phosphate hydrate complexes of singly and doubly charged magnesium ions: Structure,energies, and spin states

For mixed magnesium phosphate hydrate complexes containing Mg²⁺ and Mg⁺ cations and HPO₄²⁻, HPO₄⁻, and H₂P₂O₇²⁻ anions, theoretical analysis of the electronic structure and energies has been performed at the model level in order to predict the actual role of these systems in various reactions that occur in the catalytic sites of ATP synthesizing enzymes. The calculations (DFT/B3LYP, MP2 with the 6–31G* basis set) of isolated aqua complexes Mg(H₂O) _n ^p (n = 1−6, p = 0, +1, +2) show that their relative stability monotonically increases with increasing n in each series and sharply decreases at a given n in going from the charged systems of Mg²⁺ (4–16 eV) and Mg⁺ (2–7 eV) to the neutral systems of Mg (<2 eV). An even higher stability is predicted for mixed magnesium complexes. The energies of fragmentation of mixed Mg²⁺ complexes into singlet phosphate and Mg²⁺-containing fragments at n = 0–4 are within 6–27 eV, and the energies of fragmentation into the corresponding radical ions are within 3–10 eV; for the Mg⁺ complexes, the fragmentation energies are also high (6–14 eV). The reasons for the enhanced stability of the complexes of both types have been analyzed with allowance for the predicted specific features of the electron density redistribution upon complex formation. Typical changes in the geometry of the P- and Mg-containing fragments caused by formation of mixed complexes have been discussed in the framework of the vibronic model of heteroligand systems. The high stability of all mixed magnesium complexes relative to various fragmentation products presumably rules out any dissociative processes in them in the course of ATP synthesis with the participation of phosphorylating enzymes.