Extended tetrahedron

These molecules are evaluated by recognizing the presence of an extended tetrahedron (80A). 5 normal tetrahedral atom is represented by 79 and if the atoms a—were expanded by grossly extending the bond lengths, an extended tetrahedron such as 80A would be obtained. Rather than a chiral atom, 80A contains a chiral axis (see X—Y in 80B) and this can be used to assign priorities. This model requires that 80B not be interconvertible with its mirror image 81 (i.e., rotation about the chiral axis X—Y must not interconvert 80 and 81). 

Allene 82 has a chiral axis since there are four different groups at each corner of the extended tetrahedron. These can be assigned priorities a— d (83A) by the usual rules and this at first glance suggests 83B (obtained by rotating 83A so the a-b-c sequence is in front and the d-atom is to the rear) as the structure to be used for... 

Biaryls such as 88A can be analyzed with this extended tetrahedron rule. The top aromatic ring is prioritized as a,b for the 2,6 substituents, as is the bottom ring (see 89A). The near-far rule leads to 89B and an (R) configuration. 9 reasonable question is Which aryl ring is on top and which is on the bottom of the... 

There have been several new observations on alkene cleavage. Marcus A. Tius of the University of Hawah and Bakthan Singaram of the University of Cahfomia, Santa Cruz have found (Tetrahedron Lett. 2008, 49, 2764) that epoxides such as 17 are cleaved directly by NalO, providing a simple alternative to ozonolysis. Rolando A. Spanevello of the UniversitM Nacional de Rosario has extended (Tetrahedron 2007, 63, 11410)... 

The coordination conditions can be expressed in a chemical formula using a notation suggested by F. Machatschki (and extended by several other authors for recommendations see [35]). The coordination number and polyhedron of an atom are given in brackets in a right superscript next to the element symbol. The polyhedron is designated with a symbol as listed in Fig. 2.2. Short forms can be used for the symbols, namely the coordination number alone or, for simple polyhedra, the letter alone, e.g. t for tetrahedron, and in this case the brackets can also be dropped. For example ... 

At one time it was believed that cyclooctane occurs in the extended crown form and the saddle conformation as shown below but on the basis of calculations of minimum energy strain, Hendrickson (1964) and Wiberg (1965) suggested that neither of the above two forms is the correct picture. R. Srinivasav and T. Srikrishnan (Tetrahedron 27, 5, 1009-1012, 1971) showed that the molecule exists as the boat-chair form in a number of crystalline derivatives. 

Fig. 2.1 Configurations of the tetrahedral units and chain, double chain, and sheet structures in the silicate and aluminosilicate minerals. (A) Two-dimensional representation of a single silicate tetrahedron. (A ) Two-dimensional representation of an extended silicate chain. (B) Three-dimensional representations of single tetra-hedra in two orientations. The apexes of the tetrahedra point above or below the plane of the paper. (B ) Three-dimensional representations of extended silicate chains showing different orientations of the tetrahedra in two of the many possible configurations. Single chain pyroxenes (C), wollastonite (D), rhodonite (E). Double chains amphiboles (F). Sheets as found in the serpentines, micas, and clays (G).

S Entropy on the tetrahedron approximation. If the treatment is extended to the case of a tetrahedral cluster, diis immediately raises the number of required equations to (2 ) variables. As already indicated, the pair approach is not sufficient to adequately describe the f.c.c. lattice, where an additional variable Zijta is needed where i, j, k, I can take values 1, 2, 3... corresponding to various atoms or vacancies. The energy expression corresponding to the tetiahedra is then given by... 

A further structural possibility, which exists in the elements of the fourth group, is a lattice infinitely extended in space in which each atom is surrounded by four others in a tetrahedron, and in which the... 

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