The Effects of Chemical Bonding at Subatomic Resolution: A Case Study on α-Boron

Area of Science:

• Crystallography
• Materials Science
• Quantum Chemistry

Background:

• Aspherical electron density deformations in atomic cores can cause core asphericity shifts during crystallographic refinements.
• These shifts are particularly noticeable with high-resolution experimental data (sin(θ)/λ > 1.0 Å⁻¹).
• Core asphericity shifts are approximately two orders of magnitude smaller than those from valence shell deformations and are primarily dipolar for first-row atoms.

Purpose of the Study:

• To analyze the resolution dependence of core asphericity shifts in alpha-boron.
• To develop and validate an Extended Hansen-Coppens multipolar model (EHCM) for accurately describing these shifts.
• To assess the impact of core asphericity shifts on bond length determination and the effectiveness of the EHCM in compensating for them.

Main Methods:

• Theoretical structure factor calculations were used to develop an appropriate Extended Hansen-Coppens multipolar model (EHCM).
• The developed EHCM was tested against experimental high-resolution single-crystal diffraction data for alpha-boron (sin(θ)/λ ≤ 1.6 Å⁻¹).
• Analysis focused on the resolution dependence of core asphericity shifts and their effect on bond length deviations.

Main Results:

• Core asphericity shifts in alpha-boron were found to be on the order of 4-6·10⁻⁴ Å, which are small but significant at high resolution.
• The EHCM effectively compensated for these bond length deviations.
• A strong correlation between additional EHCM parameters and positional parameters hindered the free refinement of all core model parameters.

Conclusions:

• Accurate crystallographic refinements using high-resolution data necessitate proper treatment of core asphericity shifts.
• The Extended Hansen-Coppens multipolar model (EHCM) or equivalent methods are highly recommended for high-quality, high-resolution diffraction data.
• While EHCM can compensate for core asphericity shifts, careful parameterization is needed due to potential correlations.