Theoretica chimica acta

, Volume 37, Issue 3, pp 233–250 | Cite as

The coupling algebra of trigonally subduced crystal field eigenvectors

  • Bryan R. Hollebone
  • J. C. Donini


The general theory of subduction of eigenvectors between infinite groups is used to derive a finite group subduction operator and define the corresponding subduction coefficients. The coupling behaviour of these subduced eigenvectors can then be described in terms of 3 Γ symbols. These symbols, defined only in relation to complex basis sets are all fully real and have all phases fixed by the subduction operator. They differ from V coefficients in two phase relationships and have the advantage, unlike V coefficients, of retaining all the symmetry properties and selection rules of Wigner 3-j symbols. Appropriate label systems which render these properties in terms of simple algebras are given for all quantizing axes available in O h . The specific set of 3Γ symbols for each quantization is determined by the orientation of the coordinate axes in the Hamiltonian. The four possible orientations for trigonal quantization are examined and the operator chosen which produces eigenvectors with conventional conjugate phases and a fully real set of 3Γ symbols.

Key word

Crystal field theory 


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Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Bryan R. Hollebone
    • 1
  • J. C. Donini
    • 1
  1. 1.Department of ChemistryUniversity of AlbertaEdmontonCanada

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