Atomic/Ionic Radius as Mathematical Limit of System Energy Evolution.

Area of Science:

• Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Classical definitions of atomic and ionic radii lack a unified theoretical basis.
• Existing models often require empirical adjustments, limiting cross-element comparisons.

Purpose of the Study:

• To propose a novel, physically interpretable definition of atomic and ionic radii.
• To develop a generalized method applicable across various oxidation states.
• To establish a basis for direct, constant-free comparison of radii between different elements.

Main Methods:

• Utilizing conceptual density functional theories and electron density fundamental response functions.
• Developing a generalized computational scheme for radius estimation.
• Testing the proposed method against established empirical data (e.g., Shannon radii).

Main Results:

• The new definition provides a consistent and physically meaningful measure of atomic and ionic radii.
• The method successfully estimates radii for atoms in diverse oxidation states.
• The calculated radii show good correlation with classical estimates while offering direct comparability.

Conclusions:

• The proposed density functional theory-based definition offers a robust and universally applicable approach to atomic and ionic radii.
• This method enhances the understanding of size-related phenomena and chemical trends.
• It eliminates the need for empirical fitting constants, facilitating more accurate inter-element comparisons.