Hydrogen bonding has been studied in a model system, originally devised for the KcsA K+ ion channel, using density functional calculations. The model was to represent the putative gating region of the channel. Four acetic acids here are fixed at approximately 4-fold symmetry; six water molecules are added. Initial configurations had two water molecules in the center of the near-square defined by the carboxyls of the acetic acids, plus one water at each corner on the outside. Certain configurations of the acetic acids allow an extra water molecule to move into the center of the group; a move of 0.1 Angstrom by the acetic acids suffices to produce this jump (>2 Angstrom). In certain cases, the inner and outer water positions were nearly isoenergetic. Atoms in molecules (AIM) and natural bond orbital (NBO) provide complementary techniques for studying the changes in bonding and in electron density that accompany the different positions of the water molecules, including discontinuous changes in the topology of bonding. Two principle conclusions result: (1) All hydrogen bonds in this system belong to a single continuum with respect to their AIM and bonding properties, over the range of strength and length of bonds, irrespective of whether the oxygen is a water oxygen or bonded to a carbon in a carboxyl group. (2) Trajectories in molecular dynamics simulations are unlikely to sample such discontinuities correctly; this is likely to apply to systems other than that modeled here.