The properties of H2O and D2O are investigated using PIMD simulations at T ≥ 210 K, P = 1 bar. Anomalous maxima in thermodynamic response functions are found, supporting the presence of a liquid–liquid critical point at P > 0.

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.

Water and hydrogen are examples of substances proposed to exhibit a liquid-liquid critical point (LLCP) at conditions where nuclear quantum effects are relevant. The LLCP is usually accompanied by lines of maxima in density ρ and thermodynamic response functions, such as isothermal compressibility κ T and isobaric heat capacity C P , in the supercritical region of the P-T plane. In the case of water, the ρand κ T-maxima lines can be accessed in experiments, while, instead, the LLCP has not been observed due to rapid crystallization. In this work, we study the nuclear quantum effects on a monatomic liquid that exhibits waterlike anomalous properties and a LLCP. By performing path-integral Monte Carlo simulations with different values of the Planck's constant h, we are able to explore how the location of the LLCP in the P-T plane and, in particular, the maxima lines in the supercritical region, shift as the system evolves from classical, h = 0, to quantum, h > 0. We find that as the quantum nature of the liquid (as quantified by h) increases and the atoms in the liquid become more delocalized, the LLCP shifts towards higher pressures and lower temperatures while the LLCP volume remains constant. Similar shifts (towards higher pressures and lower temperatures) are found in the case of the C P-and κ T-maxima lines. Instead, the ρ-maxima line extends towards higher temperatures and expands over a wider pressure interval as the liquid becomes more quantum. It follows that the nuclear quantum effects on the location of the LLCP may be estimated from the shift in C P-and κ T-maxima lines but not on measurements of the ρ-maxima line. Interestingly, nuclear quantum effects considerably alter the slope of the liquid-liquid coexistence line and C P-maxima line in the P-T plane while the slope of the κ T-maxima line along the Widom line is barely affected. We discuss briefly the implications of our results to the case of H 2 O/D 2 O.

We study the nuclear quantum effects (NQE) on the thermodynamic properties of low-density amorphous ice (LDA) and hexagonal ice (I h ) at P = 0.1 MPa and T ≥ 25 K. Our results are based on path-integral molecular dynamics (PIMD) and classical MD simulations of H 2 O and D 2 O using the q-TIP4P/F water model. We show that the inclusion of NQE is necessary to reproduce the experimental properties of LDA and ice I h . While MD simulations (no NQE) predict that the density ρ(T) of LDA and ice I h increases monotonically upon cooling, PIMD simulations indicate the presence of a density maximum in LDA and ice I h . MD and PIMD simulations also predict a qualitatively different Tdependence for the thermal expansion coefficient α P (T) and bulk modulus B(T) of both LDA and ice I h . Remarkably, the ρ(T), α P (T), and B(T) of LDA are practically identical to those of ice I h . The origin of the observed NQE is due to the delocalization of the H atoms, which is identical in LDA and ice I h . H atoms delocalize considerably (over a distance ≈ 20−25% of the OH covalent-bond length) and anisotropically (preferentially perpendicular to the OH covalent bond), leading to less linear hydrogen bonds HB (larger HOO angles and longer OO separations) than observed in classical MD simulations.

We perform path integral molecular dynamics (PIMD) simulations of a monatomic liquid that exhibits a liquid-liquid phase transition (LLPT) and liquid-liquid critical point. PIMD simulations are performed using different values of the Planck's constant h, allowing us to study the behavior of the liquid as nuclear quantum effects (NQE, i.e., atoms delocalization) are introduced, from the classical liquid ( h=0) to increasingly quantum liquids ( h>0). By combining the PIMD simulations with the ring-polymer molecular dynamics (RPMD) method, we also explore the dynamics of the classical and quantum liquids. We find that (i) the glass transition temperature of the low-density liquid (LDL) is anomalous, i.e., TgLDL(P) decreases upon compression. Instead, (ii) the glass transition temperature of the high-density liquid (HDL) is normal, i.e., TgHDL(P) increases upon compression. (iii) NQE shift both TgLDL(P) and TgHDL(P) towards lower temperatures but NQE are more pronounced on HDL. We also study the glass behavior of the ring-polymer systems associated to the quantum liquids studied (via the PI formulation of statistical mechanics). There are two glass states in all the systems studied, LDA and HDA, which are the glass counterpart of LDL and HDL. In all cases, the pressure-induced LDA-HDA transformation is sharp, reminiscent of a first-order phase transition. In the low-quantum regime, the LDA-HDA transformation is reversible, with identical LDA forms before the compression and after the decompression. However, in the high-quantum regime, the atoms become more delocalized in the final LDA than in the initial LDA, raising questions on the reversibility of the LDA-HDA transformation.

Experimental techniques, such as cryo-electron microscopy, require biological samples to be recovered at cryogenic temperatures (T ≈ 100 K) with water being in an amorphous ice state. However, (bulk) water...

We perform path-integral molecular dynamics (PIMD) and classical MD simulations of H2O and D2O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density ρ(T), isothermal compressibility κT(T), and self-diffusion coefficients D(T) of H2O and D2O are in excellent agreement with available experimental data; the isobaric heat capacity CP(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 H2O and D2O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H2O and D2O 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 H2O, from PIMD simulations, is located at Pc = 167±9 MPa, Tc = 159±6 K, and ρc = 1.02±0.01 g/cm3. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D2O is estimated to be Pc = 176 ± 4 MPa, Tc = 177 ± 2 K, and ρc = 1.13±0.01 g/cm3. 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, Pc = 203 ± 4 MPa, Tc = 175 ± 2 K, and ρc = 1.03 ± 0.01 g/cm3). 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 Tc for D2O and, particularly, H2O suggest that improved water models are needed for the study of supercooled water.