Linear free energy relationships for metal–ligand complexation: Bidentate binding to negatively-charged oxygen donor atoms

Stability constants for metal complexation to bidentate ligands containing negatively-charged oxygen donor atoms can be estimated from the following linear free energy relationship (LFER): log KML = χOO(αO log KHL,1 + αO log KHL,2) where KML is the metal–ligand stability constant for a 1:1 complex, KHL,1 and KHL,2 are the proton–ligand stability constants (the ligand pKa values), and αO is the Irving–Rossotti slope. The parameter χOO is metal specific and has slightly different values for five and six membered chelate rings. LFERs are presented for 21 different metal ions and are accurate to within approximately 0.30 log units in predictions of log KML values. Ligands selected for use in LFER development include dicarboxylic acids, carboxyphenols, and ortho-diphenols. For ortho-hydroxybenzaldehydes, α-hydroxycarboxylic acids, and α-ketocarboxylic acids, a modification of the LFER where log KHL,2 is set equal to zero is required. The chemical interpretation of χOO is that it accounts for the extra stability afforded to metal complexes by the chelate effect. Cu–NOM binding constants calculated from the bidentate LFERs are similar in magnitude to those used in WHAM 6. This LFER can be used to make log KML predictions for small organic molecules. Since natural organic matter (NOM) contains many of the same functional groups (i.e. carboxylic acids, phenols, alcohols), the LFER log KML predictions shed light on the range of appropriate values for use in modeling metal partitioning in natural systems.