Cooperativity in Al3+ Hydrolysis Reactions from Density Functional Theory Calculations

Aqua/hydroxo mononuclear Al3+ species in aqueous solution are investigated using density functional theory (DFT B3LYP/6-311++G(d,p)) and the polarized continuum model (PCM). Optimized gas-phase geometries have been obtained for the species Al(OH) n (H2O) m (3−n)+ in which n = 0, 1, 2, 3, or 4 while (n + m) = 4, 5, or 6. For Al(OH)2(H2O)4 1+ the cis and trans geometries were considered. The structures were analyzed in terms of water and hydroxide M−O and O−H distances, which are shown to be strongly modulated by water hydrolysis. The atomic charges were computed and the electronic structure of these complexes is discussed. The conversion from one aqua-/hydroxo- species to another follows independent hydrolysis and dehydration reactions for which the aqueous Gibbs free energies have been estimated by means of constructing thermodynamic cycles. Results clearly demonstrate that the dehydration reaction is increasingly favorable as hydrolysis proceeds. Similarly, as the complex coordination number decreases the hydrolysis reaction proceeds increasingly more favorably. The aqueous Gibbs free energy of each species, relative to Al(H2O)6 3+ , has been determined by combining the appropriate Gibbs free energies of the hydrolysis and dehydration reactions demonstrating that the additive effect is quite complex showing a gradual transition from preferring the 6-coordination to 5-coordination to 4-coordination as a function of ligand hydrolysis, in agreement with published experimental and theoretical work. We have also computed the equilibrium constants of each of the above reactions and, using [H+] as a parameter, estimated the mole fraction of each species as a function of pH. This offers a clear demonstration that the qualitative hydrolysis behavior, e.g., cooperativity, of aqueous Al3+ species is obtained at the B3LYP/IEF-PCM level of theory.