Cluster molecules with extended bonding networks

1 Cluster molecules with extended bonding networks 

As usual, let us begin with a discussion of geometric ideas relevant to a transition from molecular clusters to the solid state. 

Take a closer look at [A Ris]3- to size up the problem. A couple of questions come to mind. How are the geometric and electronic structures of [A169Ri8]3-connected Are the polyhedral shapes of the various shells important or do other 

Clearly, these giant clusters are going to be a difficult problem if treated in the manner of small, molecular clusters. But if we can t handle the [A Ris]3- cluster, you ask, what approach can we use to understand that of bulk Al The molecular perspective we have taken thus far makes the problem look far worse. With 1023 Al atoms don t we need to consider 3 x 1023 valence electrons and 4 x 1023 atomic functions for the simplest MO treatment Well, yes, but fortunately for substances in the form of single crystals translational symmetry provides a straightforward way around the problem. It is presented in the next section. 

The six atoms that define an octahedral hole, when excised from the lattice, constitute an octahedral cluster. Further, ahexa-capped octahedral cluster, generated by the fusion of six tetrahedral clusters, three up and three down, can also be cut 

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Of the many hypotheses of the structure of liquid water, that ofPople (1951), as modified by Sceats, Stavola and Rice (1979), agrees very well with all experimentally determined properties. In this model, water is formulated as a continuous polymer in which H2O units are united by a network of hydrogen bonds that extend throughout the whole liquid which becomes, in this sense, one large molecule. This formulation is compatible with all recorded physical properties. No support remains for older ideas of flickering clusters , icebergs , monomeric inclusions , or other types of discontinuity. 

In this section, we extend the application of the primitive cluster model discussed in Sec. 2.5.4 to examine the solvation thermodynamics of simple solutes in the water-like solvent. The model is schematically described in Fig. 3.21b. The only new feature that is added here compared with the model discussed in Sec. 2.5.4 is that clusters of water-like particles contain holes in which solute molecules can be accommodated. This feature is the analog of the cavities formed by the network of hydrogen-bonded molecules in real water. 

We discuss a solution of molecules ( monomers ) with functionality f > 3 (in general) from each molecule may emanate zero to f bonds to neighboring molecules and thus this molecule may participate in the formation of a large cluster which is called a macromolecule. Two monomers in the same cluster or macromolecule are thus connected directly or indirectly (through other monomers in the same cluster) by such bonds whereas two monomers in two different macromolecules are not connected by such bonds. We denote the number of monomers in one macromolecule by s and then call this macromolecule also an s-cluster an isolated monomer without bonds to its neighbors is thus designated as an 1-cluster with s = 1. (For simplicity, we also call s the mass of the macromolecule, i.e. we set the molecular weight of the monomers equal to unity in the theoretical discussions.) Under certain conditions, an infinite cluster can be formed, i.e. a network which extends from one end of the sample to the other. 

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