Liquid-Liquid Transition in Water from First Principles

A long-standing question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles.

Figure 1

Density from isothermal-isobaric simulations. Mass density ($\rho$) vs time ($t$) trajectories for simulations with $N=192$ molecules at $T=235\mathrm{K}$ and (a) $P=3000\mathrm{bar}$, (b) $P=3200\mathrm{bar}$, and (c) $P=3400\mathrm{bar}$. In each panel, the orange trajectory was initialized in a high-$\rho$ configuration, and the blue trajectory was initialized in a low-$\rho$ configuration.

Figure 2

Free energy surfaces from umbrella sampling (US) simulations. Free energy ($F$) as a function of $\rho$ and $s_2$ from US simulations with $N=192$ molecules at $T=235\mathrm{K}$ and (a) $P=3000\mathrm{bar}$, (b) $P=3200\mathrm{bar}$, and (c) $P=3400\mathrm{bar}$. In the left subfigure of each panel, contours represent $1k_{B}T$. In the right subfigure of each panel, the solid blue line represents $F$ averaged over all $s_2$ values, with the shaded regions representing 95% confidence intervals.

Figure 3

Phase coexistence from multithermal-multibaric (MTMB) simulations. (a) Free energy ($F$) as a function of $\rho$ and $s_2$ from MTMB simulations with $N=192$ molecules at $T=225\mathrm{K}$ and $P=3525\mathrm{bar}$. (b) $F$ vs $\rho$ at various $T$ and $P$ as marked. Shaded regions represent 95% confidence intervals. (c) Liquid-liquid binodal (solid black line), approximate critical point location (shaded blue region), and line of maximum isothermal compressibility (dashed black line) in the $T\text{−}P$ plane.