The ground state of the oxygen molecule is calculated by various methods of coupled cluster approaches and many body perturbation theory using a double zeta plus polarization basis set and the UHF reference state. All the methods employed are capable of describing the oxygen molecule near the equilibrium bond length and the separated atom, but do not correctly depict the breaking of the multiple bond. For this basis set, including more correlations does not necessarily improve the agreement with experiment for molecular properties such as bond lengths and dissociation energies.