X-ray atomic orbital analysis. I. Quantum-mechanical and crystallographic framework of the method

Area of Science:

• Crystallography
• Quantum Chemistry
• Materials Science

Background:

• Traditional X-ray crystal structure analysis uses atoms as the fundamental scattering units.
• Understanding electron distribution and transfer within crystal structures is crucial for materials science.

Purpose of the Study:

• To introduce X-ray atomic orbital analysis (XAO) as a novel method for crystal structure analysis.
• To detail the methodology for determining atomic orbitals and electron populations within a unit cell.
• To demonstrate XAO's applicability in tracing electron transfer and analyzing electron-density distribution.

Main Methods:

• XAO analysis divides atoms into subshell electrons, treating each subshell as a pseudo-atom.
• Atomic orbitals (AO's) and their electron populations are determined using linear combinations of s/p/d/f orbitals.
• Perturbation theory and refinement against observed structure factors are employed to calculate AO coefficients, maintaining orthonormality.

Main Results:

• XAO enables the determination of AO's and electron populations for each subshell.
• Electron transfer among AO's in crystals can be traced by varying environmental conditions.
• The method is particularly applicable to electron-density distribution analysis in ionic solids, including nonstoichiometric structures.

Conclusions:

• XAO provides a detailed view of electronic structure in crystals by focusing on subshell electrons.
• The derived AO's are applicable to multi-electron systems, offering insights beyond traditional atomic scattering.
• XAO enhances the analysis of electron density and transfer phenomena in crystalline materials.