– a revisit from first-principles*

Cobalt Oxide (Co₃O₄) has emerged as a highly promising material for a wide variety of energy technologies, including hydrogen generation through solar-water-splitting and Li ion batteries. Yet, a detailed understanding of the electronic properties of this material is largely lacking. For example, contradicting experimental results have been reported for the optical gap, leading to two commonly reported values of 0.8 eV and 1.6 eV. Here we have employed hybrid functional calculations compliant with the generalized Koopmans' theorem, to demonstrate that the intrinsic band gap of Co₃O₄ is ~1.6 eV. Meanwhile, the ~0.8 eV transition found experimentally is due to the presence of polaron or defect states. In particular, our calculations predict the spontaneous formation of electron and hole polarons, that in turn exhibit significant contribution to the absorption spectra of the material and are responsible for the optical excitation at 0.8 eV. Finally, we resolve the nature of the stable spin states of electron and hole polarons, and we discuss how the interaction between polarons with n-type dopants (carbon) could improve the electrical conductivity of this intrinsic p-type material.