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Deriving the Hirshfeld partitioning using distance metrics.

Farnaz Heidar-Zadeh1, Paul W Ayers1, Patrick Bultinck2

  • 1Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada.

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The Hirshfeld partitioning method for molecules can be improved by minimizing distances to reference pro-atom densities. This offers a new approach to understanding atomic contributions in chemical systems.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Hirshfeld partitioning is a method to analyze atomic properties in molecules.
  • Existing interpretations include heuristic 'stockholder' and information-theoretic approaches.
  • A need exists for alternative, mathematically rigorous interpretations.

Purpose of the Study:

  • To propose a novel interpretation of Hirshfeld partitioning based on distance minimization.
  • To provide an alternative to existing heuristic and information-theoretic methods.
  • To generalize the findings to a broader class of divergence measures.

Main Methods:

  • Minimizing the generalized Hellinger-Bhattacharya distance between atomic densities and reference pro-atom densities.
  • Selecting reference pro-atoms by minimizing the distance between pro-molecule and true molecular densities.
  • Extending the methodology to f-divergences.

Main Results:

  • Atoms in Hirshfeld partitioning naturally minimize a specific distance metric to reference pro-atoms.
  • A clear criterion for choosing reference pro-atoms is established via density-based distance minimization.
  • The proposed method offers a new perspective on Hirshfeld partitioning.

Conclusions:

  • The distance-minimization approach provides a robust and mathematically grounded interpretation of Hirshfeld partitioning.
  • This work extends the applicability of Hirshfeld partitioning and related methods.
  • The findings offer a valuable alternative for analyzing electron density in molecules.