We generate trial structures for oxygen dimer formation as follows. The second coordination sphere of each oxide ion (corresponding to the nearest oxygen coordi-FIG. . Schematic outlining the dimer-structure searching procedure we have adopted in layered NiO2. Oxygen atoms are shown in red, and nickel in grey. 1. Each symmetrically distinct oxygen in the structure is selected and each of its nearest oxygen neighbours identified, 2. each pair is selected in turn and 3. moved to be separated by 1.2 Å, 4. 1-2 of the nickel ions that coordinate to the displaced oxygen atoms are selected at random and projected into the vacant layer, away from the O-O dimer. Following these steps, the atoms are subjected to small random displacements. These trial structures are then relaxed to search for low energy dimer reconstructions.