Based on an accurate first principles description of the energetics in H-bonded KDP, we conduct a first study of nuclear quantum effects and of the changes brought about by deuteration. Cluster tunneling involving also heavy ions is allowed, the main effect of deuteration being a depletion of the proton probability density at the O-H-O bridge center, which in turn weakens its proton-mediated covalent bonding. The ensuing lattice expansion couples selfconsistently with the proton off-centering, thus explaining both the giant isotope effect, and its close connection with geometrical effects.