Wydział Chemii

Marcin Stępień

1999

Wiadomości Chemiczne

53

17-64

Naukowa

Polski

Artykuł

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 concerned 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.Point groups, derived in the opening section, are by far the most popular symmetry descriptors albeit applicable only to instantaneous configurations of molecules. Point groups, providing little information on the actual structure of a molecule, can be extended into so called framework groups [11] 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 [38] 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 [51]. 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 particular attention to realizability of automorphisms and chirality of graphs.

https://www.dbc.wroc.pl/dlibra/publication/13298/edition/12116/content?ref=desc