Estimation of Stability Constants of Copper(II) Bis-chelates by the Overlapping Spheres Method

The method of overlapping spheres (OS) was applied for the estimation of stability constants (β2) of sets of (binary) copper(II) bis-complexes with 1,2-diaminoethanes (N = 14), aliphatic amino acids and their N-alkylated derivatives (N = 11), and naturally occurring amino acids (N = 9), along with a set of 16 mixed (ternary) copper(II) bis-complexes with naturally occurring amino acids. The central sphere, with the radius, Rv, 300 or 400 pm, was situated at the copper atom. The OS volumes (V*) of the central sphere and the van der Waals spheres of the surrounding atoms were calculated from the structures of bis- or corresponding mono-complexes and correlated with the log β2 values. Both approaches yielded similar results, differing in the reproduction of stability constants by less than 20 %. Bivariate linear regression was performed for mixed complexes, using (V*1 + V*2) and (V*1 – V*2) as independent variables (V*1 and V*2 correspond to the OS values for the two constituting chelate rings). The bivariate linear regression gave r = 0.961 and the reproduction of experimental data from 0.00 to 0.16 log β units (S.E.cv = 0.08 log β units)