The lanthanide contraction revisited.

A complete, isostructural series of complexes with La-Lu (except Pm) with the ligand TREN-1,2-HOIQO has been synthesized and structurally characterized by means of single-crystal X-ray analysis. All complexes are 1D-polymeric species in the solid state, with the lanthanide being in an eight-coordinate, distorted trigonal-dodecahedral environment with a donor set of eight unique oxygen atoms. This series constitutes the first complete set of isostructural complexes from La-Lu (without Pm) with a ligand of denticity greater than two. The geometric arrangement of the chelating moieties slightly deviates across the lanthanide series, as analyzed by a shape parameter metric based on the comparison of the dihedral angles along all edges of the coordination polyhedron. The apparent lanthanide contraction in the individual Ln-O bond lengths deviates considerably from the expected quadratic decrease that was found previously in a number of complexes with ligands of low denticity. The sum of all bond lengths around the trivalent metal cation, however, is more regular, showing an almost ideal quadratic behavior across the entire series. The quadratic nature of the lanthanide contraction is derived theoretically from Slater's model for the calculation of ionic radii. In addition, the sum of all distances along the edges of the coordination polyhedron show exactly the same quadratic dependence as the Ln-X bond lengths. The universal validity of this coordination sphere contraction, concomitant with the quadratic decrease in Ln-X bond lengths, was confirmed by reexamination of four other, previously published series of lanthanide complexes. Owing to the importance of multidentate ligands for the chelation of rare-earth metals, this result provides a significant advance for the prediction and rationalization of the geometric features of the corresponding lanthanide complexes, with great potential impact for all aspects of lanthanide coordination.