On the relevance of tunneling for the isotope effect in KDP

First-principles calculations for KH2PO4 (KDP) show that hydrogen off-center (OC) ordering in the ferroelectric phase is accompanied by electronic charge delocalization from the acceptor and localization at the donor oxygen within the O-H...O bonds. This induces P atoms off-centering in the PO4 tetrahedrons and pairing with K+ ions along the tetragonal axis, thus developing macroscopic polarization. Centered H are collectivelly unstable. However, if the protons are centered, the P and K atoms are stable in their centered positions. In addition, off-centering of a single proton is not energetically favorable. Only correlated proton motions, involving also displacements of heavier atoms, exhibit significant double wells, thus questioning the role of tunneling in isotope effects.