Polyhedron edges

Electron precise clusters with exactly one electron pair per polyhedron edge ... 

The electrons supplied by the ligands and the valence electrons of the n metal atoms of an M cluster are added to a total electron number g. The number of M-M bonds (polyhedron edges) then is ... 

This mode of calculation has been called the EAN rule (effective atomic number rule). It is valid for arbitrary metal clusters (closo and others) if the number of electrons is sufficient to assign one electron pair for every M-M connecting line between adjacent atoms, and if the octet rule or the 18-electron rule is fulfilled for main group elements or for transition group elements, respectively. The number of bonds b calculated in this way is a limiting value the number of polyhedron edges in the cluster can be greater than or equal to b, but never smaller. If it is equal, the cluster is electron precise. 

If there are not enough electrons for all of the polyhedron edges, 3c2e bonds on the triangular polyhedron faces can be the next best solution to compensate for the lack of electrons. This solution is only possible for deltahedra that have no more than four edges (and faces) meeting at any vertex. These include especially the tetrahedron, trigonal bipyramid and octahedron. 

Limits of the mutual rotation of vertex-sharing tetrahedra and of vertex-sharing octahedra and the resulting bond angles at the bridging atoms. The minimum distance between vertices of different polyhedra (dotted) was taken to be equal to the polyhedron edge... 

Table 16.1 Bond angles at the bridging atoms and distances between the central atoms M of linked tetrahedra and octahedra (disregarding possible distortions). The distances are given as multiples of the polyhedron edge length...

Skeletal (Polyhedron-Edge) Bond Orders for Anions BnHn ... 

Yet other factors influence the interatomic distances in nido- and orocAwo-boranes, for example whether the polyhedron edges border the open face of the polyhedral fragment, and if so whether they are sewn... 

Hp n, 3, and are the numbers of polyhedron vertices at which 1, 2, 3 or 4 polyhedron edges (M-M bonds) meet, respectively. Polyhedra with five or more edges per vertex are generally not electron precise (for this reason no numbers n, occur in the equations). Therefore, the expected valence electron numbers for some simple polyhedra are ... 

The notation of polyhedron edges corresponds to that used in Fig. 5.15. 

In a solid represented by packing of anion-centred polyhedra, the polyhedron edges represent possible ... 

Metal-metal bonds are localized on the polyhedron edges. 

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