Rovibrational bound states of the O(2)((3)Σ(g)(-), v = 0)-O(2)((3)Σ(g)(-), v = 0) dimer in its singlet electronic state have been obtained by solving the time-independent Schrödinger equation for the nuclear degrees of freedom. We have employed two different ab initio potential energy surfaces, based on high level multiconfigurational methods, which are expected to give upper and lower bounds for the real values of the interaction. Results are compared with spectroscopy experiments as well as with calculations using other semi ab initio and empirical interaction potentials. For the two ab initio potentials studied here, the ground vibrational state has a rectangular geometry and behaves as a semi-rigid molecule. The associated rotational constant is found in very good agreement with high resolution spectra. However, the computed dissociation energy and the frequency of the torsion mode are larger than previous experimental determinations, and possible reasons for these discrepancies are discussed. On the other hand, we have computed the splitting between the rovibrational states of the singlet and triplet electronic states and have found a fair agreement with measurements of the dimer spectra in a solid rare gas host.