text: The rate of reaction for the ionization reaction
  :2 HO → HO + OH
  depends on the activation energy, ΔE. According to the Boltzmann distribution the proportion of water molecules that have sufficient energy, due to thermal population, is given by
  where k is the Boltzmann constant. Thus some dissociation can occur because sufficient thermal energy is available. The following sequence of events has been proposed on the basis of electric field fluctuations in liquid water. Random fluctuations in molecular motions occasionally (about once every 10 hours per water molecule) produce an electric field strong enough to break an oxygen–hydrogen bond, resulting in a hydroxide (OH) and hydronium ion (HO); the hydrogen nucleus of the hydronium ion travels along water molecules by the Grotthuss mechanism and a change in the hydrogen bond network in the solvent isolates the two ions, which are stabilized by solvation. Within 1 picosecond, however, a second reorganization of the hydrogen bond network allows rapid proton transfer down the electric potential difference and subsequent recombination of the ions. This timescale is consistent with the time it takes for hydrogen bonds to reorientate themselves in water.
  The inverse recombination reaction
  :HO + OH → 2 HO
  is among the fastest chemical reactions known, with a reaction rate constant of  at room temperature. Such a rapid rate is characteristic of a diffusion-controlled reaction, in which the rate is limited by the speed of molecular diffusion.