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Topological atomic displacements, Kirchhoff and Wiener indices of molecules

Estrada, E. and Hatano, N. (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.