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

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.