  Path integral Monte Carlo (PIMC) simulations with very simple models were
used in order to unveil the physics behind the isotope effects in H-bonded
ferroelectrics. First, we studied geometrical effects in the H-bonds caused by
deuteration with a general three-site model based on a back-to-back double
Morse potential plus a Morse potential between oxygens, fitted to explain
different general features for a wide set of H-bonded compounds. Our model
results show the Ubbelohde or geometrical effect (GE), i.e., the expansion of
the H-bond with deuteration, in agreement to what is observed in H-bonded
ferroelectrics with short H-bonds. Moreover, adjusting the potential parameters
to ab initio results, we have developed a 1D model which considers the bilinear
proton-proton interaction in mean-field to study nuclear quantum effects that
give rise to the GE in KDP crystals. PIMC simulations reveal that protons
tunnel more efficiently than deuterons along the 1D chain, giving rise to a
strong attraction center that pulls the oxygens together. This mechanism, which
is based on the correlation between tunneling and geometrial modifications of
the H-bonds, leads to a strong GE in the ordered phase of the chain at low
temperature which is in good agreement with the experimental data.
