Relativistic Hirshfeld atoms in a molecule: An information-theoretic view, with application to Drude oscillator dispersion models
Abstract
Several ad hoc dispersion models for density-functional theory are based on the use of Hirshfeld (or "stockholder") partition of a molecular charge density, which provides an in situ definition of atomic size. We show that a recently introduced "optimized" quantum Drude oscillator model for dispersion admits a closed-form solution in terms of the Lambert W function, whose branches identify the compact and diffuse oscillator solutions. The compact solution determines the C8 (dipole-quadrupole) dispersion coefficient analytically from the free-atom polarizability, C6 coefficient, and van der Waals radius, without any reference C8 data. Next, we provide a formal basis for a relativistic version of the atoms-in-molecule Hirshfeld partition. Using four-component Dirac-Hartree-Fock densities for isolated atoms defines a strictly positive deformation field that carries the relativistic changes in atomic density into the Hirshfeld partition. A uniqueness theorem for the non-relativistic case is extended to relativistic Hirshfeld atoms and admits an asymptotic expansion through quadratic order in the fine-structure constant. Normalization requires the relativistic density correction to reshape the reference atom while preserving its population. Finally, four-component polarizabilities and C6 coefficients are reported for closed-shell atoms and ions, which supply the reference data required to extend atoms-in-molecules dispersion models into the heavy-element regime. Periodic trends are observable in a scalar contraction factor that measures relativistic effects.
Related
- Integrated Experimental and Computational Investigation of Fluorinated Benzoylthiourea Derivatives: Structural Characterization, Hirshfeld Surface Analysis, Antioxidant Activity, and MAO–B Inhibitory Potential for Parkinson’s Disease
- Crystal structure, Hirshfeld surface analysis, computational study, molecular docking predictions and biological evaluation of a new Schiff base (E)-2-((2,4-dichlorobenzylidene)amino)aniline
- Synthesis, Crystal Structure, Hirshfeld Surface, Vibrational Thermal Analyses, and NLO Properties of a New Hybrid Material: 2,4-Diamino-6-Phenyl-1,3,5-Triazinium Perchlorate, Supported by DFT Calculations
- Synthesis, crystal structure, Hirshfeld surface analysis and halogen-involving interactions in a bromo/chloro-substituted Schiff base 1-(3-bromo-4,5-dimethoxyphenyl)-N-(2,4-dichlorophenyl)methanimine
- Eco-friendly Synthesis of 3-Methyl-4-arylmethyleneisoxazol-5(4H)-ones. Crystal Structure, Hirshfeld Surface Analysis, and Theoretical Study
BibTeX
@misc{paice2026relativistic,
title = {{Relativistic Hirshfeld atoms in a molecule: An information-theoretic view, with application to Drude oscillator dispersion models}},
author = {Keegan Paice and John M. Herbert},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01624},
eprint = {2610.01624},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01624},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Relativistic Hirshfeld atoms in a molecule: An information-theoretic view, with application to Drude oscillator dispersion models
AU - Keegan Paice
AU - John M. Herbert
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01624
UR - https://arxiv.org/abs/2610.01624
AB - Several ad hoc dispersion models for density-functional theory are based on the use of Hirshfeld (or "stockholder") partition of a molecular charge density, which provides an in situ definition of atomic size. We show that a recently introduced "optimized" quantum Drude oscillator model for dispersion admits a closed-form solution in terms of the Lambert W function, whose branches identify the compact and diffuse oscillator solutions. The compact solution determines the C_8 (dipole-quadrupole) dispersion coefficient analytically from the free-atom polarizability, C_6 coefficient, and van der Waals radius, without any reference C_8 data. Next, we provide a formal basis for a relativistic version of the atoms-in-molecule Hirshfeld partition. Using four-component Dirac-Hartree-Fock densities for isolated atoms defines a strictly positive deformation field that carries the relativistic changes in atomic density into the Hirshfeld partition. A uniqueness theorem for the non-relativistic case is extended to relativistic Hirshfeld atoms and admits an asymptotic expansion through quadratic order in the fine-structure constant. Normalization requires the relativistic density correction to reshape the reference atom while preserving its population. Finally, four-component polarizabilities and C6 coefficients are reported for closed-shell atoms and ions, which supply the reference data required to extend atoms-in-molecules dispersion models into the heavy-element regime. Periodic trends are observable in a scalar contraction factor that measures relativistic effects.
ER -