An ab initio study of the isomerization of Mg- and Ca-pyrophosphates

Ab initio calculations were performed on gas-phase calcium and magnesium dications chelated with various anionic pyrophosphate species: H₂P₂O₇²-, HP₂O₇^3- and P₂O₇^4-. The cleavage of the pyrophosphate into a metaphosphate and an orthophosphate complexed to either calcium or magnesium was also investigated. The studied isomerization reaction of the metal-pyrophosphate complexes can be written as [M·H(N)P₂O₇](N-2) → [PO₃·M·H(N)PO₄](N-2) where M = Mg, Ca, and N = 0, 1, 2. Geometries for the complexes were optimized with the self-consistent-field (SCF) level of theory, and the total energy for each system was subsequently calculated with the second-order Moller-Plesset perturbation (MP2) method using 6-31+G** basis functions for the H, O, and P atoms and valence double-ζ basis functions polarization augmented with a diffuse function (pVDZ+) for the Mg and Ca atoms. Zero-point energies (ZPE) and entropies were calculated with the SCF harmonic frequencies from which enthalpies and Gibbs free energies were also estimated. The ab initio isomerization energies of all of the calcium-containing complexes were positive and had a large contribution lower contribution of correlation. These calculated gas-phase isomerization energies may provide an explanation to the observation that pyrophosphatases utilize magnesium complexes as substrates for the hydrolysis of pyrophosphates but do not utilize calcium complexes.