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Symmetry adaption

II. Representations on symmetric polyhedra

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Abstract

Stimulated by the invention of an algebraic formula for the coefficients of symmetry-adapted linear combinations in a previous paper [1], the representations induced by the edge vectors of a symmetric, molecular polyhedron AmBnCp... are studied in detail. The following objects are defined (in brackets the analogous, common objects): Complete systems of standard functions (spherical harmonics), polyhedral vector coupling coefficients (3jm-symbols), polyhedral Racah coefficients (6j-symbols), polyhedral isoscalar factors (isoscalar factors). The algebraic properties and evaluation methods of these coefficients are discussed in order to be used in subsequent papers on quantities depending on symmetry-adapted orbitals and symmetry coordinates.

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References

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Authors and Affiliations

  1. Institut für Chemie, Universität Regensburg, Universitätsstraße 31, D-8400, Regensburg, Germany

    Gerhard Fieck

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  1. Gerhard Fieck
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Fieck, G. Symmetry adaption. Theoret. Chim. Acta 49, 187–198 (1978). https://doi.org/10.1007/BF00550030

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  • DOI: https://doi.org/10.1007/BF00550030

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