C 60 and the icosahedral group Ih: Simplification methods and group-theoretical applications |
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Authors: | Weiler R. Hurren Dorian M. Hatch |
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Affiliation: | 1. Department of Physics , The Citadel , Charleston, SC, 29409, USA;2. Department of Physics and Astronomy , Brigham Young University , Prow, UT, 84602, USA |
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Abstract: | Group-theoretical methods are used to induce “global” distortions of C 60 from basis function(s) of a single “local” distortion in two cases: (1) The 60 vibrational modes arising from radial displacements of carbon atoms are found in terms of basis functions of A′, the one-dimensional symmetric representation of Cs; (2) The 24 vibrational modes arising from tangential displacements of hypothetical atoms placed at pentagon centers are found in terms of basis functions of E 1, the vector irreducible representation of C5v . The induction process is simplified by an icon notation (v) or (vμ) which uniquely labels the operations in Ih if μ,v = 0, 1, 2, 3, 4 and under/over lining of a digit is included. These icons describe the transformations IUSvTSμ of Felix Kline referred to a five-fold z-axis and two-fold x-axis and serve to label and “distinguish” symmetrically equivalent points of the truncated icosahedron. |
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Keywords: | C 60 Icosahedral group theory Molecular distortions |
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