Toward Quantitatively Accurate Calculation of the Redox-Associated Acid-Base and Ligand Binding Equilibria of Aquacobalamin

Redox processes in complex transition metal-containing species are often intimately associated with changes in ligand protonation states and metal coordination number. A major challenge is therefore to develop consistent computational approaches for computing pH-dependent redox and ligand dissociation properties of organometallic species. Reduction of the Co center in the vitamin B12 derivative aquacobalamin can be accompanied by ligand dissociation, protonation, or both, making these properties difficult to compute accurately. We examine this challenge here by using density functional theory and continuum solvation to compute Co-ligand binding equilibrium constants (K_on/off), pK_as, and reduction potentials for models of aquacobalamin in aqueous solution. We consider two models for cobalamin ligand coordination: the first follows the hexa, penta, tetra coordination scheme for Co^III, Co^II, and Co^I species, respectively, and the second model features saturation of each vacant axial coordination site on Co^II and Co^I species with a single, explicit water molecule to maintain six directly interacting ligands or water molecules in each oxidation state. Comparing these two coordination schemes in combination with five dispersion-corrected density functionals, we find that the accuracy of the computed properties is largely independent of the scheme used, but including only a continuum representation of the solvent yields marginally better results than saturating the first solvation shell around Co throughout. PBE performs best, displaying balanced accuracy and superior performance overall, with RMS errors of 80 mV for seven reduction potentials, 2.0 log units for five pK_as and 2.3 log units for two log K_on/off values for the aquacobalamin system. Furthermore, we find that the BP86 functional commonly used in corrinoid studies suffers from erratic behavior and inaccurate descriptions of Co-axial ligand binding, leading to substantial errors in predicted pK_as and K_on/off values. These findings demonstrate the effectiveness of the present approach for computing electrochemical and thermodynamic properties of a complex transition metal-containing cofactor.