MX4 molecule

The coordination geometries of MIV in compounds or mixed-valence complexes, in contrast to Mn, tend to exhibit high symmetries the MX4 molecules are tetrahedral and [MXf,]2- units adopt the octahedral (or slightly distorted) configuration. 

Escalante and coworkers have studied in detail the contribution of relativistic effects to the geometries of MX4 molecules. The changes in M—X bond distances (AR) caused by relativistic effects are presented graphically in Figure 7a. It was found that for the bromides and iodides, relativity causes M-X bond contraction which increases (excluding the tin compounds) as one descends group 14 (Figures 7a). For fluorides and chlorides,... 

According to Pauling the polarity p of a chemical bond is the measure of its ionicity. It is related to the dipole moment /x by the equation p = iXi/d, where d is the interatomic distance. The polarity of M—X bonds in MX4 molecules is illustrated in Table 4. The polarity of a specific M—X bond increases significantly as M changes from C to Si, and it diminishes slightly on going from Si to Ge, Sn and Pb. At the same time, the polarity of a specific M—X bond decreases sharply as the atomic number of the halogen X increases. 

In the triiodide example we considered the rearrangements of 2 and 3 elements, the atomic labels, corresponding to the permutation groups IP2 of order 2 and P3 of order 6. Readers should convince themselves that the permutations of the four labels associated with the vertices of a tetrahedron (or the ligands X of a tetrahedral MX4 molecule) form the permutation group P4 of order 24. 

An alternative representation of the permutation groups can be given in configuration space. Here we need one dimension for each internal coordinate of interest, and this number may be greater than the number of elements (atomic labels) to be permuted. As we have seen, this is not the case for the simplest examples we have studied. For the linear triiodide anion we need a two-dimensional coordinate system, the interatomic distances a and b, and there are just two atomic labels of the terminal atoms for the triangular triiodide anion we need a three-dimensional space and there are three atomic labels. But for a tetrahedral MX4 molecule there are 10 distances (4M-X and 6X-X) that need to be considered and only four atomic labels. For this example, the permutations of the labels produce 24 equivalent points in the ten-dimensional space of the internal coordinates (which can be reduced to 9 dimensions if the redundancy among the X-X distances is taken into account see Section 1.3.1). 

Table 2.4. One choice of symmetry coordinates for a tetrahedral MX4 molecule, emphasizing the action of the twofold symmetry operations of the tetrahedron...

Fig. 2.2. Projection of MX4 molecule with Cartesian coordinate system showing ligands 1 and 2 above the plane of the paper, ligands 3 and 4 below. The X axis runs perpendicular to the plane of the paper...

The two-dimensional problem with the triangles is analogous to the chemically more interesting three-dimensional problem concerning inversion of configuration of a tetrahedron. For a distorted tetrahedral MX4 molecule there are 24 ways of labeling the vertices, i.e. 24 isometric distortions from symmetry and there are also 24 ways of labeling the vertices of the enantiomeric tetrahedron. Thus, the rele-... 

The foregoing discussion implicitly raises two questions. (1) Why do the Group IV elements not form MX2 compounds, since this would save most of the promotion energy to the V4 valence state, and (2) how is it that the V4 valence state leads to the formation of a tetrahedral MX4 molecule, in which all M—X bonds are equivalent when an sp3 configuration has electrons in two differently shaped orbitals. We reserve the second of these questions for the next Section. The first can be answered fairly easily. 

The structure correlation method has been applied to derive information about a variety of other reaction paths, for example, for weakening and ultimate fission of one bond of a tetrahedral MX4 molecule to give a planar MX3 species (5n1-reaction type) [48] and nucleophilic addition at carbonyl C-atom [49]. From analysis of the conformations of Ph3P=0 fragments [50], the stereoisomerization path could be mapped and identified as corresponding to a two-ring flip mechanism [51]. 

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