The energies of each structure found via this search are shown in fig. . After this initial relaxation process, we highlight three distinct classes of structure that emerge from the search. First, there is the (delithiated but otherwise) "pristine" layered structure of R 3m NiO 2 . Next, there are a minority of structures in which a nickel ion has migrated into the vacant layer but the dimer has broken apart during relaxation. These are labelled as "unstable dimer" structures: the dimer initialised by the structure generation process is not locally stable after geometry relaxation. The third structure type, which forms the majority of the relaxed structures, are those in which the oxygen dimer has remained locally stable. Of all of these, we find that the lowest-energy system is the original layered R 3m NiO 2 system.