Five-coordinate transition metal complexes and the value of τ5: observations and caveats

The τ5 parameter, first proposed by Addison and coworkers, is the principal measure of the geometry of five-coordinate transition metal complexes, with τ5 = 0 said to describe a perfect square pyramidal geometry and τ5 = 1 a perfect trigonal pyramidal geometry. Therefore, the geometries of all five-coordinate complexes are assumed to lie on a continuum between these two extremes. Herein we show that there are a significant number of examples of transition metal complexes having τ5 > 1, leading to an equatorially distorted trigonal bipyramidal geometry with the transition metal ion lying out of the plane of the equatorial donor atoms. We also show that complexes having τ5 = 0 and displaying perfect square pyramidal geometry are very much the exception, and that the majority of complexes for which τ5 = 0 have the metal ion sitting above the mean plane of the donor atoms in the square plane, in a basally distorted square pyramidal geometry. Density functional theory computations on a number of these complexes show that the structural distortions are inherent features of the complexes, and not merely the result of intermolecular interactions