Ab Initio Melting Properties of Water and Ice from Machine Learning Potentials

Abstract: Liquid water exhibits several important anomalous properties in the vicinity of the melting temperature ($T_{\mathrm{m}}$) of ice Ih, including a higher density than ice and a density maximum at 4~$<sup>{\circ}$C. Experimentally, an isotope effect on $T_{\mathrm{m}}$ is observed: the melting temperature of H$<em>2$O is approximately 4~K lower than that of D$_2$O. This difference can only be explained by nuclear quantum effects (NQEs), which can be accurately captured using path integral molecular dynamics (PIMD). Here we run PIMD simulations driven by Deep Potential (DP) models trained on data from density functional theory (DFT) based on SCAN, revPBE0-D3, SCAN0, and revPBE-D3 and a DP model trained on the MB-pol potential. We calculate the \tm of ice, the density discontinuity at melting, and the temperature of density maximum ($T</em>{\mathrm{dm}}$) of the liquid. We find that the model based on MB-pol agrees well with experiment. The models based on DFT incorrectly predict that NQEs lower $T_{\mathrm{m}}$. For the density discontinuity, SCAN and SCAN0 predict values close to the experimental result, while revPBE-D3 and revPBE0-D3 significantly underestimate it. Additionally, the models based on SCAN and SCAN0 correctly predict that the $T_{\mathrm{dm}}$ is higher than $T_{\mathrm{m}}$, while those based on revPBE-D3 and revPBE0-D3 predict the opposite. We attribute the deviations of the DFT-based models from experiment to the overestimation of hydrogen bond strength. Our results set the stage for more accurate simulations of aqueous systems grounded on DFT.