Theoretica chimica acta

, Volume 73, Issue 4, pp 247–277 | Cite as

Permutation representations in molecular symmetry

  • Gerhard Fieck
Article
  • 38 Downloads

Abstract

The reducible representations of the point groups are generally studied because of their relevance to molecular orbital and vibration theory. Triple correlations within the polyhedra are described by group-theoretical invariants that are related to the permutation representations and termed polyhedral isoscalar factors. These invariants are applied in theorems on matrix elements referring to the symmetry-adapted bases at different centres. Further invariants or geometrical weight factors inter-relate different types of reduced matrix elements of irreducible tensors (generalization of the Wigner-Eckart theorem to the polycentric case). As a demonstration a complete tabulation is given for the point group C.

Keywords

Polycentric molecules Permutational representations Symmetry adaption Irreducible tensors Wigner-Eckart theorem 

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References and notes

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Gerhard Fieck
    • 1
  1. 1.Schule Marienau Nr. 11DahlemFederal Republic of Germany

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