How to Model the Electrode Potential

A critical issue in the ab initio description of electrochemical interfaces is the correct incorporation, or the realistic modeling, of the effect of the electrode potential. Essentially two different approaches have been employed in the literature, which, in statistical-mechanical terms, may be referred to as canonical and grand canonical .  

In the canonical or constant number of electrons mode, an isolated cluster or slab is placed in an external electric field. At the level of the Schrodinger equation, the electric field is simply added as an extra term to the Hamiltonian. As a result of the external field, the cluster/slab becomes polarized, with a positive surface charge on one 

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