Local coordination polyhedra

Local coordination polyhedra the Jensen notation 7 Table 1.2 The fourteen Bravais lattices in three dimensions... 

Fig. 1.4 The local coordination polyhedra and associated Jensen symbols that characterize the elemental ground-state structure types. After Villars and Daams (1993).

With these considerations in mind, Gregorian et al. (1989) proposed a model which allows to derive the local distortions for Pr3+ in LaCh from high-pressure experiments. The basic assumption of this model is that the local coordination polyhedra of the Pr3+ ion in two different host lattices with the same type of ligand complexes should be identical, as soon as all multiplet centroids of the Pr3+ ion are energetically equal in both hosts. 

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,... 

There is sometimes ambiguity as to which nearest neighbours to assign to the local coordination polyhedron. This is illustrated by the two different puckered layer structure types which are displayed by the most stable polymorphs of phosphorus and arsenic respectively. They may both be thought of as resulting from the breaking of three bonds about each atom on a simple cubic lattice as shown in Fig. 1.5. The layers then distort Black... 

Determination of local coordination geometry. The position and intensity of the peaks in the pre-edge region do not solely depend upon the oxidation state of the absorber transition metal, but also upon the shape of the site (coordination polyhedron) where the absorber is located in the structure (Galas and Petiau 1983). An increase in coordination number provokes a positive energy shift, while the intensity of the peak is proportionally reduced (Waychunas et al. 1983). 

This is in agreement with the experimental finding that the crystal structures of related zwitterionic spirocyclic A, 5t-silicates, such as 1-3, only fit with the structure of the model species 10a (both carboxylate oxygen atoms in the axial sites of a distorted trigonal-bipyramidal S/-coordination polyhedron) [1-10], On the other hand, the energy differences between the local minimum 7a and the two transition states 7d and 7e (7a/7d, 30.8 kJ mol 7a/7e, 33.8 kJ mol ) are very similar to those calculated for the local minimum 10a and the related square-pyramidal transition states lOd and lOe (lOa/lOd, 29.6 kJ mol lOa/lOe, 31.4 kJ mol ) [9, 28],... 

At the same time, there are two aspects of this synthesis which require special discussion. These are the creation of complex compounds with definite manner of localization of the coordination bond (regioselective synthesis) and programmed structure (polyhedron-programmed synthesis). 

A polyhedron of anions, which may be localized electrons, is formed about each cation. All compounds may be viewed as coordination compounds. 

The VD polyhedra model also allows one to introduce two important parameters describing distortion of the atomic coordination [16, 17], The first of these is the Da vector that originates in the A atom and ends in the centroid of the VD polyhedron. According to [18], length of the Da vector is proportional to the gradient of the local electric field created by the atoms surrounding the A atom in the structure. The second parameter is the second moment of inertia, Gs, which describes the deviation of the VD polyhedron from an ideal sphere and characterizes uniformity of distribution of the X and Z atoms around A. For an ideal sphere, G3 = 0.077, whereas for an ideal AXg octahedron (which correspond to a cubic VD polyhedron), G3 = 0.0833 [17]. 

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