Understanding Stability Trends along the Lanthanide Series

The stability trends across the lanthanide series of complexes with the polyaminocarboxylate ligands TETA^4? (H₄TETA=2,2′,2′′,2′′′‐(1,4,8,11‐tetraazacyclotetradecane‐1,4,8,11‐tetrayl)tetraacetic acid), BCAED^4? (H₄BCAED=2,2′,2′′,2′′′‐{(1,4‐diazepane‐1,4‐diyl)bis(ethane‐2,1‐diyl)]bis(azanetriyl)}tetraacetic acid), and BP18C6^2? (H₂BP18C6=6,6′‐(1,4,10,13‐tetraoxa‐7,16‐diazacyclooctadecane‐7,16‐diyl)bis(methylene)]dipicolinic acid) were investigated using DFT calculations. Geometry optimizations performed at the TPSSh/6‐31G(d,p) level, and using a 46+4fⁿ ECP for lanthanides, provide bond lengths of the metal coordination environments in good agreement with the experimental values observed in the X‐ray structures. The contractions of the Ln³⁺ coordination spheres follow quadratic trends, as observed previously for different isostructural series of complexes. We show here that the parameters obtained from the quantitative analysis of these data can be used to rationalize the observed stability trends across the 4f period. The stability trends along the lanthanide series were also evaluated by calculating the free energy for the reaction La( L )]^n+/?_(sol)+Ln³⁺_(sol)→Ln( L )]^n+/?_(sol)+La³⁺_(sol). A parameterization of the Ln³⁺ radii was performed by minimizing the differences between experimental and calculated standard hydration free energies. The calculated stability trends are in good agreement with the experimental stability constants, which increase markedly across the series for BCAED^4? complexes, increase smoothly for the TETA^4? analogues, and decrease in the case of BP18C6^2? complexes. The resulting stability trend is the result of a subtle balance between the increased binding energies of the ligand across the lanthanide series, which contribute to an increasing complex stability, and the increase in the absolute values of hydration energies along the 4f period.