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Topological atomic displacements, Kirchhoff and Wiener indices of molecules

Estrada, E. and Hatano, N., University of Strathclyde, New Professors Fund (Funder) (2010) Topological atomic displacements, Kirchhoff and Wiener indices of molecules. Chemical Physics Letters, 486 (4-6). pp. 166-170. ISSN 0009-2614

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Abstract

We provide a physical interpretation of the Kirchhoff index of any molecules as well as of the Wiener index of acyclic ones. For the purpose, we use a local vertex invariant that is obtained from first principles and describes the atomic displacements due to small vibrations/oscillations of atoms from their equilibrium positions. In addition, we show that the topological atomic displacements correlate with the temperature factors (B-factors) of atoms obtained by X-ray crystallography for both organic molecules and biological macromolecules.