Stereochemistry of complexes with double and triple metal-ligand bonds: a continuous shape measures analysis

To each coordination polyhedron we can associate a normalized coordination polyhedron that retains the angular orientation of the central atom-ligand bonds but has all the vertices at the same distance from the center. The use of shape measures of these normalized coordination polyhedra provides a simple and efficient way of discriminating angular and bond distance distortions from an ideal polyhedron. In this paper we explore the applications of such an approach to analyses of several stereochemical problems. Among others, we discuss how to discern the off-center displacement of the metal from metal-ligand bond shortening distortions in families of square planar biscarbene and octahedral dioxo complexes. The normalized polyhedron approach is also shown to be very useful to understand stereochemical trends with the help of shape maps, minimal distortion pathways, and ligand association/dissociation pathways, illustrated by the Berry and anti Berry distortions of triple-bonded [X≡ML4] complexes, the square pyramidal geometries of Mo coordination polyhedra in oxido-reductases, the coordination geometries of actinyl complexes, and the tetrahedricity of heavy atom-substituted carbon centers.