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 protonmediated 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.Potassium dihydrogen phosphate (KH 2 PO 4 , or KDP) belongs to a family of ferroelectric (FE) crystals where molecular units are linked by hydrogen bonds, the ferroelectricity being connected to proton off-center ordering in the bonds. A characteristic feature of this family is the large increase in the Curie temperature T c upon deuteration. In this particular case, it goes from ≃ 122 K in KDP to ≃ 229 K in the deuterated compound (DKDP). The origin of this huge isotope effect is still controversial, and has been mostly understood in terms of the quantum tunneling model proposed by Blinc, [1] later modified by inclusion of the coupling between proton motion and the K-PO 4 dynamics.[2] While direct experimental indications of tunneling have recently emerged [3], the connection between proton tunneling and isotope effect remains unclear. There is in fact strong evidence, [4,5] that isotope substitution acts rather through a geometrical modification of the hydrogen bonds, [6] with an expansion of the O-H-O distance. The proton off-centering, and thus the corresponding increase of lattice parameter upon deuteration, appear to be remarkably correlated to the increase of order parameter and of T c . These findings stimulated new theoretical work where some of these facts could be addressed without invoking tunneling, [7] however so far only at a rather phenomenological level.In the first part of this letter we investigate, using electronic structure calculations within Density Functional Theory (DFT), the relationship between proton ordering, polarization, and geometry in KDP. In the second part, we introduce a study of energy and subsequently the quantization of the collective ion displacements in small KDP clusters, embedded in a host paraelectric lattice. These calculations demonstrate the difference between deuterated and protonated KDP, the more delocalized proton bridging the oxygens and pulling them together more effectively than the deuteron. This phenomenon, which is at the root of the geometric effect, is further illustrated by solving in the last part a selfconsistent nonlinear model.For the DFT calculations we use two different approaches: one employing a basis set of confined pseudoatomic orbitals (SIESTA), [8] another a plane wave (PPW) representation.[9] For the first we choose a double-zeta basis set with polarization functions, and an orbital confinement energy E c = 50 meV. In the second, we set the energy cutoff to...

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