Ab Initio Study of the Hydrolysis Reactions of Neutral and Anionic Mg−Pyrophosphate Complexes in the Gas Phase

Ab initio calculations were performed to study the stability of various anhydrous and monohydrated complexes of Mg²⁺ with pyrophosphates and orthophosphates at the self-consistent-field (SCF) and second-order perturbation (MP2) levels of the theory, using a 6-31+G** basis set with diffuse and polarization functions. New equilibrium geometries were found for the anhydrous Mg−pyrophosphate complexes, that modify previous estimates of the isomerization energies. It is found that the interaction with the water molecule stabilizes the pyrophosphates with respect to the metaphosphate-containing complexes, thus modifying the reaction energies to such an extent that the isomerization results are endothermic and nonspontaneous for the dianionic complex. However, the hydrolysis reactions are all exothermic and spontaneous. Moreover, it is found that the water molecule readily breaks upon interacting with the dianionic complex, producing a hydroxide anion:  H₂O + [Mg·P₂O₇]^2- → [HO·Mg·HP₂O₇]^2-, and the resulting dianionic complex is much more stable than the isomer with a metaphosphate. It is shown that this result is consistent with both an associative and a dissociative mechanism for the hydrolysis. Finally, the estimate of free energies of solvation by means of the polarizable continuum model (PCM) yield values for the free energies of hydrolysis that are close to the experimental data.