Theoretical Studies of the Hydration of Metaphosphate with One, Two, and Three Molecules of Water

The reactions of metaphosphate anion (PO₃⁻) with one, two, and three molecules of water have been studied theoretically with up to 6-31+G* geometry optimizations and MP4/6-31+G** energy evaluations. H₂O forms a planar six-membered cyclic hydrogen-bonded complex with PO₃⁻. The addition of a second H₂O forms a second ring. The calculated complexation enthalpies and entropies for these two processes match reasonably well with those observed experimentally for the gas-phase reactions (Keesee, R. G.; Castleman, A. W., Jr. J. Am. Chem. Soc. 1989, 111, 9015). For the addition of a third H₂O, several isomeric complexes have been located. The complex with the H₂O nearly perpendicular to the PO₃⁻(H₂O)₂ complex is found to be the most stable at each level of optimization. The calculated entropy change with this structure agrees well with the reported value of the third-step hydration in the gas phase. A four-centered transition structure is found for the conversion of the complex to dihydrogen orthophosphate for each reaction. The transition structure involves considerable breaking of one of the water O-H bonds and has a barrier of activation of about 20 kcal/mol with respect to the reactants. For the hydration with two and three water molecules, a six-membered-ring transition structure is also located which is more stable than the four-centered transition structure by several kilocalories/mole.