Cluster four-connect

Fig. 8.6. Representation of 14 multivariately characterized objects in a two-dimensional space of variables where the clusters are connected into four groups (a) and classified into two differently chosen groups (b,c), respectively d shows a nested clustering of B within A... 

In Section 13.2 and Fig. 13.2.5, the structure of /3-R105 boron is described in terms of large B84 (Bi2a Bi2 B6o) clusters and B10-B-B10 units. Each Bio unit of C3v symmetry is fused with three B6 half-icosahedra from three adjacent B34 clusters, forming a B28 cluster composed of four fused icosahedra, as shown in Fig. 13.4.11(a). A pair of such B2s clusters are connected by a six-coordinate B atom to form a B57 (B28-B-B28) unit. 

The deltahedron for n = 10, a bicapped square antiprism, exhibits two four-connect and eight five-connect vertices. Hence, for one heteroatom in a ten vertex c/oso-cluster we have 1 - and 2-isomers and two heteroatoms in 1,10-, 1,6-1,2-, 2,3-, 2,4-, 2,6- 2,8-isomers. Different placements generate different cluster stabilities. A rule of thumb is that the more electronegative element prefers the lower-connectivity vertex. Multiple heteroatoms more electronegative than B prefer non-adjacent positions as far apart as possible. Rearrangement to the most stable isomeric form need not be fast. In the case of icosahedral clusters, for example, the barrier to rearrangement is large and isomers can be isolated. 

Small four-connect metal-carbonyl clusters and the 14n + 2 rule... 

To summarize this long section on metal effects, we can state metal clusters can mimic main-group clusters (late-metal clusters with acceptor ligands) metal clusters with four-connect or higher vertices can be described with localized bond models (early-metal clusters with donor ligands) and metal clusters can have reduced (Pt clusters) or no tangential bonding (Au clusters). The characteristically more... 

For the four-connect, seven-sep, closo-octahedral series shown in Figure 5.3 examples of the B, [B6H6]2, and metal, H2Ru6(CO)i8, clusters are known... 

At one level the explanation is trivial. As pointed out in the discussion of the differences between three-connect and four-connect clusters, it is possible to generate the same geometry with differing electron counts. Thus, if we consider the clusters in Figure 5.14 as M4 metal clusters then one can generate a square shape... 

Electron-precise cluster systems can be seen to be a more complex version (three-connect units) of chains (one-connect units) and rings (two-connect units), leading up to an extended solid (four-connect units, e.g. the diamond structure). This is most easily appreciated for homonuclear examples, for example, (1) and (2). For the mixed systems like (3), two distinct descriptions are possible - as a 4-atom cluster or as a trinuclear metal complex with a /U.3-P cap. In many cases, the difference is of little consequence however, in others, proper choice of description can lead to analyses of significant conceptual value. 

For a metal with eight valence electrons, electron precise carbonyl structures see Electron Precise Compound) are M(C0)5 and [M(CO)4]3, which are known for all three metals of the iron group, albeit with quite different properties for the different metals. The next member, [M(CO)3]6, is not formed since a four-connected vertex requires more metal-metal bonding orbitals than can be arranged on the surface of a sphere. Bonding orbitals directed towards the inside of the cluster, however, form MOs that will accommodate more electrons than would be predicted by an 18 valence electron count for each metal see Eighteen Electron Compounds), that is, 86 instead of 84 for a six-vertex closo cluster see Closo Cluster). This situation is realized in the iron group by the anions [M6(CO)i8], M = Fe, Ru, Os (isolectronic to M6(CO)i6, M = Co, Rh, Ir). 

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