The Tetrahedral Geometry

The tetrahedral angle 9t is obtained from the following simple geometric considerations (see Fig. A.l). Consider a cube with edge 1. The diagonal a is calculated using the Pythagorean theorem, i.e. 

If the distance between the center and one of the vertices of the cube b/1 in Fig. A.l) is taken as the nearest-neighbor distance between two oxygen atoms in ordinary ice (2.76 A), then the 

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The tetrahedral geometry of methane is often explained with the valence shell electron pair repulsion (VSEPR) model The VSEPR model rests on the idea that an electron pair either a bonded pair or an unshared pair associated with a particular atom will be as far away from the atom s other electron pairs as possible Thus a tetrahedral geomehy permits the four bonds of methane to be maximally separated and is charac terized by H—C—H angles of 109 5° a value referred to as the tetrahedral angle... 

The tetrahedral geometry of the bonding at the carbon atoms has bond angles of 109.5°. 

According to X-ray data (Fig. 4), a molecule of 2,2,6-trimethyl-1,3-dioxa-2-silacyclohex-5-ene-4-thione has a very strained planar cycle in which the tetrahedral geometry of the silicon atom is strongly distorted. The O Si O (103.7(1)°) and C Si C (115.1(1)°) bond angles differ considerably from the ideal tetrahedral angle (109.5°), and the Si-O bonds (1.668(2) and 1.675(2) A) are much longer than the average value of 1.645 A.78... 

The shell model can be modified to take into account further aspects of the solid being modeled. In particular, angular-dependent terms can be added. These are important in materials such as silicates where the tetrahedral geometry about the silicon atoms is an important constraint. These aspects can be explored via the sources listed in Further Reading at the end of this chapter. 

According to the E.A.N. rule, all clusters of four atoms possessing the tetrahedral geometry require a total of 60 valence electrons. A tetrahedron with six two-electron/two-center bonds corresponding to the... 

By analogy with iron complexes, let us discuss the tetrachlorocobalt-ate(II) dianion [C0CI4]2-, the tetrahedral geometry of which is illustrated in Figure 80.123... 

The tetrahedral geometry of the [Fe4(CO)i3]2 precursor is lost, being replaced by a butterfly structure. The Fe2-Fe3 bond constitutes the body of the butterfly, while the FelFe2Fe3 and Fe4Fe2Fe3 triangles constitute the wings. It can be seen that the carbide carbon atom is positioned half way between the tips of the two wings. 

Five- and six-membered rings are quite common in organic compounds because of the tetrahedral geometry of the carbon atom. Hydrocarbons are reluctant to form new C—C bonds. Even so, five- and six-membered hydrocarbon rings can be created naturally, as proved by the composition of petroleum. This reaction was first achieved in research in 1936 by means of heterogeneous catalysts (7- ). 

The tetrahedral geometry resultant from these sp -hybridized nitrogen and oxygen atoms is found to exist in both ammonia and water. Bond angles in... 

Another zinc-utilizing enzyme is carbonate/dehydratase C (Kannan et al., 1972). Here, the zinc is firmly bound by three histidyl side chains and a water molecule or a hydroxyl ion (Fig. 27). The coordination is that of a distorted tetrahedron. Metals such as Cu(II), Co(Il), and Mn(ll) bind at the same site as zinc. Hg(II) also binds near, but not precisely at, this site (Kannan et al., 1972). Horse liver alcohol dehydrogenase (Schneider et al., 1983) contains two zinc sites, one catalytic and one noncatalytic. X-Ray studies showed that the catalytic Zn(II), bound tetrahedrally to two cysteines, one histidine, and water (or hydroxyl), can be replaced by Co(II) and that the tetrahedral geometry is maintained. This is also true with Ni(Il). Insulin also binds zinc (Adams etai, 1969 Bordas etal., 1983) and forms rhombohedral 2Zn insulin crystals. The coordination of the zinc consists of three symmetry-related histidines (from BIO) and three symmetry-related water molecules. These give an octahedral complex... 

A change in co-ordination number, e.g. Isopropanolic CoCl at 25 °C exists in its pink octahedral geometry around the Co ion and changes to the blue of the tetrahedral geometry at 75... 

Thus, although pepstatin still may be considered a transition-state analog inhibitor owing to the tetrahedral geometry at C-3 of statine, pepstatin is also a collected-... 

In Fig. 3 we show a cross section of the Jahn-Teller surface around the tetrahedral geometry. The simplest Jahn-Teller intersection is of T t2 type (i.e., a triply degenerate electronic state whose components are coupled via a triply-degenerate vibration). Optimization of a triply degenerate conical intersection is not routinely possible at present. The vibrational modes of Td Fe(C0)4 span Qa 2 1 2E T 4T2, so there are clearly several candidate vibrations. This T t type of... 

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