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Theoretica chimica acta

, Volume 42, Issue 2, pp 111–144 | Cite as

Quotients of group algebrae in the calculation of intermediate ligand field matrix elements

  • John C. Donini
  • Bryan R. Hollebone
Article

Abstract

The structure of the classes of symmetry elements excluded during the subduction of the representations of SU(2) onto the finite group 0* is shown to quantitatively define the relationship of the coupling algebrae of these two groups. This relationship is formalized as a quotient algebra. This quotient algebra is realized as 3Γ-like symbols which exist whether or not the quotient can be defined as a group. These symbols distribute the value of a reduced matrix element of SU(2) onto the subduced reduced matrix elements of O* and are termed Partition Coefficients. Since the structure of the excluded symmetry classes is independent of the quantization of O*, these Partition Coefficients can be used to define the values of the matrix elements of O* without reference to the form of its basis set. Thus, the choice of physical interpretation of the ligand field is unimportant. The strong field, weak field, Russell-Saunders and j-j coupling models are all unified in terms of the Partition Coefficients and the 3Γ symbols which are appropriate to the quantization.

Key words

Ligand field theory 

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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

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

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