By D Bonchev, D.H Rouvray

Topology is turning into more and more vital in chemistry as a result of its speedily turning out to be variety of functions. the following, its many makes use of are reviewed and the authors count on what destiny advancements could deliver. This paintings exhibits how major new insights might be won by means of representing molecular species as topological constructions referred to as topographs. The textual content explores carbon constructions, constructing how the soundness of fullerene species may be accounted for and in addition predicting which fullerenes could be so much strong. it truly is mentioned that molecular topology, instead of molecular geometry, characterizes molecular form and numerous instruments for form characterization are defined. numerous of the attention-grabbing rules that come up from relating to topology as a unifying precept in chemical bonding idea are mentioned, and particularly, the unconventional suggestion of the molecular topoid is proven to have various makes use of. The topological description of polymers is tested and the reader is lightly guided in the course of the nation-states of branched and tangled polymers. total, this paintings outlines the truth that topology is not just a theoretical self-discipline but additionally person who has sensible functions and excessive relevance to the entire area of chemistry.

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**Example text**

Its equation in rectangular coordinates is y 2z 2 + z 2* 2 + x 2y 2 + xyz= 0 ( 11) so that it is a surface of the fourth order. In addition to its even connectivity num ber and its lines of self intersection, the heptahedron has another im portant property, which is characteristic of surfaces of even connectivity. Let us imagine the surface to be a thin membrane with a beetle taking a walk from a fixed point p. Directly opposite p on the other side of the membrane there is a point p' 32 Chemical Topology that coincides with p if the membrane is replaced by the original surface.

2 Knots and their Chirality Knot theory [2,3] is a subfield of topology, which traces its mathem at ical origins to the 19th century work of Gauss, Listing, Helmholtz, Kelvin, Maxwell, and Tait [49,50]. In the century since the compilation of the first knot table, considerable progress has been made in the mathematical aspects of knot theory. Very recently knot theory has proven to be chemically relevant in the analysis of enzyme action on D N A [4]. The idea of a knot in topology is different than the knots encountered in everyday life.

4 Euler Relation for Topo-Graphs and Embeddings The ground-work for a closer contact to molecular theory has now been set. A molecular graph may be viewed as a topological complex of 1-dimensional manifolds joined together at nodes. The nodes correspond to atoms and the different 1-manifolds correspond to chemical bonds. The adjective “topological” on complex indicates that two complexes are considered equivalent if homeomorphic. These complex manifolds might be termed string complexes, or being in correspondence with the usual discrete graphs, they might be termed topo-graphs.