The determination of free energy of hydration of water ions from first principles.

We model the auto-ionization 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 non-bonded 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 pKa 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 auto-ionization process.