Topological Atomic Displacements, Kirchhoff and Wiener Indices of Molecules

Details Topological Atomic Displacements, Kirchhoff and Wiener Indices of Molecules Topological Atomic Displacements, Kirchhoff and Wiener Indices of Molecules

2009-12-14

arxiv.org/abs/0912.2628v2

Chem. Phys. Lett. 486 (2010) 166-170

Physics

Chemical Physics

16 pages, the final version accepted for publication in Chem. Phys. Lett

Scientific paper

10.1016/j.cplett.2009.12.090

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.

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