Thermodynamic radii of lanthanide ions derived from metal-ligand complexes stability constants

Here, we describe two sets of thermodynamic ionic radii (r(1)andr(2)) of lanthanide ions derived from the analysis of large set of the stability constants log beta(1)and log beta(2)of the ML and ML(2)complexes of lanthanide ions M (from Ce(3+)to Lu3+) with organic ligands (L) in water. It has been demonstrated that the stability constants of two metals M(i)and M(j)with a given ligand L are related by simple equations log beta(j)(1) = r(1)(i)/r(1)(j.)log beta(i)(1)and log beta(j)(2) = r(2)(i)/r(2)(j.)log beta(i)(2)which formally correspond to purely electrostatic interactions between spherical cations with organic molecule. Predictive performance of these equations was assessed in fivefold cross-validation procedure. The standard deviation (s) of predictions varies from 0.3 to 1.0 for log beta(1)and from 0.4 to 1.2 for log beta(2)as a function of the difference of Shannon ionic radii (Delta r(ij)) of M(i)and M-j:s(1) = 0.27 + 4.25 Delta r(ij)for log beta(1)ands(2) = 0.39 + 5.16 Delta r(ij)for log beta(2). The new radiir(1)andr(2)steadily decrease across the Ln series, i.e., they follow the same trend as Shannon effective radii of lanthanide ions. The calculations were performed using experimental data on 2854 log beta(1)values for 445 organic ligands and 947 log beta(2)values for 156 organic ligands in the complexes with 13 metals.