Symbols coordination polyhedra

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 ... 

Coordination polyhedron around atom A Complete symbol Alternative simplified symbols... 

Pearson symbol and prototype Space group symbol and number Lattice parameters (pm) Wyckoff positions (WP) Representative coordinates x,y, z of the 1st WP Occupancy Coordination polyhedron code Average polyhedron radius (pm) AET... 

A Inclusion of structural information. The names described so far detail ligands and central atoms, but give no information on stereochemistry. The coordination number and shape of the coordination polyhedron may be denoted, if desired, by a polyhedral symbol. These are listed in Table 4.4. Such a symbol is used as an affix in parentheses, and immediately precedes the name, separated from it by a hyphen. This device is not often used. 

Table 1.1 gives the structures of the elements at zero temperature and pressure. Each structure type is characterized by its common name (when assigned), its Pearson symbol (relating to the Bravais lattice and number of atoms in the cell), and its Jensen symbol (specifying the local coordination polyhedron about each non-equiyalent site). We will discuss the Pearson and Jensen symbols later in the following two sections. We should note,... 

Different geometrical arrangements of the atoms attached to the central atom are possible for all coordination numbers greater than one. The coordination polyhedron (or polygon in planar molecules) may be denoted in the name by an affix called the polyhedral symbol. This descriptor clearly distinguishes isomers differing in the geometries of their coordination polyhedra. 

Figure 8.29. Relationship between the shifts of some inorganic calcium compounds and the mean Ca-O distance of the coordination polyhedron. Full circles denote oxides, full squares denote silicates and full diamonds denote carbonates. The open symbols denote sulphates and phosphate.

Coordination polyhedron Coordination number Polyhedral symbol... 

The conversion of 3D conformations to symbolic representations is also easy except for a potential ambiguity in selecting the applicable coordination polyhedron. 

Since Ca is not directly surrounded by Ti atoms, the first polyhedron symbol is dropped however, the first comma cannot be dropped to make it clear that the 12co refers to a cuboctahedron formed by 12 O atoms. Ti is not directly surrounded by Ca, but by six O atoms forming an octahedron. O is surrounded in planar (square) coordination by four Ca, by two linearly arranged Ti and by eight O atoms forming a prism. 

The region within which k is considered (—n/a first Brillouin zone. In the coordinate system of k space it is a polyhedron. The faces of the first Brillouin zone are oriented perpendicular to the directions from one atom to the equivalent atoms in the adjacent unit cells. The distance of a face from the origin of the k coordinate system is n/s, s being the distance between the atoms. The first Brillouin zone for a cubic-primitive crystal lattice is shown in Fig. 10.11 the symbols commonly given to certain points of the Brillouin zone are labeled. The Brillouin zone consists of a very large number of small cells, one for each electronic state. 

For all the structures included, the environmental data by Daams et al. (1991) are given indicating for every atom the corresponding coordination number (CNE) and the polyhedron code. The symbols of the elements at the vertices of this polyhedron are then listed in the order of increasing distances from the central atom. 

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 ... 

Attempts to produce descriptors similar to cis and trims for stereochemicidly more complicated coordination entities have tailed to achieve generality, and labels such as foe and mer are no longer recommended. Nevertheless, a diastereoisomeric structure may be indicated for any polyhedron using a configuration index as an affix to the name or formula. Finally, the chiralities of enantiomeric structures can be indicated using chirality symbols. 

---