Six-connected nets

There are two basic geometries for six-connected nodes octahedral and trigonal prismatic, one or both may be present in these nets. We encountered octahedral nodes in the pcu-net in Chapter 5, now we will look at some other nets. 

All example is found as the copper dimer net in [Cu2(isonicotinato)3]-(is-2/3l2) ll20, see figure 9.13. Note that this compound, obtained under hydrothermal conditions, also contain a polyiodide network [17], 

---

In Chapter 5 we saw the important class of compounds based on the six-connected pcu (primitive cubic packing, or a-Polonium) net, and we also encountered the five-connected bnn or boron nitride net. In this chapter we will explore higher connectivities further, starting with the five-connected and six connected nets and then going on to the mixed 3 5, 3 6,4 5 4 6 and 5 6 nets. We will also briefly look at some seven and eight connected nets. 

Wells did not treat the higher connected nets in as much detail as the others in his books, [1-3] so our major source of data for the nets in this chapter is the RCSR database [4]. There is also a website dedicated to six-connected nets [5]. 

We will consider one more net of this class since it is important to see how trigonal prismatic nodes can connect to trigonal nodes (the RCSR lists another seven three- and six-connected nets). 

We know of no examples of this net and will therefore move on to the four-and six-connected nets. 

It is w orth noting that there arc several more ways in which links may be removed from the peu net to give new four- and six-connected nets. 

Quartz, which is chiral, has a 6482 topology (Wells uses the designation 6482-b, reserving 6482-a for the more symmetrical NbO net discussed below). In the structures of [M Au(CN)2 2], M is Zn or Co, M provides the 4-connected centers and Au(CN)2 acts as an approximately linear bridging group to generate quartz-like nets [31]. Six such nets, all of the same hand, then interpenetrate [31]. 

Figure 1. Triangulation numbers T = (fp+hk + k2) represented on an equilateral triangular net. An icosadeltahedron (see figure 2) with a five-fold vertex at the origin of this net and a neighbouring five-fold vertex at a lattice point of index h, k will have A = 207 triangular facets, V6 = lOfT1— 1) six-connected vertices, and V5 = 12 five-vertices.

They are illustrated in Fig. 3.9(a). The last is the only plane 6-connected net, and evidently plane nets with more than six lines meeting at every point are not... 

From the topological standpoint the Re03 structure is the simplest 3D framework structure for a compound AX3 built of octahedral AXe groups, for it is based on the simplest 3D 6-connected net. More complicated structures of the same general type are known, that is, structures in which every octahedron is joined to six others through their vertices. The tungsten bronzes have structures of this kind... 

The objective of topological nomenclature is not only to accurately describe a structural arrangement but also to inform the reader of the overall structure in terms of its components. It is often noted that the casual reader of a paper that uses topological descriptions of coordination frameworks does not appreciate the subtleties of topological nomenclature. Thus alternative approaches have been described. Structure with high connectivity can be particularly difficult to appreciate and thus an alternative approach based on the interconnectivity of two-dimensional nets, or subnet tectons, has been described [7]. This approach relies on the basis that many simple two-dimensional nets are readily visualised (such as simple square-based 44 nets, or honeycomb arrangements, 63 nets) and many highly connected nets are built from the intersection of these relatively simple nets. This approach works for all structures reported to date and may prove valuable for complex and intricate structures, notably those with connectivity over six. 

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. ... 

Figure 5 The rtl or rutile net in Cr(II)[C3(CN)5]2-2CH3CN H20, is pictured to the left with solvent molecules shown as dashed spheres. Six-connected vertices (nodes) are at Cr and three-connected vertices at the central ligand carbon (see Figure 4). To the right,...

Figure 8 Schematic vertex assignment (a) and the most symmetric form of the sab net (b) found in MOF-CJ3 and UCT-1. Note that vertices are chosen where there are no atoms in the center of the Zn-cluster (six connected, blue) and in the middle of the benzene rings (three connected, red). .

With a little experience, and by comparing the experimental net with ideal nets from the databases, most of the common high-symmetry nets can be identified without the use of additional computations. However, some caution is required, as some nets contain the same building blocks. For example, in Figme 12, we compare the dia net, the most common of the four-connected nets based on the tetrahedron, and the Ion net (the lonsdaleite net) also based on tetrahedrons. These two nets may look quite similar if viewed from certain directions, or if very distorted, because both contain only six-rings. 

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 7.21 Some rare uninodal four-connected nets, see Table 7.1. Some characteristics of these nets are mmt interconnected sheets of six-rings in boat configuration, zni columns of squares linked by two corners and interlinked by the remaining two, cag parallel interlinked crankshafts, gsi four-fold helices of opposing chirality, each helix links to six other helices, neb parallel zigzag bands, unh, chiral, five-rings.

Figure 8.14 A Shows the tiny hole (1.7 A 0.8 A) formed by the -Zn-O-O-Zn-O-O- six-atMti rings when atomic van der Waals radii are used to generate surfaces. B An alternative net assignment of [Zn(HP03)H2N(CH2)2NH2)o.5] [15) puts six-connected nodes at the centres of the -Zn-0-0-7.11-0-0- six-atom rings give a pcu (primitive cubic packing, section 5.2.8) net...

Nets with higher connectivity than four are not so common, possibly since there are no obvious commercially available organic building blocks that can be used. This one of the reason often cited for turning to coordination chemistry when it comes to network building. The number of coordination geometries is much extended compared to carbon, and for example six-connected nodes are readily available. The problem is, however, that the commonly used coordination polymer linkers such as 4,4 -bipyridine are sterically demanding and it is difficult to fit six of these around a small transition metal ion as Fe ". ... 

This is the net formed by the nickel and arsenic atoms in NiAs (a classical inorganic type structure [10]) at it is shown in Figure 9.7. The vertex symbols are 4-4AA-4-4-4-4-4-4-4-4- - - and 4-4-4-4-4-4-42-42-42-64-64-64-64-64-64 and the genus is 9. Note that half of the six-connected nodes are not octahedral but have a trigonal prismatic geometry. 

Figure 9.7. The NiAs or nia net. Note that half of the six-connected nodes have a trigonal prismatie geometry, and thus not octahedral.

---