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The Scaled Hirshfeld Partitioning: Mathematical Development and Information-Theoretic Foundation.

Farnaz Heidar-Zadeh¹

¹Department of Chemistry, Queen's University, 90 Bader Lane, Kingston, ON K7L-3N6, Canada.

Entropy (Basel, Switzerland)

|March 28, 2026

Summary

This summary is machine-generated.

We introduce scaled Hirshfeld, an efficient method for calculating atomic charges in molecular electronic structure. This new approach improves upon Hirshfeld

Keywords:

Hirshfeld partitioning methods additive variational Hirshfeld atomic charges atoms in molecules condensed reactivity descriptors information-theoretic atoms scaled Hirshfeld

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Area of Science:

Computational Chemistry
Quantum Chemistry
Molecular Modeling

Background:

Atomic charges are crucial for understanding molecular electronic structure.
Existing methods like Hirshfeld's stockholder partitioning are widely used.
Developing efficient and accurate methods for atomic charge calculation is essential for computational chemistry.

Purpose of the Study:

To introduce a computationally efficient extension of Hirshfeld's stockholder partitioning method, termed scaled Hirshfeld.
To provide a rigorous mathematical foundation for the scaled Hirshfeld method.
To demonstrate the improved accuracy of scaled Hirshfeld charges for molecular properties.

Main Methods:

Development of the scaled Hirshfeld method by scaling neutral proatom densities.
Implementation of a fixed-point iterative algorithm to compute proatom scaling coefficients.
Equivalence established with the information-theoretic additive variational Hirshfeld method.

Main Results:

The scaled Hirshfeld method yields larger atomic charges compared to the original Hirshfeld method.
The method maintains computational efficiency.
Improved description of molecular dipole moments and electrostatic potentials was achieved.

Conclusions:

The scaled Hirshfeld method offers a computationally efficient and mathematically rigorous approach to atomic charge calculation.
This method provides enhanced accuracy for molecular electronic structure analysis.
The scaled Hirshfeld method is a valuable tool for developing advanced computational models.