Excited spin states are important for reactivity, catalysis, and magnetic applications. This work examines the relative energies of the spin states of O atom, Fe2+ ion, and FeF2 and characterizes their excited spin states. Both single-configuration and multireference methods are used to establish the character of the lowest singlet excited state of all three systems and the lowest triplet excited state of Fe2+ and FeF2. We find that the conventional representation of the orbital occupancies is incorrect in that the states have more unpaired electrons than the minimum number required by their total electron spin quantum number. In particular, we find that, for a given spin state, an electronic configuration with more than 2S unpaired electrons is more stable than the configuration with 2S unpaired electrons (where S is the spin of the system). For instance, triplet FeF2 with four unpaired electrons is lower in energy than triplet FeF2 with two unpaired electrons. Such highly open-shell configurations are labeled as hyper open-shell electronic configurations in this work and are compared to ordinary open-shell or closed-shell electronic configurations. The hyper open-shell states considered in this work are especially interesting because, unlike typical biradicals and polyradicals, the unpaired electrons are all on the same center. This work shows that the conventional perspective on spin-state energetics that usually assumes ordinary open shells for single-centered radicals needs modification to take into account, whenever possible, hyper open-shell configurations as well.