Fortuitous Error Attenuation in Hirshfeld Charges from Gaussian-Based Spherical Atomic Densities

Area of Science:

• Computational chemistry
• Quantum chemistry
• Electronic structure theory

Background:

• Spherical atomic electron densities are fundamental for promolecular densities and Hirshfeld stockholder weights.
• Gaussian-type orbital (GTO) basis sets are widely used in electronic structure calculations.

Purpose of the Study:

• To systematically compare GTO-derived spherical atomic densities with reference Slater-type orbital (STO) densities.
• To evaluate the impact of these atomic density differences on promolecular densities and Hirshfeld partition weights.

Main Methods:

• Hartree-Fock wave functions were computed using various GTO basis sets (STO-3G, 6-31G*, 6-311G*, def2TZVP, cc-pVTZ, ANO-pVTZ).
• GTO-derived densities were compared to reference STO densities for atoms He to Kr.
• Analysis included radial behavior, density derivatives (|∇ρ(r)|, |∇ρ(r)|/ρ(r)), promolecular densities, and Hirshfeld partition weights.

Main Results:

• Flexible GTO basis sets capture the overall radial behavior of STO densities but show discrepancies in near-nuclear and asymptotic regions.
• Density derivatives highlight limitations of GTO expansions in describing electron-nucleus cusps and long-range decay.
• Atomic discrepancies transfer to promolecular densities and Hirshfeld weights, affecting spatial distribution.
• Hirshfeld population differences are small for flexible basis sets, despite local weight deviations.

Conclusions:

• Gaussian-based spherical densities provide reliable Hirshfeld populations and charges with adequate basis sets.
• Density derivatives, promolecular densities, and local partition weights are sensitive indicators of atomic reference density quality.