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Hirshfeld partitioning from non-extensive entropies

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Abstract

We show that the statistical divergence measures associated with non-extensive thermodynamic entropy functions—specifically the Tsallis, Réyni, Sharma–Mittal, supraextensive, and H-divergences—are associated with the Hirshfeld atoms-in-molecules partitioning. This extends the treatment of Nalewajski and Parr (J Phys Chem A 109:3957–3959, 2005), (for the extensive Shannon entropy) to non-extensive entropy measures. It also extends the work of Heidar-Zadeh and Ayers (J Chem Phys 142(4):044107, 2015), (for divergence measures that are local density functionals) to non-local functionals. These results dramatically extend the mathematical framework that one can use for similarity-based atoms-in-molecules partitioning.

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Acknowledgements

The authors thank NSERC and Compute Canada for funding. FHZ acknowledges support from Vanier-CGS fellowship and Ghent University Scholarship for a Joint Doctorate.

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Authors and Affiliations

  1. Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON, Canada

    Farnaz Heidar-Zadeh, Ivan Vinogradov & Paul W. Ayers

  2. Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000, Ghent, Belgium

    Farnaz Heidar-Zadeh

  3. Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052, Zwijnaarde, Belgium

    Farnaz Heidar-Zadeh

Authors
  1. Farnaz Heidar-Zadeh
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  2. Ivan Vinogradov
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  3. Paul W. Ayers
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Correspondence to Farnaz Heidar-Zadeh or Paul W. Ayers.

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Heidar-Zadeh, F., Vinogradov, I. & Ayers, P.W. Hirshfeld partitioning from non-extensive entropies. Theor Chem Acc 136, 54 (2017). https://doi.org/10.1007/s00214-017-2077-z

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