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Open Access research with a European policy impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the European Policies Research Centre (EPRC).

EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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A graph theoretic approach to atomic displacements in fullerenes

Estrada, Ernesto and Hatano, N. and Matamala, A.R. (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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Abstract

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.