Density-optimized radial exponents for X-ray charge-density refinement from ab initio crystal calculations.

Area of Science:

• Crystallography
• Quantum Chemistry
• Materials Science

Background:

• The Hansen-Coppens multipole formalism is crucial for analyzing experimental and theoretical charge densities in crystals.
• Understanding the behavior of kappa and kappa' parameters is essential for accurate charge density refinement.

Purpose of the Study:

• To investigate trends in kappa and kappa' parameters derived from periodic density-functional theory (DFT) calculations.
• To establish relationships between atomic charges and multipole parameters for different elements and bonding environments.
• To provide reference values for multipole parameters to aid in charge density refinement.

Main Methods:

• Periodic density-functional theory (DFT) calculations were performed on 25 molecular crystals.
• Structure factors were derived from DFT calculations to refine kappa and kappa' parameters using the Hansen-Coppens formalism.
• Systematic analysis of parameter trends across different atomic species (C, N, O) and bonding environments was conducted.

Main Results:

• A strong correlation was observed between net atomic charges and kappa parameters, with negative atoms showing expansion.
• Kappa' parameters demonstrated consistency within specific bonding environments, particularly for carbon and oxygen.
• Nitrogen exhibited greater variability in kappa' values, necessitating environment-specific tuning.

Conclusions:

• Average kappa and kappa' values for carbon and oxygen can serve as useful constraints in charge density refinements, especially for large molecules.
• The relationship between atomic charge and kappa parameters offers a pathway to constrain multipole refinements for complex molecular systems.
• Refined multipole parameters provide insights into chemical bonding and electronic structure.