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 H2O and D2O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density rho(T), isothermal compressibility kappa(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 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 P-c = 167 +/- 9 MPa, T-c = 159 +/- 6 K, and rho(c) = 1.02 +/- 0.01 g/cm(3). Isotope substitution effects are important; the LLCP location in q-TIP4P/F D2O is estimated to be P-c = 176 +/- 4 MPa, T-c = 177 +/- 2 K, and rho(c) = 1.13 +/- 0.01 g/cm(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 +/- 4 MPa, T-c = 175 +/- 2 K, and rho(c) = 1.03 +/- 0.01 g/cm(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 for D2O and, particularly, H2O suggest that improved water models are needed for the study of supercooled water.