Abstract
The reducible representations of the point groups are generally studied because of their relevance to molecular orbital and vibration theory. Triple correlations within the polyhedra are described by group-theoretical invariants that are related to the permutation representations and termed polyhedral isoscalar factors. These invariants are applied in theorems on matrix elements referring to the symmetry-adapted bases at different centres. Further invariants or geometrical weight factors inter-relate different types of reduced matrix elements of irreducible tensors (generalization of the Wigner-Eckart theorem to the polycentric case). As a demonstration a complete tabulation is given for the point group C 4υ.
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References and notes
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cf. [6]
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Fieck, G. Permutation representations in molecular symmetry. Theoret. Chim. Acta 73, 247–277 (1988). https://doi.org/10.1007/BF00527414
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DOI: https://doi.org/10.1007/BF00527414