Topological coordination numbers and coordination reciprocity from electron-density distributions

Area of Science:

• Quantum chemistry
• Solid-state physics
• Crystallography

Background:

• Traditional coordination number calculations often overlook atomic size effects and electron density distribution.
• Existing methods like Voronoi-Dirichlet partitioning (VDP) may not fully capture nuanced coordination scenarios in complex structures.

Purpose of the Study:

• To develop a generalized topological effective coordination number (tCN) approach.
• To incorporate coordination reciprocity and geometrical weighting for chemically meaningful coordination numbers.
• To provide a more accurate method for analyzing atomic coordination in diverse crystal structures.

Main Methods:

• Utilizing triangulated surface data sets from the Quantum Theory of Atoms in Molecules (QTAIM) interatomic surfaces.
• Calculating solid angles subtended at nuclear positions by diatomic contact surfaces.
• Developing weighting functions based on geometrical properties of areas to rank sub-coordination scenarios.

Main Results:

• The tCN approach naturally includes the effect of varying atomic sizes, unlike VDP.
• Differences between VDP and tCN results were observed even in highly symmetrical element structures due to electron density decay.
• The method effectively ranks multiple sub-coordination scenarios in complex structures like TiNiSi type compounds, providing relative weights.

Conclusions:

• The tCN method offers a more precise and comprehensive characterization of atomic coordination compared to VDP.
• It is particularly advantageous for analyzing complex intermetallic phases and provides valuable input for AI-driven structure-property relationship studies.