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Energy levels of paramagnetic ions: Algebra. III. The case of d N ions in cubical symmetry
Author(s) -
Kibler Maurice,
Grenet Geneviève
Publication year - 1985
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.560280205
Subject(s) - hamiltonian (control theory) , isotropy , physics , anisotropy , homogeneous space , ion , symmetry group , symmetry operation , coulomb , symmetry (geometry) , quantum mechanics , mathematical physics , geometry , mathematics , electron , mathematical optimization
The formalism developed in the first two papers of this series is applied to the investigation of a new weak‐field model. This crystal‐field model lies on the use of a symmetry‐adapted weak‐field basis and an effective Hamiltonian involving in a symmetrical way both spin‐ and orbit‐dependent contributions. Some general properties of this Hamiltonian are studied and complete calculation of its matrix elements is conducted in a symmetry‐adapted weak‐field basis in the case of an arbitrary configuration nl N in any symmetry. The case of a configuration nd N in octahedral symmetry is fully explored. In this case, the proposed weak‐field model is restricted to a 12‐parameter model which accounts for isotropic and anisotropic Coulomb interactions, isotropic and anisotropic spin‐orbit interactions, and crystal‐field interactions. A comparison between this 12‐parameter weak‐field model and the 14‐parameter strong‐field model is established. Equivalence between the latter two models requires two constraint relations to be satisfied for some strong‐field parameters. These two relations are examined with various viewpoints.