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Theoretica chimica acta

, Volume 42, Issue 2, pp 97–110 | Cite as

The coupling symbols and algebrae of subducible, octahedrally projected ligand field eigenvectors

  • John C. Donini
  • Bryan R. Hollebone
Article

Abstract

The 3Γ symbols required for the application of the Wigner-Eckart theorem to strong ligand field matrix elements are derived for complex basis functions quantized on the C 4 Z , C 3 XYZ , C 2 Z and C 2 XY axes of an octahedron. This scheme provides a standardized analysis technique for the matrix elements of subgroups in each of the four physically significant chains of the double group O h * . This standardization yields the minimum necessary number of ligand field parameters in any subgroup and makes possible the direct comparability of equivalent parameters in different symmetries. A unique numerical labelling for both representations and complex components on each axis provides both a simple component selection rule algebra and numerical phase factors governing permutation and conjugation of the 3Γ symbols.

Key words

Ligand field eigenvectors 

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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • John C. Donini
    • 1
  • Bryan R. Hollebone
    • 2
  1. 1.Department of ChemistrySt. Francis Xavier UniversityAntigonishCanada
  2. 2.Department of ChemistryUniversity of AlbertaEdmontonCanada

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