Eleven stationary geometries of quartet O4+ have been studied by ab initio methods. The geometries were optimized at the complete active space self-consistent field (CASSCF) level of theory and the energies were calculated by the multiconfigurational second order pertubation method (CASPT2), using double-zeta plus polarization (DZP), triple-zeta plus double polarization (TZ2P), average atomic natural orbital (ANO) [5s4p2d] and average ANO [6s5p3d2f] basis sets. The rectangular and trans-planar structures are found to be the most stable, with an energy barrier to conversion between the two at the threshold of dissociation. Both have a delocalized hole and are stable relative to separated O2 and O2+ by 11.0 and 11. 5 kcal/mol for the rectangular and the trans-planar structure, respectively, compared with the experimentally deduced energy in the range of 9.2 to 10.8 kcal/mol. The adiabatic ionization potentials of O4 and O2 are computed to be 11.67 and 12.21 eV, while experimental values are 11.66 and 12.07 eV, respectively. The vibrational frequencies have been computed for all degrees of freedom at the CASSCF level of theory. Symmetry breaking is found to be a particular problem in the computation of the antisymmetric stretch frequency for the delocalized structures at the CASSCF level of theory. Attempts to rectify these problems using the restricted active space self-consistent field (RASSCF) method leads to additional difficulties, but further analysis yields insight into the symmetry breaking and problems with earlier calculations. Finally, a nonorthogonal configuration interaction (CI) calculation based on the interaction of localized CASSCF wave functions using the complete active space state interation (CASSI) method leads to a balanced treatment of the antisymmetric stretch which is free from symmetry breaking. The study explains the four most prominent absorption frequencies observed in the partially unassigned IR spectrum of 04+ isolated in solid neon as the antisymmetric OO stretch, and the combination band of the symmetric and antisymmetric OO stretch of both the rectangular and trans-planar structures.