Hexagonal resonator

The two Kekule structures for benzene have the same arrangement of atoms but differ m the placement of electrons Thus they are resonance forms and neither one by Itself correctly describes the bonding m the actual molecule As a hybrid of the two Kekule structures benzene is often represented by a hexagon containing an inscribed circle... 

Resonance can also occur with many organic molecules, including benzene, QHe, which is known to have a hexagonal ring structure. Benzene can be considered a resonance hybrid of the two forms... 

Benzene, C6H(l, is another molecule best described as a resonance hybrid. It consists of a planar hexagonal ring of six carbon atoms, each one having a hydrogen atom attached to it. One Lewis structure that contributes to the resonance hybrid is shown in (11) it is called a Kekulc structure. The structure is normally written as a line structure (see Section C), a simple hexagon with alternating single and double lines (12). 

From comparison of the optical properties of particles deposited on the same substrate and differing by their organization (Figs. 7 and 8) it can be concluded that the appearance of the resonance peak at 3.8 eV is due to the self-organization of the particles in a hexagonal network. This can be interpreted in terms of mutual dipolar interactions between particles. The local electric field results from dipolar interactions induced by particles at a given distance from each other. Near the nanocrystals, the field consists of the ap-... 

Each of the eight hyperfine resonances is an unresolved quadmpole doublet, due to the quadmpole interaction of Os in the hexagonal Os metal source. The authors have interpreted the hyperfine fields in terms of core polarization, orbital and spin-dipolar contributions. 

Figure 5.36. Schematic representation of the fullerene C60 molecule. Notice its highly symmetric structure (truncated icosahedron) in which all carbon atoms are identical and are located at the connection between two hexagons and one pentagon. The bond lengths are 138.6 pm for the bonds common to two hexagons (having a double-bond resonant structure) and 143.4 pm for the hexagon-pentagon common bonds. The bonding therefore seems to be not completely delocalized as in graphite.

Figure 2. Near-field intensity portraits of a WG-Uke mode in (a) a square microdisk resonator and (b) a bow-tie mode in a quadrupolar (stadium) resonator and (c) a monopole mode in a hexagonal photonic crystal defect cavity (Boriskina, 2005).

Figure 7.2 (A) Bond lengths for the five different sets of C-C bonds and favored electronic resonance structure of [(Et3P)2Pt]6C5o determined by X-ray crystal structure analysis. (B) 48-Electron rc-system produced by the saturation of six double bonds in the octahedral sites of leaving eight linked benzenoid hexagons.

Figure 13.4 C(7)-C(8) isomer resulting from monoaddition of benzyne to Cjg and Kekul resonance structure of C70, illustrating the benzenoid character of the equatorial hexagons.

This isomer represents the first example of a [5,6]-adduct in which the fusion bond remains intact. This addition mode was explained by the relatively high double bond character of the [5,6]-bond C(7)-C(8), which underlines the importance of the Kekule structure of C7Q that involves the benzenoid hexagons at the equatorial belt. No such resonance structure is required to describe the proper bonding situation within C50 (see also Chapters 1 and 14). 

It has been calculated that there are 12 500 Kekule resonance structures possible for CgQ [104]. However, the two types of bonds in Cjq have different lengths, with the [6,6]-bonds being shorter than the [5,6]-bonds (see Chapter 1). Thus, the lowest energy Kekule structure of is that with all the double bonds located at the junctions of the hexagons ([6,6]-double bonds) (Figure 14.5). 

See Contact stress Hexagonal symmetry 132 Hohenberg-Kohn theorem 113 Hydrogen molecular ion 173 history 173 repulsive force 185 resonance interaction 177 van der Waals force 175 Hydrogen on silicon 336 Image force 56—59, 72, 93 concept 56 effect on tunneling 74 field emission, in 56 jellium model, in 93 observability by STM 72... 

See Scanning tunneling spectroscopy Superconductors 332—334 Surface Brillouin zone 92 hexagonal lattice 133 one-dimensional lattice 123, 128 square lattice 129 Surface chemistry 334—338 hydrogen on silicon 336 oxygen on silicon 334 Surface electronic structures 117 Surface energy 96 Surface potential 93 Surface resonance 91 Surface states 91, 98—107 concept 98... 

Uwada T, Asahi T, Masuhara H, Ibano D, Fujishiro M, Tominaga T (2007) Multiple resonance modes in localized surface plasmon of single hexagonal/triangular gold nanoplates. Chem Lett 36(2) 318-319... 

---