Evidence of a liquid–liquid phase transition in H$$_2$$O and D$$_2$$O from path-integral molecular dynamics simulations

Abstract

We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H$$_2$$ 2 O and D$$_2$$ 2 O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density $$\rho (T)$$ ρ ( T ) , isothermal compressibility $$\kappa _T(T)$$ κ T ( T ) , and self-diffusion coefficients D(T) of H$$_2$$ 2 O and D$$_2$$ 2 O are in excellent agreement with available experimental data; the isobaric heat capacity $$C_P(T)$$ C P ( T ) obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H$$_2$$ 2 O and D$$_2$$ 2 O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H$$_2$$ 2 O and D$$_2$$ 2 O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H$$_2$$ 2 O, from PIMD simulations, is located at $$P_c = 167 \pm 9$$ P c = 167 ± 9 MPa, $$T_c = 159 \pm 6$$ T c = 159 ± 6 K, and $$\rho _c = 1.02 \pm 0.01$$ ρ c = 1.02 ± 0.01 g/cm$$^3$$ 3 . Isotope substitution effects are important; the LLCP location in q-TIP4P/F D$$_2$$ 2 O is estimated to be $$P_c = 176 \pm 4$$ P c = 176 ± 4 MPa, $$T_c = 177 \pm 2$$ T c = 177 ± 2 K, and $$\rho _c = 1.13 \pm 0.01$$ ρ c = 1.13 ± 0.01 g/cm$$^3$$ 3 . Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects (i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water, $$P_c = 203 \pm 4$$ P c = 203 ± 4 MPa, $$T_c = 175 \pm 2$$ T c = 175 ± 2 K, and $$\rho _c = 1.03 \pm 0.01$$ ρ c = 1.03 ± 0.01 g/cm$$^3$$ 3 ). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of $$T_c$$ T c for D$$_2$$ 2 O and, particularly, H$$_2$$ 2 O suggest that improved water models are needed for the study of supercooled water.

The Importance of Nuclear Quantum Effects on the Thermodynamic and Structural Properties of Low-Density Amorphous Ice: A Comparison with Hexagonal Ice

“…This study complements previous works 34,37,40−42 that explore the NQE on the thermodynamic, dynamics, and structural properties of q-TIP4P/F water, H 2 O and D 2 O, in the liquid state. Compared to the NQE reported in liquid water at T > 240 K (P = 0.1 MPa), 40,41 the NQE reported here for LDA and ice I h are profound.…”

“…As shown in refs and , the isothermal compressibility of water κ P ( T ) = 1/ B ( T ) from PIMD simulations is considerably smaller than observed in experiments. It follows from refs and that the inclusion of NQE cannot reproduce the volume fluctuations (i.e., κ P ( T )) in liquid water. Yet, NQE are sufficient (and necessary) to reproduce such fluctuations in ice I h and LDA.…”

“…Interestingly, while PIMD simulations of q-TIP4P/F water in the solid state (ice I h and LDA) are in remarkably good agreement with experiments, this is not the case in supercooled liquid water. As shown in refs and , the isothermal compressibility of water κ P ( T ) = 1/ B ( T ) from PIMD simulations is considerably smaller than observed in experiments. It follows from refs and that the inclusion of NQE cannot reproduce the volume fluctuations (i.e., κ P ( T )) in liquid water.…”

Correlated Fluctuations of Structural Indicators Close to the Liquid–Liquid Transition in Supercooled Water

“…Despite many controversies, , cutting-edge experimental efforts are now entering in the no-mans land, − providing increasingly stronger hints at the possibility that the LLT actually exists in real water . In many numerical models of water, however, a LLT has been predicted to exist, ,− including models based on neural network potentials and models including quantum nuclear effects . In other models, the existence of a liquid–liquid critical point has been rigorously proven. − In silico, a liquid–liquid critical point has also been clearly identified in colloidal models mimicking, at the nano- and micron-scale, the tetrahedral binding of water. − …”

“… 14 In many numerical models of water, however, a LLT has been predicted to exist, 9 , 17 − 21 including models based on neural network potentials 22 and models including quantum nuclear effects. 23 In other models, the existence of a liquid–liquid critical point has been rigorously proven. 24 − 30 In silico, a liquid–liquid critical point has also been clearly identified in colloidal models mimicking, at the nano- and micron-scale, the tetrahedral binding of water.…”