We develop a density functional theory model for the electrochemical growth and dissolution of Li2O2 on various facets, terminations, and sites (terrace, steps, and kinks) of a Li2O2 surface. We argue that this is a reasonable model to describe discharge and charge of Li-O2 batteries over most of the discharge-charge cycle. Because non-stoichiometric surfaces are potential dependent and since the potential varies during discharge and charge, we study the thermodynamic stability of facets, terminations, and steps as a function of potential. This suggests that different facets, terminations, and sites may dominate in charge relative to those for discharge. We find very low thermodynamic overpotentials (<0.2 V) for both discharge and charge at many sites on the facets studied. These low thermodynamic overpotentials for both discharge and charge are in very good agreement with the low kinetic overpotentials observed in recent experiments. However, there are other predicted paths for discharge/charge that have higher overpotentials, so the phase space available for the electrochemistry opens up with overpotential. © 2013 American Institute of Physics.