Evidence of a liquid–liquid phase transition in H₂O and D₂O from path-integral molecular dynamics simulations

We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of HFormula: see textO and DFormula: see textO using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density Formula: see text, isothermal compressibility Formula: see text, and self-diffusion coefficients D(T) of HFormula: see textO and DFormula: see textO are in excellent agreement with available experimental data; the isobaric heat capacity Formula: see text 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 HFormula: see textO and DFormula: see textO exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for HFormula: see textO and DFormula: see textO 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 HFormula: see textO, from PIMD simulations, is located at Formula: see text MPa, Formula: see text K, and Formula: see text g/cmFormula: see text. Isotope substitution effects are important; the LLCP location in q-TIP4P/F DFormula: see textO is estimated to be Formula: see text MPa, Formula: see text K, and Formula: see text g/cmFormula: see text. 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, Formula: see text MPa, Formula: see text K, and Formula: see text g/cmFormula: see text). 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 Formula: see text for DFormula: see textO and, particularly, HFormula: see textO suggest that improved water models are needed for the study of supercooled water.