QSPR ensemble modelling of the 1:1 and 1:2 complexation of Co2+, Ni2+, and Cu2+ with organic ligands: relationships between stability constants

Quantitative structure–property relationship (QSPR) modeling of stability constants for the metal:ligand ratio 1:1 (logK) and 1:2 (logβ2) complexes of 3 transition metal ions with diverse organic ligands in aqueous solution was performed using ensemble multiple linear regression analysis and substructural molecular fragment descriptors. The modeling was performed on the sets containing 396 and 132 (Co2+), 613 and 233 (Ni2+), 883 and 257 (Cu2+) logK and logβ2 values, respectively. The models have been validated in external fivefold cross-validations procedure as well as on the external test set containing new ligands recently reported in the literature. Predicted logK and logβ2 values were calculated as arithmetic means of several hundred individual models (consensus models) using their applicability domains in averaging. The root mean squared error of predictions varies from 0.94 to 1.2 (logK) and from 1.2 to 1.4 (logβ2) which is close to observed experimental systematic errors. Linear correlations between experimental logK values for pair of metal ions were evaluated. For all metal ions and ligands forming both 1:1 and 1:2 complexes the following ratio is observed: logβ2/logK = 1.8 ± 0.1, n = 492.