Edge-bonded structure

Figure 1.19 The structure and bond angles of ethene. The plane of the atoms is perpendicular to the paper. The dashed edge bonds project behind the plane of the paper, and the solid wedge bonds project in front of the paper.

Solving the simultaneous equations (2a) and (2b) leads to y = 3 and t = n — 2, implying the presence of three B-B bonds and n — 2 B-B-B bonds in the boron skeleton. Since a deltahedron with n vertices has In — 4 faces, the n — 2 B-B-B bonds cover exactly half of the faces. In this sense a Kekule-type structure for the deltahedral boranes B H 2- has exactly half of the faces covered by B-B-B bonds just as a Kekule structure for benzene has half of its edges covered by C=C double bonds. In 1977 Lipscomb and co-workers [29] reported a variety of such Kekule-type localized bonding structures with the lowest energies for deltahedral boranes. These structures were computed using wave functions in the differential overlap approximation. 

In solid state physics, the sensitivity of the EELS spectrum to the density of unoccupied states, reflected in the near-edge fine structure, makes it possible to study bonding, local coordination and local electronic properties of materials. One recent trend in ATEM is to compare ELNES data quantitatively with the results of band structure calculations. Furthermore, the ELNES data can directly be compared to X-ray absorption near edge structures (XANES) or to data obtained with other spectroscopic techniques. However, TEM offers by far the highest spatial resolution in the study of the densities of states (DOS). 

Structure X-N8 differs from V-N8 by only one high-coordination edge bond and the presence or absence of such a bond would not affect the coordination numbers of either carbon. There is no precedent to indicate that the more desirable 55-bridge hydrogens in V-X8, as opposed to the 65-bridge hydrogens in X-N8, would constitute a sufficient... 

In studies on the absorption-edge fine structure in organometallic complexes, Pauling s valence bond theory may be used in explaining the fine structure. 

Graphical modeling can also be useful in representing the elements of the transfer matrix, J], adopted by Klein et ah, [13] Fig 3 shows the five Kekule valence-bond structures of enanthrene and their local states In this case one needs a directed graph with weighted edges and loops ... 

Each Kekule valence-bond structure corresponds to a perfect match of the edges of the polyhex graph, see ref- 38-J- Riordan, An Introduction to Combinatorial Analysis Wiley, New York (1958) C-L- Liu, Introduction to Combinatorial Mathematics, McGraw-Hill, New York (1968)- A chemical version on rook boards may be found in C-D- Godsil and 1- Gutman, Croat- Chem-Acta- 54, 53 (1981). 

Figure 7.26. Electron energy-loss spectroscopy (EELS) spectra. Shown (top) is a representative EELS spectrum of a nickel oxide sample. A typical EELS spectrum shows a zero-loss peak that represents the unscattered or elastically scattered electrons, the near-edge fine structure (ELNES), and extended energy-loss fine structure (EXELFS). Also shown (bottom) are the fingerprint regions of an EELS spectrum, just beyond the core-electron edges, which provide information regarding the detailed bonding and chemical environment of the desired element.

D Structures. When the building blocks are unique or when dealing with the large variety of ordinary chemical structures, a 2D representation is used. In mathematical terms, this is a "graph" of the structure, which consists of a set of "nodes" (atoms) connected by "edges" (bonds). The important atom infor-... 

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