  Molecular oxygen has been the subject of many observational searches as
chemical models predicted it to be a reservoir of oxygen. Although it has been
detected in two regions of the interstellar medium, its rarity is a challenge
for astrochemical models. In this paper, we have combined the physical
conditions computed with smoothed particle hydrodynamics (SPH) simulations with
our full gas-grain chemical model Nautilus, to study the predicted O2 abundance
in interstellar material forming cold cores. We thus follow the chemical
evolution of gas and ices in parcels of material from the diffuse interstellar
conditions to the cold dense cores. Most of our predicted O2 abundances are
below 1e-8 (with respect to the total proton density) and the predicted column
densities in simulated cold cores is at maximum a few 1e14 cm-2, in agreement
with the non detection limits. This low O2 abundance can be explained by the
fact that, in a large fraction of the interstellar material, the atomic oxygen
is depleted onto the grain surface (and hydrogenated to form H2O) before O2 can
be formed in the gas-phase and protected from UV photo-dissociations. We could
achieve this result only because we took into account the full history of the
evolution of the physical conditions from the diffuse medium to the cold cores.
