Application of the Permutation Group to Stereoisomer Generation for Computer Assisted Structure Elucidation

  • James G. Nourse
Part of the Lecture Notes in Chemistry book series (LNC, volume 12)


The purpose of this paper is to describe a recent effort to generate, classify, and enumerate the stereoisomers of all organic chemical structures consistent with a given empirical formula. The resulting theory is then converted into an algorithm which is programmed for a computer. The resulting program is used as an aid for computer assisted structure elucidation (1). The proper group theoretical formulation is the key to the solution of the problem and will be discussed here. Simply stated, the problem is to generate, classify and enumerate the possible stereoisomers for an organic chemical structure of defined constitution. (Constitution is the specification of the atoms in the molecule and their connectivity by bonds).


Equivalence Class Symmetry Group Conjugacy Class Permutation Group Wreath Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.(a)
    L. M. Masinter, N. S. Sridharan, J. Lederberg, and D. H. Smith, J. Amer. Chem. Soc., 96, 7702 (1974).CrossRefGoogle Scholar
  2. 1.(b)
    R. E. Carhart, D. H. Smith, H. Brown, and C. Djerassi, J. Amer. Chem. Soc., 97, 5755 (1975).CrossRefGoogle Scholar
  3. 2.
    J. G. Nourse, J. Amer. Chem. Soc., 97, 4594 (1975).CrossRefGoogle Scholar
  4. 3.
    C. A. Mead, Top. Curr. Chem., 49, 1 (1974).Google Scholar
  5. 4.
    R. W. Robinson, F. Harary, and A. T. Balaban, Tetrahedron, 32, 355 (1976).CrossRefGoogle Scholar
  6. 5.
    J. G. Nourse, R. E. Carhart, D. H. Smith, and C. Djerassi, J. Amer. Chem. Soc., submitted.Google Scholar
  7. 6.
    W. T. Wipke and T. M. Dyott, J. Amer. Chem. Soc., 96, 4834 (1974).CrossRefGoogle Scholar
  8. 7.
    R. S. Cahn, C. K. Ingold, and V. Prelog, Angew. Chem. Int. Ed. Engl., 5, 385 (1966). See footnote on p. 397. We are merely pointing out a difficulty in designing a system of nomenclature, not proposing a new system.CrossRefGoogle Scholar
  9. 8.(a)
    G. Polya, Acta Math., 68, 145 (1937).CrossRefGoogle Scholar
  10. 8.(b)
    B. A. Kennedy, D. A. McQuarrie, and C. H. Brubaker, Jr., Inorg. Chem., 3, 265 (1964).CrossRefGoogle Scholar
  11. 9.(a)
    A. Kerber, “Representations of Permutation Groups. II”, Springer-Verlag, New York, 1975.Google Scholar
  12. 9.(b)
    A. Kerber, Discrete Math., 13, 13 (1975).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • James G. Nourse
    • 1
  1. 1.Computer Science Dept.Stanford UniversityStanfordUSA

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