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.