3 The Grotthuss Mechanism and Hydrogen-bonded Chains

It has long been recognized-remarkably, for 200 years-that protons have the potential for a unique mode of transport in water ^{[31] [b]} and, by extension, in other highly connected hydrogen bonding systems. ^[32], ^[33], ^[34] The Grotthuss mechanism involves a simple shift of hydrogen bonds to effectively relocate a net protonic charge from one position to another without significantly moving the mass of the proton. In water, this process contributes at least four-fifths of the measured transfer number of hydrogen ions, and the ionic mobility of H ⁺ is about seven times that of Na ⁺. Current views of the Grotthuss mechanism have the rate limiting event as the breaking of one or two critical hydrogen bonds outside the primary solvation sphere of the proton charge, allowing reorganization of the first shell from a hydronium, H ₃O ⁺ (or Eigen ion, H ₉O ₄ ⁺ = H ₃O ⁺(H ₂O) ₃), to a Zundel ion, H ₅O ₂ ⁺, as a transition intermediate (Figure 2). The proton then redistributes along its own coordinate between the two oxygen atoms and further solvation adjustments can trap it at the new oxygen, in the form of a new H ₃O ⁺. ^[35] The electrostatic energies are the same in the initial and final states, of course, and are also of little consequence in the transition intermediate-the...