Liquid-liquid Phase Transition in Supercooled H₂O and D₂O: A Path-Integral Computer Simulation Study

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 κ_T(T), and self-diffusion coefficients D(T) of H₂O and D₂O are in excellent agreement with available experimental data; the isobaric heat capacity 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 the 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 find that the differences in the LLCP location from PIMD and MD simulations of H₂O and D₂O suggest that nuclear quantum effects play an important role in the thermodynamics of water around the LLCP. Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques.