Cluster-based electrons

As holds for other cluster systems, certain magic cluster electron counts exist, which indicates for a certain cluster-halide ratio and interstitial present the filling of all bonding molecular orbitals and therefore the thermodynamically most stable situation. For main group interstitial atoms these are 14 cluster-based electrons whereas for transition-metal interstitials the magic number is 18 [1, 10-12]. All of these phases are synthesized by high-temperature solid-state chemical methods. A remarkable variety of different structure types has been... 

Molecular orbital calculations51 have indicated that the optimum number of cluster-based electrons (i.e., those that occupy the molecular orbitals responsible for bonding) is 14 for main-group-centered clusters and 18 for transition-metal-... 

Nearly all of these cluster phases fall in the family A x[M0Xi2(Z)IX3. Zirconium clusters occur in structures for all n between 0 and 6, as well as with x alkali-metal cations (A ) per cluster over the same range. (A few phases are also known with Ba2 +. ) Accepting for the moment the condition that 14 cluster-based electrons are optimal when Z has s and p valence orbitals, we can devise diverse ways in which 14-e counts can be achieved via the three variables x, n and the number of electrons brought by Z. Some sample categories are given in Table 1 for a few of the many dozen compositions known with Zr0Cli2Z-type clusters. 

When it comes to isolated or oligomeric clusters, there is only a limited number of examples. They may all be derived from [R (Z)]X, 2X units (fig. 46). The most oxidized example is Cs2Lu[Lu6(C)]Cli8 with only 9 electrons for mtra-cluster bonding. It forms red transparent crystals. Other quaternary halides with isolated octahedra all with a single carbon atom or the dicarbon unit have 11 to 15 cluster-based electrons (box 8). 

Electronically, these cluster units contain either two ([Rio(C2)2]Xi6-type and derivatives), one ([Rio(C2)2]Xi7) or zero ([Rio(C2)2]Xi8) excess electrons when the ionic model is used, or 26, 25 and 24 cluster-based electrons, respectively, in the covalent model. See for theoretical calculations Satpathy and Andersen (1985). 

TABLE 2 A Compilation of Cluster-Based Electron (CBE) per One Formula Unit and Important Interatomic Distances, in pm, for ZRg Xi2R-Type Compounds ... 

FIGURE 11 Schematic cutouts of molecular orbital diagrams of (left) an (Re) cluster of the [ R5 X i2X 6] type and its combination with an endohedral T atom (right) to an 18 cluster-based electrons (CBEs) TRg cluster (middle). 

TABLE 6 TR3 X3 Cluster Halides, Structure Types, Cluster-Based Electron (CBE), and Mean Distances (in pm) —Cont d... 

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