  We compute accurate potential energy curves of O$_2$ up to O$_2^{2+}$ for
states that are energetically accessible in the photon energy range 20 to 42
eV. We find the dissociation limits of these states and the atomic fragments to
which they dissociate. We use the Velocity Verlet algorithm to account for the
nuclear dynamics of O$_2$ using these computed potential energy curves. Through
the use of Monte Carlo simulations which monitor the nuclear motion and
electronic structure of the molecule, we obtain kinetic energy release
distributions of the O$^+$ + O$^+$ atomic fragments of O$_2$ exposed to an XUV
pulse in the photon energy range. We compare these theoretical kinetic energy
release distributions with results obtained from experiment.
