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We perform path integral molecular dynamics (PIMD) simulations of a monatomic liquid that exhibits a liquid–liquid phase transition and liquid–liquid critical point. PIMD simulations are performed using different values of 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 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., [Formula: see text] decreases upon compression. Instead, (ii) the glass transition temperature of the high-density liquid (HDL) is normal, i.e., [Formula: see text] increases upon compression. (iii) NQE shift both [Formula: see text] and [Formula: see text] toward lower temperatures, but NQE are more pronounced on HDL. We also study the glass behavior of the ring-polymer systems associated with the quantum liquids studied (via the path-integral formulation of statistical mechanics). There are two glass states in all the systems studied, low-density amorphous ice (LDA) and high-density amorphous ice (HDA), which are the glass counterparts 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 compression and after 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. 

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$$\rho (T)$$$\rho \left(T\right)$, isothermal compressibility$$\kappa _T(T)$$${\kappa }_T\left(T\right)$, and self-diffusion coefficientsD(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\left(T\right)$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\pm 9$ MPa,$$T_c = 159 \pm 6$$$T_c=159\pm 6$ K, and$$\rho _c = 1.02 \pm 0.01$$${\rho }_c=1.02\pm 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\pm 4$ MPa,$$T_c = 177 \pm 2$$$T_c=177\pm 2$ K, and$$\rho _c = 1.13 \pm 0.01$$${\rho }_c=1.13\pm 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\pm 4$ MPa,$$T_c = 175 \pm 2$$$T_c=175\pm 2$ K, and$$\rho _c = 1.03 \pm 0.01$$${\rho }_c=1.03\pm 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.

 

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 can exist in two amorphous ices at P < 1 GPa, low-density amorphous (LDA) ice at low pressures and high-density amorphous ice (HDA) at high pressures; HDA is ≈20–25% denser than LDA. While fast/plunge cooling at 1 bar brings the sample into LDA, high-pressure cooling (HPC), at sufficiently high pressure, produces HDA. HDA can also be produced by isothermal compression of LDA at cryogenic temperatures. Here, we perform classical molecular dynamics simulations to study the effects of LDA, HDA, and the LDA–HDA transformation on the structure and hydration of a small peptide, polyalanine. We follow thermodynamic paths corresponding to (i) fast/plunge cooling at 1 bar, (ii) HPC at P = 400 MPa, and (iii) compression/decompression cycles at T = 80 K. While process (i) produced LDA in the system, path (iii) produces HDA. Interestingly, the amorphous ice produced in process (ii) is an intermediate amorphous ice (IA) with properties that fall in-between those of LDA and HDA. Remarkably, the structural changes in polyalanine are negligible at all conditions studied (0–2000 MPa, 80–300 K) even when water changes among the low and high-density liquid states as well as the amorphous solids LDA, IA, and HDA. The similarities and differences in the hydration of polyalanine vitrified in LDA, IA, and HDA are described. Since the studied thermodynamic paths are suitable for the cryopreservation of biomolecules, we also study the structure and hydration of polyalanine along isobaric and isochoric heating paths, which can be followed experimentally for the recovery of cryopreserved samples. Upon heating, the structure of polyalanine remains practically unchanged. We conclude with a brief discussion of the practical advantages of (a) using HDA and IA as a cryoprotectant environment (as opposed to LDA), and (b) the use of isochoric heating as a recovery process (as opposed to isobaric heating).