Toward an understanding of the hydrolysis of Mg-PPi. An ab initio study of the isomerization reactions of neutral and anionic Mg-pyrophosphate complexes

Abstract

an energy input is required for separating the metal cation from the phosphate anions.

Ab initio calculations were performed to study the stability of various pyrophosphate species in the gas phase: H4P2O7, H3P2O7-, H2P2O72-, HP2O73-, P2O74-, and their complexes with Mg2+. It is found that the metal cation allows the existence of highly charged anions in the gas phase. We also study the isomerization reactions Mg . H2P2O7 --> (H2PO4 . Mg . PO3), (Mg . HP2O7)(-) --> (HPO4 . Mg . PO3)(-), and (Mg . P2O7)(2-) --> (PO4 . Mg . PO3)(2-), 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. Other basis sets, including one of valence triple zeta plus polarization (vTZP) quality, were employed to check for the convergence of the results. It is found that the same mechanism occurs for the isomerizations of the three species: one of the P-O bridging bonds of the reactant is longer than the other, and the route to the products proceeds through its elongation. This asymmetry is induced by the metal cation in the case of the evenly charged anions. In all cases the metal cation coordinates the transition states and the leaving groups. The structures found for the complexes (H2PO4 . Mg . PO3), HPO4 . Mg . PO3)(-), and (PO4 . Mg . PO3)(2-) are different from those reported previously, the metal cation being enclosed by the two phosphates. The activation barrier increases with the charge of the anion, from Delta G degrees(double dagger)=5.6 kcal/mol for the neutral complex Mg . H2P2O7, to Delta G degrees(double dagger)=10.4 kcal/mol for the monoanion (Mg . HP2O7)(-), to Delta G degrees(double dagger)=13.5 kcal/mol for the dianion (Mg . P2O7)(2-). The positive value found for the energy of the isomerization (Mg . P2O7)(2-) --> (PO4 . Mg . PO3)(2-), Delta G degrees(double dagger)=1.8 kcal/mol, predicts the synthesis to be spontaneous in the gas phase, opposite of what occurs in the aqueous solution. This result supports the view that the hydration energy makes a large contribution to the energy of hydrolysis. The gas-phase hydrolysis reaction H2O + Mg2+ + H2P2O72- --> Mg2+ + H2PO4- + H2PO4- is also studied as a multistep reaction, involving the isomerization of H2O + (Mg . H2P2O7) --> H2O + (PO3 . Mg . H2PO4) as an intermediate step. It is found that the equilibrium in the gas phase yields H2PO4 . Mg . H2PO4 as the final species