Quantum mechanical treatment of the interface

The quantum mechanical treatment of the metallic surface has been developed to a large extent for metal-vacuum interfaces. Similar techniques should be applicable to the metal electrolyte interface. The main difference is that the fluid contributes not only to the electric fields in the metal surface, but also to specific chemical bonding interactions. 

It is important in the quantum mechanical treatment of the electrode interface, therefore, to have a good knowledge of the structure of the electrolyte near the electrode, and also, of the electric fields at the interface. 

The electronic density n x) satisfies the Budd-Vaimimenus sum rule [158], which is the quantum mechanics version of the dynamic balance equation 

The density profile changes as the potential is changed. If we plot the charge outside of the metal 5 as a function of the potential difference [ (0) — 0(—oo)j. We find that the electron density spill increases with the potential bias. 

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