  An accurate prediction of the surface potential at the air-water interface is
critical to calculating ion hydration free energies and electrochemical
half-cell potentials. Using Density Functional Theory (DFT), model interfacial
configurations, and a theoretical definition of the surface potential, we
report a value of +3.63~volt at 0.92~g/cc water density. A maximally localized
Wannier function analysis confirms that the surface potential is dominated by
molecular quadrupole (or "spherical second moment") contributions. We find that
the predicted surface potential depends on computational details, and conclude
that standard DFT codes may not yield surface potentials directly comparable to
existing experiments.
