Application to Real Systems - Hydrogen Evolution Oxidation Reactions

APPLICATION TO REAL SYSTEMS - HYDROGEN EVOLUTION / OXIDATION REACTIONS 

According to the energy balance the oxidation of hydrogen requires almost 32 eV about 22 eV are provided by the hydration of the proton, 9-10 eV, twice the work function, by the metal, and the rest by the potential drop between the electrode and the bulk of the solution, which is the only part that we can control experimentally. Thus, solvation plays a dominant part in the energetics, and any model for the hydrogen reaction that neglects the solvent leaves out a most important part. 

Thus we use this linear interpolation to extrapolate the DFT results, which are vahd for q = 0, to other values in the range 0 q 1. 

the total energy is the sum of the electronic energy calculated from Eq. (30) corrected by Eq. (36) and the solvent energy both, slow and fast contributions  

Now we can calculate the adiabatic potential free energy surfaces as a function of the solvent coordinate q and the distance to 

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