Some suggestions concerning a geometric definition of the symmetry group of non-rigid molecules

  • Andreas W. M. Dress
Part of the Lecture Notes in Chemistry book series (LNC, volume 12)


It is well known that the symmetry group of a rigid molecule can be considered either, geometrically, as a point group or, combinatorially, as a permutation or permutation-inversion group. For a non-rigid molecule H.C. Longuet-Higgins [1] has given a combinatorial definition of the molecular symmetry group by using his concept of feasible operations — a concept, which was based on some earlier work by J. T. Hougen [2] and has found wide-ranging applications [3–5, for instance]. Still, for two reasons it seems desirable to have a simple geometric definition of the molecular symmetry group in the non-rigid case, as well. Firstly, one can hope for a better understanding of the concept of feasibility by basing it on explicit geometric considerations. Secondly, it is just the interplay of the geometric and the combinatorial definition which constitutes an essential part of the whole theory, as has been shown by work of J. D. Louck, for instance, [6].


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  1. 1.
    Longuet-Higgins, H. C., 1963, Molec. Phys., 6, 445.CrossRefGoogle Scholar
  2. 2.
    Hougen, J. T., 1962, J. chem. Phys., 37, 1433; 1963; 38, 358.CrossRefGoogle Scholar
  3. 3.
    Stone, A. J. 1964, J. chem Phys., 41, 1568.CrossRefGoogle Scholar
  4. 4.
    Woodman, C. M., 1970, Molec. Phys., 19, 753.CrossRefGoogle Scholar
  5. 5.
    Hougen, J. T., 1975, “Catalog of Explicit Symmetry Operations...” in MTP International Review of Science: Physical Chemistry Series, ed. by D. A. Ramsay.Google Scholar
  6. 6.
    Louck, J. D., these proceedings.Google Scholar
  7. 7.
    Bunker, P. R., these proceedings and “Molecular Symmetry and Spectroscopy”, Academic Press, 1978.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Andreas W. M. Dress
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldGermany

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