Assessment of First-Principles Methods in Modeling the Melting Properties of Water

Abstract

First-principles simulations have played a crucial role in deepening our understanding of the thermodynamic properties of water, and machine learning potentials (MLPs) trained on these first-principles data widen the range of accessible properties. However, the capabilities of different first-principles methods are not yet fully understood due to the lack of systematic benchmarks, the underestimation of the uncertainties introduced by MLPs, and the neglect of nuclear quantum effects (NQEs). Here, we systematically assess first-principles methods by calculating key melting properties using path integral molecular dynamics (PIMD) driven by Deep Potential (DP) models trained on data from density functional theory (DFT) with SCAN, revPBE0-D3, SCAN0 and revPBE-D3 functionals, as well as from the MB-pol potential. We find that MB-pol is in qualitatively good agreement with the experiment in all properties tested, whereas the four DFT functionals incorrectly predict that NQEs increase the melting temperature. SCAN and SCAN0 slightly underestimate the density change between water and ice upon melting, but revPBE-D3 and revPBE0-D3 severely underestimate it. Moreover, SCAN and SCAN0 correctly predict that the maximum liquid density occurs at a temperature higher than the melting point, while revPBE-D3 and revPBE0-D3 predict the opposite behavior. Our results highlight limitations in widely used first-principles methods and call for a reassessment of their predictive power in aqueous systems.

Figures (4)

• Figure 1: (a) NQEs on the melting temperature of ice at 1 bar, defined as $T_{\mathrm{m}}-T_{\mathrm{m}}^{\mathrm{cl}}$, for DFT-based calculations (this work) and MB-pol (from Ref. bore_realistic_2023). (b) Density discontinuity between water and ice Ih at the calculated melting temperature and 1 bar from quantum simulations. (c) Difference ($\Delta T_{\mathrm{dm}-\mathrm{m}}$) between the temperature of density maximum ($T_{\mathrm{dm}}$) of quantum water and melting temperature ($T_{\mathrm{m}}$) of quantum ice at 1 bar.
• Figure 2: The $g(y)$ values for ice and water calculated by DP@MB-pol and DP@SCAN. The dots represent $y$ values at which PIMD are run. The red dashed lines show the slopes $\frac{\mathrm{d}g}{\mathrm{d}y}|_{y=0}$ predicted by an expansion of $\Delta\mu^{\mathrm{qu}- \mathrm{cl}}_{\alpha}(T)$ up to $\hbar^2$ using the perturbation theory. The black dashed lines are polynomial fitting of $g(y)$ using odd orders of $y$ up to $y^{13}$, which corresponds to an expansion of $\Delta\mu^{\mathrm{qu}- \mathrm{cl}}_{\alpha}(T)$ in even orders of $\hbar$ up to $\hbar^{14}$. The shaded area yields the quantum correction to the chemical potential $\Delta\mu^{\mathrm{qu}- \mathrm{cl}}_{\alpha}(T)$ of a single phase $\alpha$.
• Figure 3: $g_{\mathrm{OO}}(r)$ of classical water. The $g_{\mathrm{OO}}(r)$ for revPBE0-D3 is calculated with an AIMD simulation which spans 50 ps. Both DPMD and AIMD simulations are run in the $NpT$ ensemble at 300 K and 1 bar. The $g_{\mathrm{OO}}(r)$ for BPNN@revPBE0-D3 is taken from Ref. cheng_ab_2019.
• Figure 4: $g_{\mathrm{OO}}(r)$ of quantum water at $T_{\mathrm{m}}+25$ K and 1 bar. The experimental $g_{\mathrm{OO}}(r)$ is taken from Ref. skinner_benchmark_2013, with the shaded area indicating the experimental uncertainty. The $g_{\mathrm{OO}}(r)$ curves for DP models are calculated with PIMD simulations in the $NpT$ ensemble.