General method for the description, visualization and comparison of metal coordination spheres: geometrical preferences, deformations and interconversion pathways
Jw. Yao et al., General method for the description, visualization and comparison of metal coordination spheres: geometrical preferences, deformations and interconversion pathways, ACT CRYST B, 57, 2001, pp. 251-260
The coordination sphere geometry of metal atoms (M) in their complexes with
organic and inorganic ligands (L) is often compared with the geometry of a
rchetypal forms for the appropriate coordination number, n in MLn species,
by use of the k = n( n - 1)/2 L-M-L valence angles subtended at the metal c
entre. Here, a Euclidean dissimilarity metric, R-c(x), is introduced as a o
ne-dimensional comparator of these k-dimensional valence-angle spaces. The
computational procedure for R-c(x), where x is an appropriate archetypal fo
rm (e.g. an octahedron in ML6 species), takes account of the atomic permuta
tional symmetry inherent in MLn systems when no distinction is made between
the individual ligand atoms. It is this permutational symmetry, of order n
!, that precludes the routine application of multivariate analytical techni
ques, such as principal component analysis (PCA), to valence angle data for
all but the lowest metal coordination numbers. It is shown that histograms
of R-c(x) values and, particularly, scatterplots of R-c(x) values computed
with respect to two or more different appropriate archetypal forms (e.g. t
etrahedral and square-planar four-coordinations), provide information-rich
visualizations of the observed geometrical preferences of metal coordinatio
n spheres retrieved from, e.g. the Cambridge Structural Database. These map
pings reveal the highly populated clusters of similar geometries, together
with the pathways that map their geometrical interconversions. Application
of R-c(x) analysis to the geometry of four- and seven-coordination spheres
provides information that is at least comparable to, and in some cases is m
ore complete than, that obtained by PCA.