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  • 1
    Electronic Resource
    Electronic Resource
    Permutation representations in molecular symmetry (1988)
    Springer
    Theoretical chemistry accounts 73 (1988), S. 247-277 
    Details
    ISSN: 1432-2234
    Keywords: Polycentric molecules ; Permutational representations ; Symmetry adaption ; Irreducible tensors ; Wigner-Eckart theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00527414
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  • 2
    Electronic Resource
    Electronic Resource
    Symmetry adaption (1978)
    Springer
    Theoretical chemistry accounts 49 (1978), S. 211-222 
    Details
    ISSN: 1432-2234
    Keywords: Force constants ; Symmetry coordinates ; Normal vibrations ; Tetrahedral molecule
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The matrix of force constants of a symmetric molecule is reduced to its invariants (nearly diagonal form). For the case of distance dependent potentials these invariants are expressed by the derivations of the potentials and geometric factors. For the purpose of parametrization the inversions of these formulae are derived. The general equilibrium condition and the elimination of the translational and rotational coordinates are discussed. The example of the tetrahedral AB4 structure is worked out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00550032
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