Three-connected nets

But first we will take a look at geometric properties of different classes of three-connected tectons and their corresponding synthons that will have a large influence on which of the 3D-nets that will be formed. 

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For a discussion on general properties for the three-connected nets (the A1B2 and ThSi2 structures and their transition metal derivatives) see Zheng and Hoffmann (1989). Characteristic band structures were presented for these two compounds and their derivative structures (CaCuGe, LaPtSi) and other three-connected nets... 

It is important to realize that not all three-connected nets in three-dimensions lie on surfaces. A great variety of both nets and surfaces has been described, somewhat cryptically, by Wells (1977). 

The zeolite structures may also be described by two dimensional (2-D) 3-connected nets.[11] The most obvious way to generate the four-connected 3-D net from a 2-D three-connected net is to arrange one type of 2-D three-connected net into a parallel stack and to link each vertex to only one other vertex. To form a 3-D net, some of the new edges must point upward and some downward from each 2-D net. Figure 2.6 presents the 4.82... 

Applying the third alternative, it was established that this structure is, in fact, an example of a network from a weU-known type structure that many chemists are familiar with from general chemistry courses, namely the rutile (the most common form of Ti02) structure. From a topology point of view, this is one of the most symmetric, and also most abundant, of the six- and three-connected nets (6c,3c nets) and it has the symbol rtl. ... 

The geometry of the most common three-connected nets. 

Next we move on to some less common molecule-based nets. This part is divided into several chapters, starting with the three-connected nets and subsequently dealing with the other nets in order of the connectivity of the nodes. Doing so, we will not discriminate by atomic number, indeed we find that in this area, as in many others, the terms inorganic and organic are not very helpful, and instead imply heavy differences in composition and behaviour that simply do not exist. ... 

Thus, all possible ways to unite a link pair using smallest rings are counted and then added as a subscript index to the ring size as M>i-Ny2 0y,... The connectivity p is now deduced from the number of link pairs, each of these having a Mji symbol assigned to it. Thus summing the number of link pairs is equal to / (/ -1 )/2 (equation 4.1). For example for a three-connected net there will be three link pairs (Myi-Nyj-Oys) and for a four-connected net there will be six (My -Ny2-Oy3 Py4-Qy5-Ry[Pg.63]

Figure 6.1 Relevant geometric parameters for three-connected nets. To a large degree these can be controlled by the choice of building blocks although in each case there is also a span of allowed values for Ij,and ro.

Figure 6.2 Some different building blocks that form three-connected nets. The possible modes of bridging interaction are hinted by dashed lines, but can vary from case to case.

One of the more spectacular predictions of Wells occurs already in the first paper in the series The geometrical basis of crystal chemistry . In this 1954 paper he describes a chiral three connected net based on 12-rings, see Figure 6.4 [10], Another 45 years were to pass before a compound with this net was obtained by Robson and co-workers [11]. 

As there appears to be no three-connected nets based on 11-rings we move on the more numerous (10,3)-nets. 

These seem to be the most of three-connected nets containing only one kind of node and one size of ring. We will now move on to some nets with several kinds of rings. 

As pointed out by Wells, many three connected nets can be constructed by joining Tour-fold helices in different ways, and one of the nets he derived in this way was the (8 I0)-a net, see Figure 6.14. This net has vertex symbol 8-810ti and genus 5. 

Table 6.2 Summary of the three-connected nets discussed in this chapter and in chapter 5...

Four-connected nets with tetrahedral building blocks are of particular interest since they form the basis of zeolites and related materials. Zeolites are important in many areas, from large scale cracking of crude oils to the performance of washing powders in areas with hard water f I]. Thus, there is an abundant literature on the subject in contrary to the three-connected nets, and this chapter therefore will be briefer than it otherwise would have merited. 

With increasing complexity and lower symmetry we get higher values of the genus. For the three-connected nets in the RCSR database, [13] we find all values of g up to 13 with the exception of 6, 8 and 12. The highest known genus for such listed nets is 25, of which there arc 7 examples, one shown in Figure 10.11, the 3 4 connected rhr-a ret. 

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