Symmetry arguments in chemistry
Abstract
The use (and misuse) of symmetry arguments in constructing molecular models and in the interpretation of experimental observations bearing on molecular structure (spectroscopy, diffraction, etc.) is discussed. Examples include the development of point groups and space groups for describing the external and internal symmetry of crystals, the derivation of molecular symmetry by counting isomers (the benzene structure), molecular chirality, the connection between macroscopic and molecular chirality, pseudorotation, the symmetry group of nonrigid molecules, and the use of orbital symmetry arguments in discussing aspects of chemical reactivity.
Footnotes
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Abbreviations: MO, molecular p orbital; AO, atomic p orbital.
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↵ * Lewis Carroll’s Through the Looking Glass makes several references to the left/right dichotomy (“Perhaps Looking-glass milk isn’t good to drink”). It was published in 1872, at a time when chemical structural theory was being challenged by the recent finding that a substance present in muscle appeared to be identical with lactic acid obtained by fermentation of milk, except that solutions of the two substances rotated plane polarized light in opposite senses. This result was incompatible with the then current chemical formulas that showed merely which atoms were joined to which—the so-called connectedness or constitution of the molecule. It was in fact the stimulus that moved van’t Hoff and Le Bel in 1874 to postulate the tetrahedral disposition of the four valencies of carbon in space and so led to the concept of stereoisomerism, the existence of isomers with the same constitution but different arrangements of the atoms in space. Looking-glass milk? Lactic acid? A coincidence? Lewis Carroll is, of course, the pseudonym of the Oxford mathematician Charles Lutwidge Dodgson, and one wonders whether he had heard about the two antipodal lactic acids from his chemical colleagues. One of his closest friends, and a Fellow of the same college, was the chemist Augustus Vernon Harcourt, and another was Sir Benjamin Collins Brodie, Waynflete Professor of Chemistry in the University of Oxford from 1855 to 1873. Carroll’s biographies have nothing to say on this matter, and neither do the diaries. The matter seems worth pursuing further.
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↵ † To avoid misunderstandings, note that if the directions of the bonds from the central atom to a, b, and c, are regarded as vectors x 1, x 2, x 3, in that order, then S corresponds to a right-handed coordinate system.
- Copyright © 1996, The National Academy of Sciences of the USA
