Pentagonal

In general, at least three anchors are required as the basis for the loop, since the motion around a point requires two independent coordinates. However, symmetry sometimes requires a greater number of anchors. A well-known case is the Jahn-Teller degeneracy of perfect pentagons, heptagons, and so on, which will be covered in Section V. Another special case arises when the electronic wave function of one of the anchors is an out-of-phase combination of two spin-paired structures. One of the vibrational modes of the stable molecule in this anchor serves as the out-of-phase coordinate, and the loop is constructed of only two anchors (see Fig. 12). 

The electronic spectrum of the radical has been recorded long before a satisfactory theoretical explanation could be provided. It was realized early on that the system should be Jahn-Teller distorted from the perfect pentagon symmetry (D5/, point group). Recently, an extensive experimental study of the high-resolution UV spectrum was reported [76], and analyzed using Jahn-Teller formalism [73],... 

Spherical, pentagonal dodecahedrane is the thermodynamically most stable CjoHjo-polycycloalkane. It is the so-called CjjHjo stabilomer . It should therefore be available by thermod5mamically controlled, e.g. acid-catalyzed, isomerization of less stable C24H20-isomers. Experiments along this line, e.g. treatment of the basketene photo-dimer with Lewis... 

At one time all cycloalkanes were believed to be planar It was expected that cyclopentane would be the least strained cycloalkane because the angles of a regular pentagon (108°) are closest to the tetrahedral angle of 109 5° Heats of combustion established that this is not so With the exception of cyclopropane the rings of all cycloalkanes are nonplanar... 

The most important stmctural variables are again polymer composition, density, and ceU size and shape. Stmctural foams have relatively high densities (typically >300 kg/m ) and ceU stmctures similar to those in Figure 2d which are primarily comprised of holes in contrast to a pentagonal dodecahedron type of ceU stmcture in low density plastic foams. Since stmctural foams are generally not uniform in ceU stmcture, they exhibit considerable variation in properties with particle geometry (103). 

XeOF square pyramid XeOF+3 disphenoid (C ) 67 XeOF-3 pentagonal 69,70... 

Fig. 11. Clathrate hydrates (a) basic structural component (H4QO2Q pentagonal dodecahedron) (b) type I host stmcture (two face-sharing 14-hedra are...

Fig. 8. Molecular stmcture of [Tj -C (CH2)5]2Zr(N2) 2(N2) (after Ref. 189). Each pentagon represents a pentamethyl cyclopentadienyl ring system.

Pyrrole has a planar, pentagonal (C2 ) stmcture and is aromatic in that it has a sextet of electrons. It is isoelectronic with the cyclopentadienyl anion. The TT-electrons are delocalized throughout the ring system, thus pyrrole is best characterized as a resonance hybrid, with contributing stmctures (1 5). These stmctures explain its lack of basicity (which is less than that of pyridine), its unexpectedly high acidity, and its pronounced aromatic character. The resonance energy which has been estimated at about 100 kj/mol (23.9 kcal/mol) is intermediate between that of furan and thiophene, or about two-thirds that of benzene (5). 

The a-rhombohedral form of boron has the simplest crystal stmcture with slightly deformed cubic close packing. At 1200°C a-rhombohedral boron degrades, and at 1500°C converts to P-rhombohedral boron, which is the most thermodynamically stable form. The unit cell has 104 boron atoms, a central B 2 icosahedron, and 12 pentagonal pyramids of boron atom directed outward. Twenty additional boron atoms complete a complex coordination (2). 

In the early 1960s it was recognized (6,187) that there were bonding similarities between the pentagonal face of the isomeric nido-Q fri ]f, ions and the well-known cyclopentadienide ion (Cp ) (Fig. 16). The isomeric nido-Q fri ]f, ions, which are commonly known as dicarboUide ions, and... 

---