The Role of Nuclear Quantum Effects in Supercooled Water and Amorphous Ice

Water is one of the most important substances on Earth and plays a fundamental role in numerous scientific and engineering applications. Interestingly, water behaves much differently than other liquids. For example, water shows an anomalous density maximum at 277 K, the solid phase (ice) is less denser than the liquid, and its thermodynamic response functions, such as the specific heat CP and isothermal compressibility κT, also increase anomalously upon cooling. In the glassy state, water can exist in two different forms, low-density and high-density amorphous ice (LDA and HDA). While water has been scrutinized for many centuries, the origin for the anomalous thermodynamic and dynamical properties of liquid and glassy water are not fully understood. A scenario that explains water anomalous behavior is provided by the liquid-liquid phase transition hypothesis (LLPT). The LLPT hypothesis postulates that water at low temperature can exist as two distinct liquids, a low-density and a high-density liquid (LDL and HDL), that are separated by a first-order phase transition line that ends at a liquid-liquid critical point (LLCP). The LLPT hypothesis is currently the explanation best-supported by experiments and computational studies. Most computational studies that focused on the phase behavior of liquid and glassy water have been performed using classical molecular dynamics simulations where nuclear quantum effects (NQE) are neglected. This can be troublesome because water is a light molecule and NQE are known to influence the structural and dynamic properties of water even at ambient conditions. For example, in H2O and D2O, the temperature of the density maxima, glass transition temperature and melting temperature are shifted by δT = 4 − 10 K, a clear sign of NQE. We note that classical MD simulations can not be used to study isotope effects (H2O and D2O) because in this technique the water O and H atoms are modeled as point particles that interact with other water molecules through electrostatic and short range interactions. In order to incorporate NQE in computer simulations one must use path integral techniques such as path integral molecular dynamics (PIMD) or path integral Monte Carlo (PIMC). In this dissertation, I will discuss results from extensive PIMD simulations using the q-TIP4P/F water model in order to explore the behavior of H2O and D2O at low temperature, including the supercooled liquid and glass states. I will show that our PIMD simulations indicate that H2O and D2O, both exhibit a LLCP at low temperatures, implying that the LLPT hypothesis is still valid when NQE are taken into account. In particular, while the phase diagram we have obtained from our PIMD simulations for H2O and D2O are qualitatively similar, NQE shift the LLCP for H2O towards lower temperatures and pressures, consistent with estimations from experiments in glassy water. I will also show that while PIMD simulations of q-TIP4P/F water can reproduce some of the thermodynamic, dynamic, and structural properties of light and heavy water remarkably well, there are notable exceptions between our simulations and experiments. For example, the CP(T) and κT(T) from our PIMD simulations deviate from experiments at low temperatures, implying that introducing NQE does not necessarily reproduce the density and entropy fluctuations observed experimentally in supercooled water. After discussing the results we have obtained from our PIMD simulations for supercooled water, I will then discuss the results I have obtained for glassy water from PIMD simulations. Our PIMD simulations show that NQE play a relevant role for glassy water at low temperatures. For example, we find from our PIMD simulations that the density of LDA and ice Ih indicate the presence of a density maximum at low temperatures, while MD simulations show that the density of LDA and ice Ih to increase monotonically upon isobaric cooling