Symmetry molecular quasi

It took the short time of one year or so to solve the structure of rhinovirus which causes the common cold. This relied on two major advances in methods. The first was the use of synchrotron radiation in data collection. Nearly a million reflections were collected on the protein crystallography facility at the Cornell Synchrotron source in a matter of days. This conveyed a speed advantage over data collection on a conventional source and also ameliorated an otherwise impossible problem of radiation damage when long exposure times were used. The far greater rate of radiation damage in the X-ray beam in relation to plant viruses is symptomatic of an inherently less stable protein capsid and the absence of quasi-symmetry. The capsid consists of 60 copies each of four proteins and the virus with about 30 % RNA has a total molecular weight of about 8.5 million. 

The synthesis of molecular carbon structures in the form of C q and other fullerenes stimulated an intense interest in mesoscopic carbon structures. In this respect, the discovery of carbon nanotubes (CNTs) [1] in the deposit of an arc discharge was a major break through. In the early days, many theoretical efforts have focused on the electronic properties of these novel quasi-one-dimensional structures [2-5]. Like graphite, these mesoscopic systems are essentially sp2 bonded. However, the curvature and the cylindrical symmetry cause important modifications compared with planar graphite. 

The extraordinary bonding properties in 16 can also be seen in a diagram of 16 (Fig. 34). In 16, an almost perfect five-numbered axis is attained, distorted only by the central Ga2 unit. This is the first time that a symmetry close to the five-numbered symmetry is observed for molecular metalloid clusters. A few solid-state modifications with five-numbered symmetry have, however, been found for compounds involving Group 13 elements. Because there is no crystallographic space group with a five-numbered axis, these compounds are summarized under the collective name quasi-crystals .83 For a better understanding of quasi-crystals,... 

The molecular planes of the two molecules in the unit cell are nearly parallel to each other and the binary axis which makes the actual 2 point group symmetry close to mm2 symmetry. The crystal is thus near to uniaxial and the "quasi-optical axis" close to the direction perpendicular to the molecular planes (assuming that the... 

The alkene metathesis reaction was unprecedented - such a non-catalysed concerted four-centred process is forbidden by the Woodward-Hoffmann rules - so new mechanisms were needed to account for the products. Experiments by Pettit showed that free cyclobutane itself was not involved it was not converted to ethylene (<3%) under the reaction condition where ethylene underwent degenerate metathesis (>35%, indicated by experiments involving Di-ethylene) [10]. Consequently, direct interconversion of the alkenes, via an intermediate complex (termed a quasi-cyclobutane , pseudo-cyclobutane or adsorbed cyclobutane ) generated from a bis-alkene complex was proposed, and a detailed molecular orbital description was presented to show how the orbital symmetry issue could be avoided, Scheme 12.14 (upper pathway) [10]. 

Imperfect symmetry can be regarded as fuzzy symmetry. The theory of fuzzy sets has found applications in many fields of engineering and natural sciences (see, e.g., references [386-393]), in particular, for the description of fuzzy molecular arrangements [103,106,251]. It is natural to consider fuzzy sets for a continuous extension of the discrete point symmetry concept to quasi-symmetric molecular structures [252,394,395]. 

It has already been mentioned that hybrid orbitals can be chosen so as to minimize the residual interactions between localized molecular orbitals . It is not uncommon for the hybrids chosen in this way to have axes that do not conform to the molecular geometry. For example, when it is said that the Cl atoms of chloroform increase the s-character of the C hybrid involved in the CH bond, an angle between the axes of the other three hybrid orbitals smaller than 109.5° is implied. In fact, the actual Cl-C-Cl bond angles are larger. Again, bent quasi-localized molecular orbitals occur independently of any deviations of the electron density in each CCl sector with respect to cylindrical symmetry around the C-Cl nuclear axis. 

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