Work

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

Year: 2026

Type: article

Abstract: Atomic charges play a central role in the analysis of molecular electronic structure and are widely used in the development of computational models. We introduce a simple and computationally efficient extension of Hirshfeld's 1977 stockholder partitioning method, called scaled Hirshfeld, in which neutral proatom densities are scaled to construct a promolecular density better adapted to the molecular electron density. We present a fixed-point iterative algorithm to compute the proatom scaling coefficients and show that this formulation is equivalent to the information-theoretic additive variational Hirshfeld method with a minimal basis. This equivalence establishes a rigorous mathematical foundation for the scaled Hirshfeld method and ensures size consistency as well as the existence of a unique solution. Numerical results demonstrate that the proposed approach yields charges larger than those obtained with the original Hirshfeld method, while retaining computational efficiency and providing an improved description of molecular dipole moments and electrostatic potentials.

Source: Entropy

DOI: 10.3390/e28030362

Author: Farnaz Heidar-Zadeh

Institution: Queen's University

Language: English

Topic: Advanced Chemical Physics Studies

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: Queen's University, Alliance de recherche numérique du Canada, Natural Sciences and Engineering Research Council of Canada