First-principles path-integral molecular dynamics study of ferroelectricity and isotope effects in KDP crystals with deep neural networks

We study the ferroelectric phase transition of KDP and DKDP with all-atom path-integral molecular dynamics (PIMD) based on a neural network potential energy model trained on density functional theory with SCAN approximation. The effective mass of the proton/deuteron used in PIMD is determined by fitting the experimental H/D off-centering, to correct for the intrinsic error of SCAN. Then, a series of calculated geometric isotope effects including the Ubbelohde effects are in satisfactory agreement with the experiments.

Based on a neural network dipole model trained on maximally localized Wannier function data, we obtain a PIMD description of the Berry-phase polarization of KDP and DKDP. The calculated spontaneous polarization agrees closely with experiments, and the deuteration is found to increase the rigidity of local dipoles, leading to a more order-disorder character of DKDP.