The hydrogen bonding network of water can be interpreted as a directed graph, where the oxygen atoms are nodes, and proton donation defines the direction of the graph. Where the graph loops back to the initial node, it is called a "simple cycle" or for the purpose of this study simply called a "cycle". Thus, analogs of an original configuration can be generated by the reversing cycles of that configuration. For lack of a better term, energy minimized configurations of water that differ from each other only by the reversals of cycles or any combination of reversals will be referred to as "polycyclomorphs" or PCMs. Candidate PCM configurations that have not yet been optimized will be referred to as "proto-PCMs". To facilitate the generation of proto-PCMs and the handling of PCMs, a set of programs collectively called Hydrocycler was developed. The programs display cycles, generate proto-PCMs in cartesian file format either stepwise or exhaustively, and analyze configurations for hydrogen bonding family membership. The generation of configurations from an initial geometry follows a depth-search algorithm, and can be thought of as the creation of a tree-like trajectory consisting of predicted near-minimum configurations. Subsequent optimization using Gaussian verifies whether the configurations are indeed near energy minima. The criterion used for being near a minimum is that it is within one default optimization run in Gaussian; that is, the number of optimization steps are within either the "maximum of 20 and twice the number of redundant internal coordinates in use" or "twice the number of variables to be optimized." Optimization runs are not restarted. In the Hydrocycler scheme, oxygen atoms are nodes, and proton donation defines the direction of the directed graph. The geometric definition used for identifying hydrogen bonds is a ÐHOO angle of less than 30° and O-O distances of 1.2Å-3.2Å. Closed loops of hydrogen bonding are identified using the algorithm by Johnson and are referred to as cycles (Figure ). By reversing the direction of the cycles, proto-PCMs are generated. The reversal is performed by a substitution of hydrogen coordinates, which may be viewed as a mirror transformation of the triangles made by H-O-O. The generation of the complete set of proto-PCMs from all combinations of reversals of cycles of a cluster, that is the anticipated hydrogen bonding family, is called an exhaustive cycle reversal search. The generated proto-PCM configurations are then used as input for subsequent optimization searches, and so on. A companion interactive program is provided to illustrate what the exhaustive cycle reversal search program does. More information regarding the individual programs is given in the Hydrocycler Github page. A single proto-PCM or PCM possesses a set of cycles that is unique to that arrangement of water molecules, while ignoring hydrogens that are not in a cycle (acyclic hydrogens). Thus, a signature of a proto-PCM or PCM can be created by concatenating the sorted cycles. For example, a configuration with cycles 0!1!2!3 and 0!1!2, where numbers correspond to oxygens, would have the signature (0, 1, 2, 0, 1, 2, 3). It is asserted that, ignoring acyclic hydrogens, the signature uniquely identifies the proto-PCM or PCM within a given a system of molecules. The compiled list of signatures from all proto-PCMs generated from a configuration, therefore, fully defines a hydrogen bonding family; this compiled list will be referred to as the "ledger". Thus, proto-PCMs, after their optimization to minima, may be evaluated against this ledger to test for conservation of hydrogen bonding family membership. Failure means they have transitioned to another family; chemically speaking, this means that there has been a change in their hydrogen bonding network after optimization. The ledger is kept in the .sig file, which is saved after the execution of the exhaustive cycle reversal search program; another program to check for membership is provided. A supplement is provided for more explanation on signatures and ledgers. A complete set of PCMs that are related only by combinations of reversals is called a "hydrogen bonding family." Any cluster that has a sufficiently high number of water molecules has numerous cycles, and the number of potential PCMs increases exponentially with the number of water molecules in a cluster. In practice, finding all PCMs of a family is impractical except for relatively small systems; this is because energy minimization needs to be demonstrated for each. Finding complete sets of proto-PCMs on the other hand is less computationally demanding, as will be shown in this study. The term hydrogen bonding family will be used here for both PCMs and proto-PCMs. All optimizations used B97D3 27 with 6-311++G(d,p) basis sets to handle dispersion, diffusion and polarity. Clusters of four to thirty-six water molecules were used to demonstrate the generation of proto-PCMs in increasing number of water molecules. Clusters of four to twenty-four water molecules were used to demonstrate how the programs can be used to discover progressively lower energy configurations.