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

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.