A graph theoretic approach to atomic displacements in fullerenes
Estrada, Ernesto and Hatano, N. and Matamala, A.R.; Cataldo, F. and Graovac, A. and Ori, O., eds. (2011) A graph theoretic approach to atomic displacements in fullerenes. In: The Mathematics and Topology of Fullerenes (Carbon Materials: Chemistry and Physics). Springer.
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We consider a classical mechanics approach to atomic displacements in fullerene molecules. The problem is reduced to the study of the graph Laplacian spectra by deriving an analytical expression for the atomic displacement due to thermal vibrations/oscillations. We then use the concepts of graph isoperimetric constant and graph expansion to prove that "among all graphs on n nodes, those with good expansion properties display the smallest topological displacements of their nodes." Consequently, fullerenes with the property of being Ramanujan graphs, i.e., Ramafullerenes, are those that exhibit the smallest atomic displacements due to thermal movement. We show that fullerenes with the smallest atomic perturbations due to thermal effects are the most stable ones. Then, relationships between atomic displacements, spectral gap, and energy are presented for different families of fullerenes.
ORCID iDs
Estrada, Ernesto ORCID: https://orcid.org/0000000230667418, Hatano, N. and Matamala, A.R.; Cataldo, F., Graovac, A. and Ori, O.

Item type: Book Section ID code: 37710 Dates: DateEvent2011PublishedKeywords: fullerenes , atomic displacement, fullerene molecules , classical mechanics, Mathematics Subjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 17 Feb 2012 12:27 Last modified: 25 Aug 2021 00:47 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/37710