The twelve-water case illustrates multi-stage analyses, which is the norm with the succeeding larger clusters. The starting configuration was constructed by adding water molecules sequentially and arbitrarily, partially optimizing with a relatively smaller basis sets (6-31G*) between steps and then to the desired basis set (6-311++G(d,p)). All larger clusters in this study were created using this procedure. The starting parent configuration was designated the reference (0 kJ/mol) and this will be the convention for the succeeding sections. The cycle reversal analyses were performed in three stages and is shown diagrammatically in Figure . A detailed explanation of the steps in the three stages will be explained to exemplify how a multistage analysis is performed. For simplicity, the filenames are omitted but the signature lengths, the maximum cycle lengths, the numbers of cycles, and the relative energies are retained. The first stage of reversing cycles produced sixteen proto-PCMs, fifteen of which optimized within the defined optimization run limits and one did not. However, of the fifteen optimized configurations, only two were shown to belong to the family of the parent configuration. In the second stage, five of the lowest energy child PCMs (-28.5kJ/mol to -35.7kJ/mol) from the first stage were arbitrarily selected as starting points for cycle reversals. From these five child PCMs, four generated thirteen proto-PCMs and one of them generated twelve proto-PCMs. Sixty-two of the sixty-four child proto-PCMs successfully optimized. In the third stage, three of the lowest energy child PCMs (-39.2 to -43.9 kJ/mol) from the second stage were arbitrarily selected as starting points. Each of these three configurations generated twelve proto-PCMs and all optimized to their respective parent PCMs hydrogen bonding family. Finally, membership of PCMs that have not matched with hydrogen bonding families from previous stages were tested for membership of hydrogen bonding families found in subsequent stages. This concluded the calculations. In summary, there were 117 proto-PCMs analyzed and only 3 did not optimize. Seven distinct families were identified and 110 PCMs matched with hydrogen bonding families. There were therefore 4 unmatched PCMs and further analyses of these were not pursued because they were of relatively higher energy than the lowest energy member of the lowest energy hydrogen bonding family. Energies and family membership from the three stages were plotted in a swarmplot shown in Figure . Table shows the energy ranges of the hydrogen bonding families found. The energy decreased from the initial parent geometry by 47 kJ/mol and difference between the maximum and minimum energies is 50 kJ/mol.