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

TL;DR

The paper benchmarks multiple Deep Potential machine-learning potentials trained on MB-pol and several DFT functionals to predict the melting properties of water and ice under nuclear quantum effects, employing PIMD, TI, MTI, and direct coexistence. It finds that MB-pol–based DP reproduces experimental melting behavior and density differences, whereas DFT-based DP models mispredict the sign of NQEs on $T_m$ and tend to misestimate the density discontinuity. The authors validate a rigorous combination of TI/MTI and perturbative MTI analysis, and demonstrate that proper training datasets are crucial for reliable predictions, including the isotope effect on melting. The results establish a robust framework for ab initio-accurate simulations of aqueous systems and highlight the strengths and limitations of current ML potentials rooted in different electronic-structure methods. Overall, the work provides guidance for developing and validating ML potentials to study delicate properties like ice melting and NQEs in water.

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~$^{\circ}$C. Experimentally, an isotope effect on $T_{\mathrm{m}}$ is observed: the melting temperature of H$_2$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 ($T_{\mathrm{dm}}$) 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.

Figures (19)

• Figure 1: The initial and final states of the direct coexistence simulation are demonstrated. The coexisting ice and water system tend to thaw at high temperatures, and ice grows at low temperatures.
• Figure 2: The density along trajectories of (a) liquid water and (b) ice from AIMD simulations in the $NpT$ ensemble. The green lines are the densities and the purple lines are the accumulated averages of the densities. The black dash lines are the average densities calculated from MD simulations of 64 H$_2$O molecules driven by DP models.
• Figure 3: Accumulated averages of the internal pressure $P$ from AIMD simulations of water with 64 H$_2$O molecules in the $NVT$ ensemble at 300 K and different densities.
• Figure 4: Average internal pressure $P$ from AIMD and DPMD simulations of water in the $NVT$ ensemble at different densities $\rho$. A quartic polynomial is fitted to the $P(\rho)$ equation of state. The gray dashed line corresponds to the pressure 1 bar. The equilibrium density at 300 K and 1 bar determined from the polynomial is shown in orange, which is $0.925\pm 0.007$ and $0.900\pm 0.002$ g/cm$^3$ from AIMD and DPMD simulations, respectively.
• Figure 5: Density isobars of classical and quantum water and ice. The densities are calculated with classical MD and PIMD simulations in the $NpT$ ensemble at 1 bar. $T_{\mathrm{dm}}$ represents the temperature of density maximum of water. $T_{\mathrm{m}}$ represents the melting temperature of ice.