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Energy levels of paramagnetic ions: Algebra. V. Weak‐field models
Author(s) -
Kibler Maurice,
Grenet Geneviève
Publication year - 1986
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560290321
Subject(s) - symmetry (geometry) , ion , field (mathematics) , octahedron , paramagnetism , physics , constraint (computer aided design) , phenomenological model , octahedral symmetry , mathematical physics , mathematics , quantum mechanics , geometry , pure mathematics
Abstract We explore a generalized weak‐field model for the description of the electronic properties of a partly filled shell( S ) ion in a crystalline field. Such a model corresponds to the one developed, in parts III and IV of this series, for d N and f N ions in cubical symmetry except that the constraint relations are relaxed. This leads to a fourteen‐parameter weak‐field model for d N ions in octahedral symmetry and to a 33‐parameter weak‐field model for f N ions in octahedral symmetry. The latter two models are completely equivalent to the corresponding strong‐field models as developed by Griffith and by Tanabe, Sugano, and Kamimura. The constraint relations of parts III and IV are further discussed. In particular, the role they play in fitting procedures is examined. As a conclusion, the weak‐field model of III and IV appears as a phenomenological version of the generalized weak‐field model introduced in this paper.