Selected sample statistics of proto-PCMs generated from single PCMs of four to thirtysix water molecules are shown in Table . Also shown are the number of hydrogen bonds, the maximum signature length, the maximum cycle size, and the maximum cycle count in the hydrogen bonding family. The increase in number of proto-PCMs with water molecules from these calculations is exponential; the relationship through curve fitting is approximately p=0.00225e 0.47w , where p is the number of proto-PCMs and w is the number of water molecules. It should be recalled that the proto-PCMs are candidates for optimization and have not yet been optimized. Therefore, they have not yet been demonstrated to optimize to configurations that belong to the hydrogen bonding family of their respective parent PCMs. Cycle reversal alone cannot change the number of hydrogen bonds, and therefore the number of hydrogen bonds is conserved between parent PCM and members of its hydrogen bonding family.