On the other hand, prospective near minima points that fail to conserve the hydrogen bonding family membership when optimized indicate reorientation of hydrogen bonding. These are configurations that have transitioned during the optimization procedure into members of other hydrogen bonding families. These new hydrogen bonding families have energy ranges that are either similar or less than the original hydrogen bonding family. Hence, nonconservation is a way to serendipitously discover lower energy hydrogen bonding families. It is yet to be demonstrated if the intentional reorientation of hydrogen bonding could also be used as a procedure to discover lower energy hydrogen bonding families. Because configurations can be classified along hydrogen bonding families and these families correspond to ranges of energies, it is only sufficient to find representative members of these families to describe entire families of configurations. This is akin to a reduction of configuration space. Relatedly, note that the elusive global minimum configuration would be associated with a hydrogen bonding family consisting of members with presumably similar lowermost energies. Therefore, it is sufficient to find a member of the hydrogen bonding family of the global minimum to determine the global minimum; that is, the global minimum configuration can be reproduced with relative ease by cycle reversals from this member. It should be emphasized that finding the global minima was not attempted in any of the analyses. The results suggest that the energy minimization of an aqueous cluster can be assisted by an iterative process of taking a low energy configuration, computing its proto-PCMs, sampling these proto-PCMs, and then optimizing the samples to determine transitions to other hydrogen bonding families. That is, by the assumption of proton transfers within cycles, some expensive quantum calculation steps may be obviated. Current AIMD studies deserve reflection considering these results. Typical recent AIMD studies on water have overall simulation times of up to 200ps for 64 water. Considering that the largest simple cycles found (Table ) span nearly all water molecules in the optimized clusters and that cycle reversals produce exponential numbers of other possible minima, then either (1) the AIMD studies had insufficient time to equilibrate if the primary mode of transformation is proton transfer along water wires, or (2) breaking hydrogen bond network topology is the primary mode of equilibration. Testing these possibilities can be aided by the method of signatures and ledgers described in this study.