The Determination of Free Energy of Hydration of Water Ions from First Principles

We model the autoionization of water by determining the free energy of hydration of the major intermediate species of water ions. We represent the smallest ions─the hydroxide ion OH^-, the hydronium ion H₃O⁺, and the Zundel ion H₅O₂⁺─by bonded models and the more extended ionic structures by strong nonbonded interactions (e.g., the Eigen H₉O₄⁺ = H₃O⁺ + 3(H₂O) and the Stoyanov H₁₃O₆⁺ = H₅O₂⁺ + 4(H₂O)). Our models are faithful to the precise QM energies and their components to within 1% or less. Using the calculated free energies and atomization energies, we compute the pK_a of pure water from first principles as a consistency check and arrive at a value within 1.3 log units of the experimental one. From these calculations, we conclude that the hydronium ion, and its hydrated state, the Eigen cation, are the dominant species in the water autoionization process.