The ubiquity of water and its involvement in geochemical, biological and environmental processes makes it arguably the one of the most important compounds on planet Earth. It is therefore not surprising that much experimental and theoretical effort have been expended in elucidating its chemical properties and behavior in gas form and in condensed states. Due in large part to the increasing pace of the development of computing technology, molecular modeling has played a significant part in our current understanding of water. Through molecular dynamics (MD), ab initio methods, and more recently, ab initio molecular dynamics (AIMD), we have gained a better picture of the configuration, and interactions of water molecules, and the energies and rates of its transformations. Fundamental to these molecular modeling methods is the statistical mechanical concept of the potential energy surface (PES), where relatively longer-lived species correspond to energy minima and transitions between them to first-order saddle points. Derivation of the PES allows the determination of the thermodynamics and kinetics of a system, through the examination of regions where stationary points that are relevant to the chemical process of interest reside. However, the PES quickly gets difficult to derive as the system size grows, and concomitantly with the increase in the number of possible hydrogen bonding configurations. Conventional ab initio studies are particularly vulnerable to this problem because the result of an optimization simulation for most cases is a single "static" representation of a local minimum near an arbitrarily assigned input. Thus, without intervention, ab initio optimizations of a complex system are invariably downhill searches along the PES, and with high probability, often lead to metastable states. On the other hand, MD incorporates kinetic energy, and is therefore able to move away from metastable states and escape local depressions of the potential energy surface; however, this comes at the cost of having an unsatisfactory handling of chemical reactivity because MD generally has no dynamic knowledge of electronic structure. With aqueous systems in particular, MD is unable to adequately describe the well-established mechanism of concerted proton transfers -or the so-called Grotthuss mechanism. More recent developments combining ab initio and MD methods such as the Car-Parrinello 9 method and atom centered density matrix propagation models 10 formally provide the solution to the weakness of either of the methods alone and have gained popularity. However, mapping out significant portions of the PES is still not practical using these methods. For example, the accepted rate of transfer of protons is anywhere between 1 to 2 picoseconds per water molecule on average 3 at room temperature. Hence, for a proton transfer to traverse a water wire 6 of N water molecules, it would need N/f to 2N/f picoseconds of simulation time, where f is the number of concurrent proton transfers. The number of concurrent proton transfers and the maximum length of water wires that can be found in a model are yet to be shown. Assuming that proton transport is the primary mechanism of arriving at equilibrium geometries, then if the water wire lengths increase proportionally with the total number of water molecules in the model, and if the number of water wires increase exponentially, then these suggest that AIMD studies at current limitations of computational time have very limited coverage of configuration space for the number of water molecules considered. It would therefore be beneficial to be able to systematically and rapidly generate nearminimum configurations for any given model with the awareness of chemistry but without the need for more expensive intermediary simulation steps. Fortunately, knowledge of already established chemical phenomena can be leveraged to develop schemes to predict near minimum configurations in the water network. Specifically, concerted proton transfer itself, which is already known to have low activation energy barriers, is employed in this study. It will be posited that the predominant concerted proton transfers in aqueous systems are within water wires forming rings because auto-ionized water is demonstrably less thermodynamically favored than neutral water. These ring-forming water wires will be called cycles. Because studies show that clusters of three or more hydrogen bonded water molecules form rings inevitably, discovering energy minima through proton transport within cycles becomes relevant when considering systems of more than three water molecules. This work aims to show, using a program for reversing hydrogen bond cycles, that significant portions of the PES terrain for water can be systematically mapped out. The similarity of the energies of systems of water molecules related to each other only by a combination of reversal of hydrogen bonds will be demonstrated. Thus, this introduces the concept of hydrogen bonding families -systems that are related to each other by the reversal of cycles and have similar energies.