The ground state potential curve of the oxygen molecule has been investigated using multi-configuration self-consistent field (MCSCF) and configuration interaction (CT) programs based upon the Graphical Unitary Group Method. Employing a (5u4p2d) Slater type orbital basis set, potential curves from several MCSCF and large-scale multi-reference CI calculations will be presented. Calculated vibrational levels and constants will be compared with existing experimental data. Emphasis has been placed on accurately describing the dissociation of this open-shell, multiply-bonded molecule.