Quantum Chemical Approach for Calculating Stability Constants of Mercury Complexes

Stability constants are central to the multiscale modeling of the thermodynamic speciation, cycling, and transport of mercury (Hg) and other contaminants in aquatic environments. However, for Hg, experimental values for many relevant complexes are not available, and for others can span ranges in excess of 10 log units. The missing data and large uncertainties lead to significant knowledge gaps in predictions of thermodynamic speciation. As an alternative to experimental measurements, thermodynamic quantities can be calculated with quantum chemical methods. Among these, density functional theory (DFT) with a polarizable continuum solvent combines accuracy with practicability. Here, we present an accurate and quick approach in which we use DFT with continuum solvation to calculate stability constants of Hg complexes with inorganic and low molecular-weight organic ligands in aqueous solution. Specifically, we use the M06/[SDD]6-31+G(d,p) level of theory in combination with a modified version of the SMD solvent model in which the solute radii are reoptimized with a scaled solvent-accessible surface approach. For the set of 37 Hg complexes used for optimization, which contain environmentally relevant functional groups and have reliable experimental stability constants, we obtain a mean unsigned error of 1.4 log units. Testing the method on an independent set of 12 Hg complexes reproduces the experimental stability constants to a mean unsigned error of 1.6 log units. This approach is a substantial step toward generally applicable rapid stability constant derivation for a wide range of Hg complexes, including those present in dissolved organic matter.