  The structure of solid oxygen has been studied at pressures from 50 to
140~GPa using static structure search methods and molecular dynamics
simulations with density functional theory and a hybrid exchange functional.
Several crystalline structures with space group symmetries {\it Pnma}, {\it
P}\,2$_{1}${\it /m}, {\it Pm} and {\it P}\,6$_3$/{\it mmc} have been identified
as candidates for the $\zeta$ phase of oxygen at 0~K. Within the hybrid
exchange functional framework and at 300~K temperature, {\it Pm} is shown to be
energetically most favorable above 111~GPa. A comparison with experimental
X-ray diffraction, spectroscopic and superconductivity measurements is provided
for all competing structures.
