We use two different ab initio quantum mechanics methods, complete active space self-consistent field theory applied to electrostatically embedded clusters and periodic many-body G(0)W(0) calculations, to reanalyze the states formed in nickel(II) oxide upon electron addition and ionization. In agreement with interpretations of earlier measurements, we find that the valence and conduction band edges consist of oxygen and nickel states, respectively. However, contrary to conventional wisdom, we find that the oxygen states of the valence band edge are localized whereas the nickel states at the conduction band edge are delocalized. We argue that these characteristics may lead to low electron-hole recombination and relatively efficient electron transport, which, coupled with band gap engineering, could produce higher solar energy conversion efficiency compared to that of other transition-metal oxides. Both methods find a photoemission/inverse-photoemission gap of 3.6-3.9 eV, in good agreement with the experimental range, lending credence to our analysis of the electronic structure of NiO.