Calculate chemical potentials to find electrode Fermi level

I'm running some simple simulations of the semiconductor-electrolyte interface and I'm having a hard time figuring out the equilibrium condition. Can someone please help me with my electrochemical potentials equation? Here's my thought flow so far:


I'm interested in finding out what is the Fermi level in the SC at equilibrium for OER: $4OH^- = O\_2 + 2H\_2O + 4e^-$. So I start by writing the condition for equilibrium:


$4\tilde \mu\_{OH^-} = \tilde \mu\_{O\_2} + 4 \tilde \mu\_{e^-} + 2 \tilde \mu\_{H\_2O}$ 


Since $O\_2$ and $H\_2O$ have no charge, their electrochemical potential is just their chemical potential ($\tilde \mu\_{O\_2} = \mu\_{O\_2}$ and $\tilde \mu\_{H\_2O} = \mu\_{H\_2O}$). 


Moreover, the $\tilde \mu\_{e^-}$ electrochemical potential of $e^-$ in my semiconductor electrode is just the Fermi level $E\_F$ I'm looking for. Keeping in mind that $\tilde \mu\_i = \mu\_i^0 + RTln(a\_i) + z\_iF\phi$ and that the activity of water $a\_{H\_2O}=1$, I arranged the balance equation to:


$E\_F = (\mu^0\_{OH^-} - \frac{1}{4}\mu^0\_{O\_2} - \frac{1}{2}\mu^0\_{H\_2O}) + RTln\left(\frac{a\_{OH^-}}{\left( \frac{p\_{O\_2}}{p^0}\right)}\right) -F\phi\_{sol}$.


I can calculate the electrical potential $\phi\_{sol}$ at the interface in the solution with the Poisson equation. I can calculate the activity coefficient $a\_{OH^-}$ based on the $[OH^-]$ concentration at the interface and of course I know the partial pressure of $O\_2$. My problem is how do I determine the chemical potentials at standard conditions from the first parantheses?


$(\mu^0\_{OH^-} - \frac{1}{4}\mu^0\_{O\_2} - \frac{1}{2}\mu^0\_{H\_2O}) = ???$ 


Could I related them somehow to the SHE electrode which I know to be approx $4.5\ eV$ vs. vacuum?


