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Variational Hirshfeld Partitioning: General Framework and the Additive Variational Hirshfeld Partitioning Method.

Farnaz Heidar-Zadeh1, Carlos Castillo-Orellana2, Maximilian van Zyl1

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We developed additive variational Hirshfeld (AVH), a novel partitioning scheme for molecular electron density. AVH provides chemically interpretable atomic charges and a robust computational approach.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Existing methods for partitioning molecular electron density have limitations.
  • Variational Hirshfeld partitioning offers a flexible framework for density approximation.
  • Need for mathematically rigorous and chemically intuitive partitioning schemes.

Purpose of the Study:

  • Introduce a general mathematical framework for variational Hirshfeld partitioning.
  • Identify the most suitable f-divergence measure for this framework.
  • Develop a novel, robust, and chemically interpretable partitioning scheme.

Main Methods:

  • Minimizing f-divergence between molecular density and basis functions.
  • Utilizing the extended Kullback-Leibler divergence.
  • Constructing pro-molecular density via linear combination of atomic/ionic densities (Additive Variational Hirshfeld - AVH).

Main Results:

  • The extended Kullback-Leibler divergence is the only suitable f-divergence measure.
  • The developed AVH method is size-consistent and yields unique solutions.
  • AVH produces chemically sensible atomic charges with minimal deformation from isolated atomic states.

Conclusions:

  • Additive Variational Hirshfeld (AVH) provides a mathematically sound and computationally robust method for electron density partitioning.
  • AVH offers a valence-bond-like decomposition of molecular density.
  • The method yields interpretable atomic charges, advancing molecular property analysis.