Permutation representations in molecular symmetry |
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Authors: | Gerhard Fieck |
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Affiliation: | (1) Schule Marienau Nr. 11, D-2121 Dahlem, Federal Republic of Germany |
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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 C4. |
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Keywords: | Polycentric molecules Permutational representations Symmetry adaption Irreducible tensors Wigner-Eckart theorem |
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