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  • Normal vibrations  (1)
  • Permutational representations  (1)
  • Racah algebra  (1)
  • 1
    Digitale Medien
    Digitale Medien
    Permutation representations in molecular symmetry (1988)
    Springer
    Theoretical chemistry accounts 73 (1988), S. 247-277 
    Details
    ISSN: 1432-2234
    Schlagwort(e): Polycentric molecules ; Permutational representations ; Symmetry adaption ; Irreducible tensors ; Wigner-Eckart theorem
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00527414
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Symmetry adaption (1978)
    Springer
    Theoretical chemistry accounts 49 (1978), S. 187-198 
    Details
    ISSN: 1432-2234
    Schlagwort(e): Symmetry-adaption ; Racah algebra ; Coordination polyhedra
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00550030
    Standort Signatur Erwartet Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    Symmetry adaption (1978)
    Springer
    Theoretical chemistry accounts 49 (1978), S. 211-222 
    Details
    ISSN: 1432-2234
    Schlagwort(e): Force constants ; Symmetry coordinates ; Normal vibrations ; Tetrahedral molecule
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00550032
    Standort Signatur Erwartet Verfügbarkeit
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