Evaluation of the Binding Constants, Bound Chemical Shifts, and Stoichiometry of Lanthanide–Substrate Complexes

Abstract

A theoretical analysis of the equilibrium between a lanthanide shift reagent, L, and a substrate, S, is presented. When [Formula: see text] then a plot of [S]0vs. (1/δ) at constant [L]0 gives a straight line whose slope is [L]0ΔB and whose y-intercept is −{(1/KB) + [L]0}, where KB is the equilibrium binding constant, δ is the induced chemical shift, and ΔB is the bound chemical shift. A more general and accurate solution using a computer programme is applicable for all ratios of [L]0/[S]0. It is also shown that the conventional procedure for evaluating ΔB leads to varying values for ΔB that are generally too small, even under the most optimal conditions. Eu(DPM)34 has a KB of ca. 34.21 mol−1 with n-propylamine and KB of ca. 9.71 mol−1 with neo-pentanol. These values increase by at least 10-fold (to ≥ 1001 mol−1) for the corresponding complexes with Eu(FOD)34 shift reagent. However, the bound chemical shifts for the Eu(FOD)3 complexes are nearly the same as for the Eu(DPM)3 complexes. Finally, it is shown definitively that the association between Eu(DPM)3 and either n-propylamine or neo-pentanol has 1:1 stoichiometry; with Eu(FOD)3 a tentative assignment of 1:1 stoichiometry can be made.