Pentagonal symmetry

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],... 

Figure 1.44 Cluster obtained spontaneously on cooling a simulated Lennard-Jones drop of 129 atoms in a molecular dynamics study. The heavy lines indicate elements of pentagonal symmetry. (After Hoare Barker, 1976).

Cyclopentadienyl thallium, T (CsHi), has been investigated recently by microwave spectroscopy.136 The cyclopentadienyl group is nearly planar and has pentagonal symmetry. It lies to one side of the thallium atom. 

Conductance measurements showed that the nicotinic receptors contain channels permeable to Na+ and other cations and that they are acetylcholine-gated ion channels. Construction of a three-dimensional image from electron micrographs at various angles of tilt shows a tube with approximate pentagonal symmetry and a narrow channel through the center (Fig. 30-23).622 624 636 Acetylcholine binds to sites on the two a subunits 3 nm away from the ion channel. 

Julg et al.24 employed an approximation based on the self consistent field molecular orbital method to evaluate the average energy per atom for various structures. They calculate that whereas the normal b.c.c. structure is more stable for clusters containing more than 106 atoms, smaller clusters prefer to take up pentagonal symmetry. However, these authors make an important point, namely, that the calculated energies for different structures are very similar. Interconversion of different structures will be facile, and external factors such as the method of deposition, level of impurities, support effects, etc., may cause the less stable structure to grow. For example, impurities on... 

Li) 24 64,66-68 different textures.69 70 However, the majority of papers have been concerned with particles having pentagonal symmetry.15,25,26,59,68,70-90 In certain circumstances structures having five-fold symmetry are stable to annealing and even after fusion of the particles.90 There have been reports also of square and regular pyramids56 91 tetrahedra,56,91 raft-shaped particles,92-94 and chain structures.95... 

Many primitive organisms have the shape of the pentagonal dodecahedron. As will be seen later, pentagonal symmetry used to be considered forbidden in the world of crystal structures. Belov [82] suggested that the pentagonal symmetry of primitive organisms represents their... 

A number of nanowire and nanorod morphologies are available but the most common are single crystalline and those with a pentagonal symmetry that results from a five-fold twinning in the seed nanoparticles. The structure of the single crystal [50-52] and pentagonal [53-55] morphologies has been established by extensive TEM analysis. 

The only known metal heptahalides are ReF7 and OSF7, the latter being stable only at low temperatures. The only other heptafluoride known is IF7. The evidence for the pentagonal symmetry of ReF7 (and IF7) has been summarized. ... 

F. Patthey, and W. D. Schneider, Conservation of chirality in a hierarchical supramolecular self-assembled stmc-ture with pentagonal symmetry, Angew. Chem., Int. Ed. 44(33), 5334-5337 (2005). 

Figure 2.4 Lattices with pentagonal symmetry cannot form (a) a fragment of a lattice with pentagonal symmetry (b, c) displacement of the fragment by a lattice vector does not extend the lattice (d) fragments with pentagonal symmetry can be part of a pattern by placing each on a lattice point...

T. Imanaka, K. Miki, Crystal structure of a novel-type archaeal Rubisco with pentagonal symmetry, Structure 2001, 9(6),... 

A number of papers have been published that report unusual symmetries for small particles such as atoms in abnormal positions, raft-like structures, close-packed structures different from the normal bulk structures and different textures (23). Among those unusual arrangements, there is a strong emphasis on the pentagonal symmetry. The conditions under which the different types of structure tend to be formed have been summarized by Yacaman et al. (256). 

The EXAFS results indicate that the lattice parameter of small particles is contracted as compared with that of the bulk metal (23). This fact is confirmed by radial electron distribution data obtained from X-ray experiments (257a,b) and also by electron diffraction measurements (257c). Both this contraction and the anomalous pentagonal symmetry can be eliminated in the case of Pt particles onto which hydrogen is adsorbed. These relaxation effects, which are found to be reversible, will not be... 

Unusual crystal structure (e.g., pentagonal symmetry) Labile surface atoms Lower melting point Larger ionization potential... 

Symmetry plays also an outstanding role to establish and to justify the possible crystal classes. Due to the principle of the space fulfillment, for a long time a pentagonal symmetry in crystallography was considered to be impossible. 

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