Chemical topology crystals, nets

In the analysis of the topology of such nets we can look for a classification scheme that will allow one to uniquely assign equal nets (up to isomorphism) derived from totally different crystal structures. Remember that the topology is not influenced by the metrical properties of the structure (angles, distances), so that a 4-connected diamondoid net is such, even if highly distorted (the geometry around the nodes could be far from tetrahedral), and also, obviously, is not dependent on the chemical nature of each node/vertex. 

A large number of different chemical classification systems exist for network topologies. These notably include those based on simple chemical compounds (e.g. diamondoid/cristabolite-type), an (n,p) system used by Wells related to that of Schlafli that classifies according to the number of links in a loop (n) and the node connectivity (p) [e.g. (6,4)]/ a three-letter system derived from that used for zeolites (e.g. dia,dia-a,dia-b,etc.and a 2D hyperbolic approach (e.g. sqc6). As an example, the chiral (10,3)-a network is known also as the SrSi2 net, srs. Laves net, Y, 3/10/cl, K4 crystal, and labyrinth graph of the G surface. 

A particularly useful approach to the analysis and design of crystal structures is to reduce the structures to simple topological networks.These networks are basically descriptions of multiply connecting nodes and the ways they connect, and are usually named after simple chemical examples of the net (e.g, diamond, NbO, a-Po) or are given numerical descriptions [e.g., (6,3), (4,4), (10,3)-a]. 

Silvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of electron localization functions. Nature 371 683-683 Slater JC (1939) Introduction to chemical physics. McGraw-Hill, New York, NY Slater JC (1964) Atomic radii in crystals. J Chem Phys 41 3199-3204 Smith JV (1953) Re-examination of the crystal stractrrre of melihte. Amer Mineral 38 643-661 Smith JV (1977) Enumeration of 4-cormected 3-dimertsional nets and classification of framework silicates. 

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