Nuclear quantum effects in a 1-D model of hydrogen bonded ferroelectrics

Abstract

A one dimensional model of a coupled hydrogen (H) bonding chain is developed and parametrized to density functional theory (DFT) calculations on squaric acid, a prototypical H-bonded antiferroelectric crystal. The energetics of single and collective proton jumps and its dependence on H-bond length, as obtained by DFT, is reproduced quite well in the model despite its simplicity where only hydrogen and oxygen atom positions in (O-H...O) H-bonds and nearest-neighbor coupling between H positions are explicitly included. Classical and path- integral molecular dynamics simulations are performed to shed light on nuclear quantum effects and how they influence the paraelectric phase transition. A large H/D isotope shift in the transition temperature TC as well as a geometric isotope effect is obtained in good agreement with experiment. Fixing the O-O bond length results in shifts of TC to higher temperature but a pronounced isotope shift of TC remains, highlighting the importance of quantum effects beyond the geometrical changes in H-bonds accompanying isotopic substitution. Intermediate between fully atomistic models and simpler Ising-type models, the proposed H-bond chain model is a useful toy model for investigating microscopic mechanisms behind phase transitions in H-bonded ferroelectrics and the detailed role of quantum fluctuations.