The inner potential in electrochemistry

Although the inner potential plays a fundamental role in electrochemistry, its precise definition is not clear. In fact, there are two different concepts: a physical quantity which can be measured by high energy electron scattering and calculated by density functional theory. For water, it is of the order of 4 V, and it is irrelevant for electrochemistry. For our purpose, the relevant quantity is the electrostatic potential experienced by an ion, which enters into the electrochemical potential. This is of the order of 0 to -0.5 V, and may be slightly different for different ions.