  Using density-functional theory in combination with a thermodynamic formalism
we calculate the relative stability of various structural models of the polar
O-terminated (000-1)-O surface of ZnO. Model surfaces with different
concentrations of oxygen vacancies and hydrogen adatoms are considered.
Assuming that the surfaces are in thermodynamic equilibrium with an O2 and H2
gas phase we determine a phase diagram of the lowest-energy surface structures.
  For a wide range of temperatures and pressures we find that hydrogen will be
adsorbed at the surface, preferentially with a coverage of 1/2 monolayer. At
high temperatures and low pressures the hydrogen can be removed and a structure
with 1/4 of the surface oxygen atoms missing becomes the most stable one. The
clean, defect-free surface can only exist in an oxygen-rich environment with a
very low hydrogen partial pressure. However, since we find that the
dissociative adsorption of molecular hydrogen and water (if also the
Zn-terminated surface is present) is energetically very preferable, it is very
unlikely that a clean, defect-free (000-1)-O surface can be observed in
experiment.
