Stability constants: comparative study of fitting methods. Determination of second-order complexation constants by (23)Na and (7)Li NMR chemical shift titration.

NMR chemical shift titration has been widely used as a method for the determination of stability constants. Systems involving metal-ligand complexation have been investigated using a number of methodologies. There are significant differences in the values reported for stability constants obtained by different experimental methods, such as calorimetry and ion selective electrode (ISE) titrations; nor has NMR chemical shift titration always yielded consistent results. Different researchers have obtained different results for the same system with results differing by as much as an order of magnitude. The chemical shift data are generally plotted against the concentration ratio of the metal and ligand for a set of solutions. A nonlinear least squares fitting method using an analytical solution of the cubic equation for the equilibrium concentration of the free ligand is used in this study and compared with methods used in the literature. Second-order association constants for the LiClO(4):12-crown-4 system in acetonitrile and the NaClO(4):12-crown-4 system in methanol are reported. Formation of both 1:1 and 1:2 metal-ligand complexes are considered. The LiClO(4):12-crown-4 acetonitrile system had been investigated previously by NMR titration but only 1:1 complexation was considered in that study. This study provides convincing evidence that both 1:1 and 1:2 complexes are important, at least, in the lithium system. A Monte Carlo investigation of the propagation of errors from the chemical shifts to the stability constants shows that the choice of data analysis methods may, in part, contribute to discrepancies and that the nonlinear nature of the model can dramatically affect the error limits on the stability constants.