Accuracy of the microsolvation-continuum approach in computing the pK(a) and the free energies of formation of phosphate species in aqueous solution.

First principles density functional theory (Perdew-Burke-Ernzerhof) calculations have been used to compute the hydration properties, aqueous-phase acid dissociation constants (pK(a)) and Gibbs free energies of formation of small polyphosphates in aqueous solution. The effect of the hydrated environment has been simulated through a hybrid microsolvation-continuum approach, where the phosphate species are simulated as microsolvated solutes, while the remainder of the bulk solvent is treated as a dielectric continuum using the COSMO solvation model. The solvation free energies of orthophosphates and pyrophosphates have been computed applying monomer and cluster thermodynamic cycles, and using the geometries optimised in the gas-phase as well as in the COSMO environment. The results indicate that the simple polarisable continuum or microsolvation-continuum models are unable to compute accurate free energies of solvation for charged species like phosphates. The calculation of the pK(a) shows that the computed values of acid dissociation constants are critically dependent on the number of water molecules n(H(2)O) included in the hydrated phosphate clusters. The optimal number n(H(2)O) is determined from the minimum value of the "incremental" water binding free energy associated with the process of adding a water molecule to a micro-solvated phosphate species. Analysis of the effect of n(H(2)O) on the free energies of orthophosphate condensation reactions shows that can vary by tenths of kcal mol(-1), depending on the particular choice of n(H(2)O) for the monomeric and dimeric species. We discuss a methodology for the determination of n(H(2)O); for the orthophosphates the "incremental" binding energy approach is used to determine n(H(2)O), whereas for the polyphosphates the number of explicit water molecules is simply equal to the effective charge of these anions. The application of this method to compute the free energy of formation of pyro- and tri-phosphates gives generally good agreement with the available experimental data.

Hydrogen transfer and hydration properties of H(n)PO4(3-n) (n=0-3) in water studied by first principles molecular dynamics simulations.

Density functional theory Perdew-Burke-Ernzerhof [Perdew et al., Phys. Rev. Lett. 77, 3865 (1996)] molecular dynamics simulations of aqueous solutions of orthophosphate species H(n)PO(4)(3-n) (n=0-3) provide new insights into hydrogen transfer and intermolecular and hydration properties of these important aqueous species. Extensive Car-Parrinello molecular dynamics simulations of the orthophosphate ion PO(4)(3-), of the hydrogen phosphate anions, HPO(4)(2-) and H(2)PO(4)(-), and of the orthophosphoric acid, H(3)PO(4), in explicit water show that the process of proton transfer from H(n)PO(4)(3-n) to the surrounding water molecules is very fast, less than 1 ps, and indicate that the dehydrogenation occurs through a concerted proton hopping mechanism, which involves H(n)PO(4)(3-n) and three water molecules. Analysis of the intermolecular H(n)PO(4)(3-n)-water structure shows that the PO(4)(3-) anions have a significant effect on the H-bonding network of bulk water and the presence of P-O(-) moieties induce the formation of new types of H-H interactions around this orthophosphate. Calculated probability distributions of the coordination numbers of the first hydration shell of PO(4)(3-), HPO(4)(2-), and H(2)PO(4)(-) show that these phosphate species display a flexible first coordination shell (between 7 and 13 water molecules) and that the flexibility increases on going from PO(4)(3-) to H(2)PO(4)(-). The strength and number of hydrogen bonds of PO(4)(3-), HPO(4)(2-), and H(2)PO(4)(-) are determined through a detailed analysis of the structural correlation functions. In particular, the H-bond interactions between the oxygen atoms of the phosphates and the surrounding water molecules, which decrease on going from PO(4)(3-) to the hydrogenated H(2)PO(4)(-) species, explain the diminished effect on the structure of water with the increasing hydrogenation of the orthophosphate anions.

Modelling the structural evolution of ternary phosphate glasses from melts to solid amorphous materials.

The local and medium-range structural properties of phosphate-based melts and glasses have been characterized by means of first principles (density functional theory) and classical (shell-model) molecular dynamics simulations. The structure of glasses with biomedically active molecular compositions, (P2O5)0.45(CaO)x(Na2O)0.55-x (x = 0.30, 0.35 and 0.40), have been generated using first principles molecular dynamics simulations for the full melt-and-quench procedure and the changes in the structural properties as the 3000 K melt is cooled down to room temperature have been compared extensively with those of the final glasses. The melts are characterized by a significant fraction of threefold (P3c) and fivefold (P5c) phosphorus atoms, but structural defects rapidly decrease during the cooling phase and for temperatures lower than 1800 K the system is free of under- and over-coordinated species. The analysis of the structures of the glasses at 300 K shows a prevalence of the metaphosphate Q2 and pyrophosphate Q1 species, whereas the number of Q3 units, which constitute the three-dimensional phosphate network, significantly decreases with the increase of calcium content in the glass. The radial and angular distribution functions indicate that higher calcium concentration in the glass leads to an increase of the rigidity of the phosphate tetrahedral network, which has been explained in terms of the calcium's higher field strength compared to that of sodium. The structural characterization of the melts and glasses obtained from first principles simulations was used to assess and validate a recently developed interatomic shell-model forcefield for phosphate-based materials. For all three compositions, our potential model is in good agreement with the first principles data. In the glass network, the forcefield provides a very good description of the split between the shorter distances of phosphorus to non-bonded oxygen and the longer distances of the phosphorus to bonded oxygen; the phosphorus-phosphorus medium-range distribution; and the coordination environment around the Na and Ca glass modifiers. Moreover, the distribution of the Qn species in the melts and glasses is in excellent agreement with the values extracted from the first principles simulations. In contrast, simulations using standard rigid ion potentials do not provide a satisfactory description of the local short-range structure of phosphate-based glasses and are therefore less suitable to model this class of multicomponent amorphous system.