By combining first-principles electronic-structure calculations with the model Hamiltonian approach, we systematically study the magnetic properties of sodium superoxide (NaO2), originating from interacting superoxide molecules. We show that NaO2 exhibits a rich variety of magnetic properties, which are controlled by relative alignment of the superoxide molecules as well as the state of partially filled antibonding molecular pi_g-orbitals. The orbital degeneracy and disorder in the high-temperature pyrite phase gives rise to weak isotropic antiferromagnetic (AFM) interactions between the molecules. The transition to the low-temperature marcasite phase lifts the degeneracy, leading to the orbital order and formation of the quasi-one-dimensional AFM spin chains. Both tendencies are consistent with the behavior of experimental magnetic susceptibility data. Furthermore, we evaluate the magnetic transition temperature and type of the long-range magnetic order in the marcasite phase. We argue that this magnetic order depends on the behavior of weak isotropic as well as anisotropic and Dzyaloshinskii-Moriya exchange interactions between the molecules. Finally, we predict the existence of a multiferroic phase, where the inversion symmetry is broken by the long-range magnetic order, giving rise to substantial ferroelectric polarization.
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