Title: S5 graphs as model systems for icosahedral Jahn-Teller problems
Authors: Ceulemans, Arnout ×
Lijnen, Erwin
Fowler, Patrick W.
Mallion, Roger B.
Pisanski, Thomas #
Issue Date: Jun-2012
Publisher: Springer-Verlag
Series Title: Theoretical Chemistry Accounts vol:131 pages:1246
Article number: DOI 10.1007/s00214-012-1246-3
Abstract: The degeneracy of the eigenvalues of the
adjacency matrix of graphs may be broken by non-uniform
changes of the edge weights. This symmetry breaking is the
graph-theoretical equivalent of the molecular Jahn–Teller
effect (Ceulemans et al. in Proc Roy Soc 468:971–989,
2012). It is investigated for three representative graphs,
which all have the symmetric group on 5 elements, S5, as
automorphism group: the complete graph K5, with 5 nodes,
the Petersen graph, with 10 nodes, and an extended K5
graph with 20 nodes. The spectra of these graphs contain
fourfold, fivefold, and sixfold degenerate manifolds,
respectively, and provide model systems for the study of
the Jahn–Teller effect in icosahedral molecules. The S5
symmetries of the distortion modes of the quintuplet in the
Petersen graph yield a resolution of the product multiplicity in the corresponding H \times g + 2h icosahedral Jahn–Teller
problem. In the extended Petersen graph with 20 nodes, a
selection rule prevents the Jahn–Teller splitting of the
sextuplet into two conjugate icosahedral triplets.
ISSN: 1432-881X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Quantum Chemistry and Physical Chemistry Section
× corresponding author
# (joint) last author

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