Lanthanide Contraction: What is Normal?

Renewed interest in lanthanide contraction results from its possible effect on the properties and applications of Ln(III) compounds and the theory related to these issues. To understand this effect, it is important to know what is a normal dependence of the contraction on the number of 4f electrons, n. The normal trend is based on recent values of ionic radii that have a linear dependence on n for coordination numbers (CNs) of 6, 8, and 9. If the normal trend is not followed, then some other interactions in the system are affecting the extent of contraction. However, the suggestion that the variation is curved and fitted by a quadratic function has become popular in recent years. This report examines the Ln(III)-to-ligand atom distances for coordination compounds with CNs of 6-9 and the nitrides and phosphides. Least-squares fits to the linear and quadratic models are applied to all of the bond distances to determine when a quadratic model is justified. The result is that complex systems show a mixture of linear and quadratic dependencies when individual bond distances are considered and that the linear model is most common and representative of the true lanthanide contraction.