General method for the description, visualization and comparison of metal coordination spheres: geometrical...

Area of Science:

• Inorganic Chemistry
• Crystallography
• Computational Chemistry

Background:

• Metal coordination sphere geometry is crucial in chemistry and materials science.
• Comparing observed geometries to archetypal forms using valence angles is common.
• Multivariate analyses like PCA are limited by atomic permutational symmetry in ML(n) systems.

Purpose of the Study:

• Introduce a new Euclidean dissimilarity metric, R(c)(x), for comparing coordination sphere geometries.
• Develop a method to visualize geometrical preferences and interconversions in metal complexes.
• Overcome the limitations of existing analytical techniques for valence angle data.

Main Methods:

• Developed a one-dimensional comparator, R(c)(x), for k-dimensional valence-angle spaces.
• Accounted for atomic permutational symmetry inherent in ML(n) systems.
• Utilized histograms and scatterplots of R(c)(x) values for visualization.

Main Results:

• R(c)(x) provides information-rich visualizations of metal coordination sphere geometries.
• Scatterplots reveal populated clusters of similar geometries and pathways of interconversion.
• Analysis of four- and seven-coordination spheres yielded comparable or superior information to PCA.

Conclusions:

• The R(c)(x) metric is a powerful tool for analyzing and visualizing coordination sphere geometry.
• This method offers a robust alternative to PCA for complex ML(n) systems.
• The approach aids in understanding geometrical preferences and dynamics in metal complexes.