Estimation of Stability Constants with Connectivity Index: Development of Bivariate and Multivariate Linear Models for Copper(II) Chelates with Oligopeptides

The equilibrium constants K1, Ka and β1 of 25 copper(II) complexes with di-(N = 15), tri-(N = 5), tetra-(N = 2), and pentapeptides (N = 3) were estimated by using linear models based on the valence connectivity index of the 3rd order (3χv). For the stability constant K1 two kinds of models were developed: bivariate models, which divide a molecule into N- and C-terminal segments, and multivariate models, which treat the connectivity index of each chelate ring as a separate variable. The models proved equally successful, yielding fair reproduction of experimental log K1 (S.E.cv = 0.16–0.19, max. error = 0.4). Overall deprotonation constant Ka was estimated from the 3χv, calculated for the whole molecule of the complex, with the addition of two indicator variables to distinguish various classes of ligands. In this way, the overall stability constant (log β1 = log K1–pKa) was reproduced with the error<0.81 (S.E. = 0.31).