The properties of molecular oxygen including its condensed phases continue to be of great relevance for the scientific community. The richness and complexity of their associated properties stem from the fact that it is a very stable diradical. Its open-shell nature leads to low-lying multiplets with total electronic spin 𝑺 = 𝟎, 𝟏, 𝟐 in the case of the dimer, (𝑶 𝟐 ) 𝟐 , and the accurate calculation of their intermolecular potentials represents a challenge to ab initio electronic structure methods. In this work we present intermolecular potentials calculated at a very high level, thus competing with the most accurate restricted potentials obtained to date. This is accomplished by drawing on an analogy between the coupled and uncoupled representations of angular momentum and restricted vs unrestricted methodologies. The 𝑺 = 𝟐 state can be well represented by unrestricted calculations in which the spins of the unpaired electrons are aligned in parallel; however for the state where they are aligned in antiparallel fashion it would seem the total spin is not well defined i.e. the well-known spin contamination problem. We show that its energy corresponds to that of the 𝑺 = 𝟏 state and perform unrestricted coupled cluster calculations for these two states. Then we obtain the 𝑺 = 𝟎 state through the Heisenberg Hamiltonian and show that this is very reliable in the well region of the potentials. We make extensive comparisons with the best restricted potentials (Bartolomei, et al Phys. Chem. Chem. Phys., 10, 1-7, 2008) and with reliable experimental determinations, a very good agreement is globally found.