By D Bonchev, D.H Rouvray

Topology is turning into more and more very important in chemistry as a result of its quickly transforming into variety of purposes. the following, its many makes use of are reviewed and the authors count on what destiny advancements could deliver. This paintings indicates how major new insights might be won by way of representing molecular species as topological buildings often called topographs. The textual content explores carbon buildings, constructing how the steadiness of fullerene species should be accounted for and likewise predicting which fullerenes may be such a lot sturdy. it really is mentioned that molecular topology, instead of molecular geometry, characterizes molecular form and diverse 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 conception are mentioned, and specifically, the radical suggestion of the molecular topoid is proven to have quite a few makes use of. The topological description of polymers is tested and the reader is lightly guided in the course of the geographical regions of branched and tangled polymers. total, this paintings outlines the truth that topology isn't just a theoretical self-discipline but in addition one who has sensible functions and excessive relevance to the complete area of chemistry.

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**Sample text**

A remarkably stable icosahedral boron hydride anion B 12H j 2 was subsequently predicted by Longuet-Higgins and Roberts in 1955 [18] and prepared by Pitochelli and Hawthorne in 1960 [19]. The icosahedral structure of B 12H i 2 was confirmed by X-ray diffraction soon after its discovery [20]. In addition, boron icosahedra were recognized in the structure of elemental boron in 1959 [21]. 4 Construction of Polyhedra: Capping and Dualization In generating actual polyhedra, the operations of capping and dualization are often im portant.

A gener alized version of Euler’s theorem is necessary to relate the numbers of vertices, edges, and faces of such non-simple polyhedra. The more complicated surfaces are homeomorphic to surfaces gen erated by drilling holes (or tunnels) through a plastic sphere. The genus, g , of such surfaces is the num ber of holes that must be drilled through a plastic sphere to make a surface homeomorphic to the surface in question. , a doughnut) is one. Surfaces of higher genus have been called pretzels because of their resemblance to pretzels.

In the m athem atical theory of graphs the corre spondence between the discrete and continuum models of graphs as well as the consequent embeddings in various closed surfaces 9 is a standard area of inquiry, which is, for instance, described in Gross and Tucker’s book [6 ] Topological Graph Theory. But, even beyond the considerations of embeddings in surfaces, it is chemically relevant to consider embeddings in 3-dimensional space, so that knots in some cycle-containing structures occur. , in references [7,8], as well as in other chapters in this book.