Three-connect clusters

For a tetrahedron, for instance, there are 4 vertices in each of which 3 edges meet it is an example of three-connected cluster. Therefore ... 

The main characteristic of cluster-type indices is that all bonds are connected to the common, central atom (star-type structure). The third-order cluster molecular connectivity index (3yc) is the first, simplest member of the cluster-type indices where three bonds are joined to the common central atom [102-104, 111-113,152-154,166,167,269]. The simplest chemical structure it refers to is the non-hydrogen part of ferf-butane. This index is then calculated using Eq. (43) ... 

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 structures and skeletal bond valences of Oss(CO)i6 and B5H52- are similar as a pair, as are also Fe5C(CO)is and B5H9. But the bonding types in the boranes and the metal clusters are not the same. Since every B atom in a polyhedral borane has three AO s for bonding of the BM skeleton, any vertex more than three-connected must involve multicenter bonds. In the transition-metal skeleton, the Mm atoms form either 2c-2e single bonds or 3c-2e multicenter bonds. 

The surface atoms of three-connect clusters have three nearest neighbors within bonding distance (Figure 2.2). Many clusters formed from p-block elements are three-connect clusters. No new bonding ideas outside of the localized two-center-two-electron bond and the eight-electron rule are required to understand most... 

In the common three-connect cluster shapes illustrated in Figure 2.3 the number of electrons that can be associated with the closed clusters is 5n, where n is the... 

Another way to count the electrons in clusters restricts the count to only those associated with cluster bonding hence, skeletal-electron pairs (sep). For three-connect clusters sep = 3/2n. The assumption that orbitals associated with cluster ligand bonding can be considered independently of orbitals associated with cluster framework bonding results in an important simplification for more complex systems. However, it is a separation that is convenient rather than rigorous. We will see... 

The polyhedral shapes pertinent to this class of clusters are the deltahedra shown in Figure 2.7. Deltahedra are polyhedra containing exclusively triangular faces. The vertex connectivities are shown on the drawings. Those for n = 4 (not shown), 6 and 12 have uniform connectivities of three, four and five hence, the cluster atom centers lie on a sphere. The others with less uniform connectivities are less spherical in shape if all edge lengths are equal. As it is a three-connect cluster, the tetrahedron... 

Let us focus on Ge and begin with three-connect clusters. A compound containing [Ge4]4- tetrahedra has been prepared from Na and Ge (Figure 2.23). [Ge]- is isoelectronic with As. In the sep count it is a three-electron cluster fragment like C-H. So the cluster is analogous to P4 with six two-center Ge-Ge bonds and four external lone pairs. One can see the power of the Zintl idea ME is equivalent to E where E is a p-block element one column to the right. 

Main-group clusters that exhibit three-connect shapes can often be described using localized two-center bonds. What is the situation for metal clusters ... 

For three-connect (and lower) main-group clusters, we concluded in Chapter 2 that a eve count is not particularly useful. However, metal cluster structures are not always easily analyzed in terms of metal connectivity. Bond distance criteria for the existence of a M-M bond are not as precise as those for an E-E bond. 

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