Inter-cluster bonding

Further effects seen with the substitution of Cl for T in the [(Zr6Z)Ii2] type are a reduction of inter-cluster I I repulsions which allows for a reduction in Zr-I inter-cluster bond lengths. The [110] section of this rhombohedral structure is shown in Fig. 5.3 and illustrates that the clusters can be described as a cubic-close-packed array, with the 3 axes running vertically through Z. Phase widths found are 0[Pg.63]

When it comes to metal-rich compounds of the alkaline earth and alkali metals with their pronounced valence electron deficiencies it is no surprise that both principles play a dominant role. In addition, there is no capability for bonding of a ligand shell around the cluster cores. The discrete and condensed clusters of group 1 and 2 metals therefore are bare, a fact which leads to extended inter-cluster bonding and results in electronic delocalization and metallic properties for all known compounds. 

Their comparatively simple crystal structures may be described as a primitive packing of quasi-molecular units, and, in a way, they represent the border line between molecular and infinitely extended units in a solid (Cheetham and Day 1992). The Mo6 type core is completely surrounded by X atoms and inter-cluster bonding essentially occurs through the Mo-X interactions. The Mo—Mo bonding between clusters is very weak. 

CAMD modeling has been used in this study to compare and partially to differentiate several postulated bituminous coal models based on their physical structures, minimum energies, and other characteristics. It is clear from the folding of the CAMD structures after molecular dynamics (especially in Figures 3c and 4c) that simple two-dimensional representations cannot adequately represent the structure of coal. Inter-cluster bonding has a powerful influence on coal structure when three-dimensional models are employed. 

In Chapter 2 (Section 2.9) we see how the cluster bonding requirements for the icosahedron, plus two-center and three-center inter-cluster bonds perfectly uses the three available valence electrons and four available valence orbitals in a covalently bonded cluster network. Once one has these advanced bonding models in hand, then the explanation of the B network structure is no more difficult than that of the C diamond structure. One purpose of this text is to provide these advanced models, but for now the solution to the problem remains hidden. Hey, a little suspense always helps the story line. At this empirical stage of the presentation you have learned that the nature of bonding (distribution of electrons) is expressed in geometry. The tricky bit is to interpret the empirical nuclear position in terms of a useful (simplest one that answers the question asked) model for the distribution of valence electrons. 

Inter-cluster bonding between the post-transition element clusters is rather common. Both Hg4" and b chain fragments inter-connect, as already discussed in the Secs. 1.29.4.3 and 1.29.4.5, and the cationic cluster chemistry of tellurium has been shown to contain examples of similar, but more elaborate inter-cluster bond-ing [17.250] (Te8 )(WCl6 )2 the inter-cluster Te-Te distance is found to be short... 

The structures of boron-rich borides (e.g. MB4, MBfi, MBio, MB12, MBe6) are even more effectively dominated by inter-B bonding, and the structures comprise three-dimensional networks of B atoms and clusters in which the metal atoms occupy specific voids or otherwise vacant sites. The structures are often exceedingly complicated (for the reasons given in Section 6.2.2) for example, the cubic unit cell of YB e has ao 2344 pm and contains 1584 B and 24 Y atoms the basic structural unit is the 13-icosahedron unit of 156 B atoms found in -rhombohedral B (p. 142) there are 8 such units (1248 B) in the unit cell and the remaining 336 B atoms are statistically distributed in channels formed by the packing of the 13-icosahedron units. 

Fig. 5.7 View of the inter-cluster connectivity in the [(Zr6B)Clii xl2+x] structure c and the zigzag chains run horizontally). The Zr-Zr bonds are emphasized, and the inner halides are omitted for clarity.

Even if one can create the SCO ligand-field around one end of a covalently-bridged dinuclear complex, the SCO might influence the ligand-field at the other end. There are many inter-dependent effects to bear in mind of a bonding, electronic and structural kind, and attempts to delineate these are given below. Inter-cluster or inter-chain effects will play difficult-to-control roles in crystalline SCO polynuclear materials, and these have already been alluded to for mononuclear complexes. 

Figure 4.31. Crystal structure of the Chevrel phase Mo6PbS8. Portions of four rhombohedral unit cells with one common Pb atom (black) are shown. The bonding between different clusters is suggested by the Mo—S inter-cluster links.

M60 octahedra (see Fig. 4.28). The solid-state structure results from the packing of such groups. The inter-cluster distances are similar to those found in the metals. According to Simon, these compounds could be described as ([Rb902]5+, 5e ) and ([Csh03]5+, 5e ) with the five electrons donated to a conduction band, both inter-and intra-cluster metal-metal bonding, in agreement with the metallic conductivity of these compounds. 

In further computational work concerned with isopropylzinc-derived species, the enthalpies and structures of the four possible closed tetramers were derived (Fig. 22). Dramatic differences from the methylzinc analogues were observed, simply because the bulk of the larger alkyl group dictates the level of inter-cluster interactions. Cubic structures directly derived from homoehiral isopropyl-dimers possessed severe and inescapable non-bonding... 

Each inter-cluster two-center-two-electron bond reduces the charge of the clusters joined by one unit each. Thus, if the clusters in Figure 8.11 are connected by two inter-cluster Ge-Ge bonds of the same type per pair, the charge of each end... 

---