chemical potential of O and H in aqueous solution

[devounoide]

Hi there:
Currently, I am studying the surface structure of a metal oxide nanoparticle in aqueous solution. But how to calculate the chemical potential of H and O in any pH-controlled aqueous solution based on VASP result is a puzzle to me.
I have found that some paper define the chemical potential of H2O in the humid environment based on VASP result to include the formation energy of water E(H2O) in the following form.
mu_H2O(p,T）=mu_H2O(0.1MPa,P)+E(H2O)+ln(p(H2O)/0.1MPa)) [Marco Fronzi, Phys. Chem. Chem. Phys., 2009, 11, 9188?9199]. However, another one define it just use the normal definition of chemical potential in chemistry to express mu_H2O(p,T）=mu_H2O(0.1MPa,P)+ln(p(H2O)/0.1MPa)), which leaves out the part E(H2O) [Qiang Sun, PHYSICAL REVIEW B 67, 205424, 2003].
The question is what exactly is calculated E0 in VASP? Are all the calculated E0 based on the same reference energy? Have calculated E0 already subtracted zero-point energy?
So, I want to know when I relate the chemical potential of one species (like H) on the atomic scale to the microscopic measurable factor experimentally like pH, do I need to have the formation energy of OH or H2O included to express the chemical potential of H?
I really appreciate anyone to help me with this.

[Venkatesh Botu]

I do not know all the answers but for a few of your questions:

1. E0 doesn't correct for ZPE
2. All the calculated energies for 0K