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Symetria molekuł a stereochemia

Stępień M.

Wiadomości Chemiczne

1999

[Z] 53, 1-2

17-64

Stereochemistry, often regarded merely as a descriptive discipline, is an inexhaustible source of mathematical problems. Group theory, topology, graph theory, etc. Are widely applied to the description of molecular architecture and conformational dynamics, to isomer counting and labelling, interpretation of spectra and more. Both mathematics and stereochemistry benefit from their marriage: new theorems are proved and new molecules synthesised. This review is concentred with molecular symmetry, an idea which, appropriately generalised, is central to stereochemistry. Depending on what we imagine a molecule to be, whether a rigid body, a set of nuclei, or a graph, the nature of symmetry operations changes. Our attempt is to demonstrate how various symmetry models work, explore their capabilities, and show how they are interrelated by virtue of their common group theoretical framework. Points groups, derived in the opening section, are by far the most popular symmetry description albeit applicable only to instantaneous configurations of molecules. Point groups, providing little information on the actual structure of a molecule, canbe extended into so called framework groups which detail the distribution of atoms over sites of different local symmetry. From the structure of minimal framework groups the frequency of various point symmetries amongst molecules can be inferred. This is illustrated with a number of examples. The following section introduces the idea of permutational symmetry and its application to non-rigid molecules. The permutation-inversion (PI) group of Longuet-Higgins is defined and exemplified, its semidirect product structure being discussed in some depth. The PI group is then used for the description of selected dynamic processes, such as the rearrangements of bullvalene or 'racemization' of Mislow's ester. Finally, the classification of nuclei used in NMR spectroscopy is expressed in terms of equivalence classes within the PI group. The final section deals with topological properties of molecules. The principles of graph theoretical approach to molecular symmetry are outlined. Topological stereoisomerism is then defined, and the synthetic philosophy of topological stereochemistry and its achievements are briefly reviewed. We end with a discussion of symmetry properties of topologically non-trivial species, paying partucular attention to realizability of automorphisms and chirality of graphs.