Quasi-chemical theory and the standard free energy of H⁺(aq)

Quasi-chemical theory and electronic structure results on inner-sphere H(H₂O)_n⁺ clusters are used to discuss the absolute hydration free energy of H⁺(aq). It is noted that this quantity is not thermodynamically measurable, and this leads to some relative misalignment of available tables of absolute hydration free energies of ions in water. The simplest quasi-chemical model produces a reasonable quantitative result in the range of -256 to -251 kcal/mol. The primitive concepts on which the model is based naturally identify the Zundel cation H₅O₂⁺ as the principal chemical structure contributing to this hydration free energy. The specific participation of an Eigen cation H₉O₄⁺ is not required in this model because the definition of that structure depends on outer-sphere arrangements, and a crude dielectric continuum model is here used for outer-sphere contributions.