Tetrahedron, views

Figure 28 is-bidentate hydroxamate ligands lie on the edges of a [Ga4Ls] tetrahedron. (View down the... 

As shown in Figure 7.29 and Problem 7.11, the Fischer projection can only be rotated in the plane of the paper 180° without changing its meaning. A rotation of 90° or 270° inverts the absolute configuration. Therefore, it is frequently desirable to translate such two-dimensional representations into a recognizable three-dimensional shape (such as a tetrahedron viewed edge-on ) before attempting to determine the order in which the substituents must be placed. 

Various ways to visualize tetrahedral and octahedral holes. A tetrahedral hole in the center of (a) a tetrahedron viewed from the side, (b) a triangle of spheres with a fourth sphere sitting on top, and (c) a triangle of spheres placed atop a single sphere. 

There are a variety of silicates, which can be viewed as various arrangements of tetrahedral oxoanions of silicon in which each Si—O bond has considerable covalent character. The differences in properties between the various silicates are related to the number of negative charges on each tetrahedron, the number of corner O atoms shared with other tetrahedra, and the manner in which chains and sheets of the linked tetrahedra lie together. Differences in the internal structures of... 

Fig. 17. Tetragonal symmetry projective view (above) and cut A-B (below) of a [LS],-layer formed by a sequence of [L,S] tetrahedrons (ideally PbFCl-t3q)e distorted CeSI-, FeOCl-, and NdSBr-types). (Redrawn from C. Dagron and F. Thevet, Ann. Ckim. 6, 67 (1971), Fig. 6, p. 77.)...

For additional evidence for this view, see Laureillard, J. Casadevall, A. Casadevall, E. Tetrahedron, 1984, 40, 4921 Helv. Chim. Acta, 1984, 67, 352 McLennan, D.J.7. Chem. Soc., Perkin Trans. 2,1981,1316. For evidence against the S>j2 (intermediate) mechanism,... 

For a discussion of radical chain reactions from a synthetic point of view, see Walling, C. Tetrahedron, 1985, 41, 3887. 

Presently it is not possible to relax the Cu lattice at the SCF level, since from a computational point of view it is composed of two different kinds of Cu atoms (those with and without the ECP). Also questions of wetting, i.e. whether the chemisorbed Be4 would prefer to remain as a tetrahedron (or distorted tetrahedron) or to spread out to a single layer are still not amenable to ab initio study. These questions have not yet been investigated using the parameterized model approach, because of the problems associated with modeling Be2 and Beg as accurately as larger Be clusters. Nonetheless, these preliminary results show that the parameterized and ab initio calculations can be used to complement each other in a multicomponent system, just as for single component systems. 

This geometrical constmction leads to the idea that the spectra in Fig. 14 may be viewed as a projection of the quantum states inside the tetrahedron onto the (E,J ) plane—a procedure that is simplified by the fact that both the Hamiltonian... 

Any hybrid orbital is named from the atomic valence orbitals from which It Is constmcted. To match the geometry of methane, we need four orbitals that point at the comers of a tetrahedron. We construct this set from one s orbital and three p orbitals, so the hybrids are called s p hybrid orbitais. Figure 10-8a shows the detailed shape of an s p hybrid orbital. For the sake of convenience and to keep our figures as uncluttered as possible, we use the stylized view of hybrid orbitals shown in Figure 10-8Z). In this representation, we omit the small backside lobe, and we slim down the orbital in order to show several orbitals around an atom. Figure 10-8c shows a stylized view of an s p hybridized atom. This part of the figure shows that all four s p hybrids have the same shape, but each points to a different comer of a regular tetrahedron. 

It was precisely a dynamic view of the molecule, replacing the static concept of the carbon tetrahedron, that was taken by Lapworth and Lowry, as they worked in Armstrong s laboratory in the 1890s and early 1900s. 

Figure 7.9a. Perspective views (first column) of the regular tetrahedron, cube and octahedron and the trigonal prism and their projections. For each of the polyhedra the same letters are used for labelling the same vertices in the different projections two letters (one within brackets) in the same position correspond to two vertices superimposed in the projection.

Figure 6.1 A view of the tetrahedral coordination of water molecules in ice is shown here. Molecules (1) and (2), as well as the central molecule, lie entirely in the plane of the paper. Molecule (3) lies in front of the plane of the paper and molecule (4) lies behind it, so that oxygens (1), (2), (3), and (4) lie at the comers of a regular tetrahedron.

The approach adopted is to view the molecule in three dimensions, imagining each atom or group to be placed at a vertex of hn appropriate polyhedron. In organic chemistry this is usually the tetrahedron with carbon at the centre. Table 3.3 (p. 18) shows the polyhedra normally encountered in organic and inorganic chemistry. It also includes for each polyhedron the polyhedral symbols to denote shape and coordination number. It is to be noted that these polyhedra are often presented in a highly formalised fashion. An octahedron is often represented with the apices rather than the octahedral faces depicted, thus ... 

Tetrahedron Cylinder with E = 1 viewed along axis viewed normal to axis Spheroids E = 0.5 E = 2... 

FIGURE 9.15 Structure of a-quartz, viewed down a six-fold ring of silicons. Note that the oxygens around each silicon are arranged in a distorted tetrahedron and that the silicons themselves project a distorted hexagon. 

If however the Q-tetrahedron (ABYZ) were treated in the usual way for specifying the chirality (by viewing towards the comer with lowest priority and determining the (R) or (S) sequence of the three comers left according to the sequence rule 2)) this might reverse several assignments (as have been deduced so far) and would result in much confusion. 

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