Russian Chemical Bulletin

, Volume 57, Issue 2, pp 235–252 | Cite as

Symmetry specified enumeration of substituted derivatives: an easy solution to the complex problem

  • S. S. Tratch
  • N. S. Zefirov


Several sophisticated methods to solution of symmetry specified enumeration problems are available in the modern literature. In this paper we propose a simple technique that allows one to manually compute the exact numbers of fixed-symmetry derivatives for a given structure either with inclusion or ignoring the substitution patterns. The basic idea of the method suggested consists in the derivation of Pólya-like cycle indices for the automorphism groups of specially constructed orbit partition graphs; the expansion of these indices and subsequent simple calculations result in the desired numbers of substituted derivatives with achiral substituents. Limitations of the new technique (and a method suggested earlier) depend on the relevance of the orbit partitions for particular subgroups of the point symmetry group. For illustration purposes, the results obtained for the prismane (D 3h ) and adamantane (T d ) structures are discussed. In the former case the numbers of substituted derivatives can be found for all subgroups of the D 3h group, whereas in the latter case these numbers can be determined for eight out of eleven subgroups of the T d point symmetry group.

Key words

substituted derivatives Pólya’s theorem symmetry specified enumeration relevance of orbit partitions substituted prismanes adamantane hetero derivatives 


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Copyright information

© Springer Science+Business Media, Inc.  2008

Authors and Affiliations

  1. 1.Department of ChemistryM. V. Lomonosov Moscow State UniversityMoscowRussian Federation

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