Potential energy landscape of a flexible water model: Equation of state, configurational entropy, and Adam-Gibbs relationship.

The potential energy landscape (PEL) formalism is a tool within statistical mechanics that has been used in the past to calculate the equation of states (EOS) of classical rigid model liquids at low temperatures, where computer simulations may be challenging. In this work, we use classical molecular dynamics (MD) simulations and the PEL formalism to calculate the EOS of the flexible q-TIP4P/F water model. This model exhibits a liquid-liquid critical point (LLCP) in the supercooled regime, at (Pc = 150 MPa, Tc = 190 K, and ρc = 1.04 g/cm3) [using the reaction field technique]. The PEL-EOS of q-TIP4P/F water and the corresponding location of the LLCP are in very good agreement with the MD simulations. We show that the PEL of q-TIP4P/F water is Gaussian, which allows us to calculate the configurational entropy of the system, Sconf. The Sconf of q-TIP4P/F water is surprisingly similar to that reported previously for rigid water models, suggesting that intramolecular flexibility does not necessarily add roughness to the PEL. We also show that the Adam-Gibbs relation, which relates the diffusion coefficient D with Sconf, holds for the flexible q-TIP4P/F water model. Overall, our results indicate that the PEL formalism can be used to study molecular systems that include molecular flexibility, the common case in standard force fields. This is not trivial since the introduction of large bending/stretching mode frequencies is problematic in classical statistical mechanics. For example, as shown previously, we find that such high frequencies lead to unphysical (negative) entropy for q-TIP4P/F water when using classical statistical mechanics (yet, the PEL formalism can be applied successfully).

A continuum of amorphous ices between low-density and high-density amorphous ice.

Amorphous ices are usually classified as belonging to low-density or high-density amorphous ice (LDA and HDA) with densities ρLDA ≈ 0.94 g/cm3 and ρHDA ≈ 1.15-1.17 g/cm3. However, a recent experiment crushing hexagonal ice (ball-milling) produced a medium-density amorphous ice (MDA, ρMDA ≈ 1.06 g/cm3) adding complexity to our understanding of amorphous ice and the phase diagram of supercooled water. Motivated by the discovery of MDA, we perform computer simulations where amorphous ices are produced by isobaric cooling and isothermal compression/decompression. Our results show that, depending on the pressure employed, isobaric cooling can generate a continuum of amorphous ices with densities that expand in between those of LDA and HDA (briefly, intermediate amorphous ices, IA). In particular, the IA generated at P ≈ 125 MPa has a remarkably similar density and average structure as MDA, implying that MDA is not unique. Using the potential energy landscape formalism, we provide an intuitive qualitative understanding of the nature of LDA, HDA, and the IA generated at different pressures. In this view, LDA and HDA occupy specific and well-separated regions of the PEL; the IA prepared at P = 125 MPa is located in the intermediate region of the PEL that separates LDA and HDA.

The Importance of Nuclear Quantum Effects on the Thermodynamic and Structural Properties of Low-Density Amorphous Ice: A Comparison with Hexagonal Ice.

We study the nuclear quantum effects (NQE) on the thermodynamic properties of low-density amorphous ice (LDA) and hexagonal ice (Ih) at P = 0.1 MPa and T ≥ 25 K. Our results are based on path-integral molecular dynamics (PIMD) and classical MD simulations of H2O and D2O using the q-TIP4P/F water model. We show that the inclusion of NQE is necessary to reproduce the experimental properties of LDA and ice Ih. While MD simulations (no NQE) predict that the density ρ(T) of LDA and ice Ih increases monotonically upon cooling, PIMD simulations indicate the presence of a density maximum in LDA and ice Ih. MD and PIMD simulations also predict a qualitatively different T-dependence for the thermal expansion coefficient αP(T) and bulk modulus B(T) of both LDA and ice Ih. Remarkably, the ρ(T), αP(T), and B(T) of LDA are practically identical to those of ice Ih. The origin of the observed NQE is due to the delocalization of the H atoms, which is identical in LDA and ice Ih. H atoms delocalize considerably (over a distance ≈ 20-25% of the OH covalent-bond length) and anisotropically (preferentially perpendicular to the OH covalent bond), leading to less linear hydrogen bonds HB (larger HOO angles and longer OO separations) than observed in classical MD simulations.

Nuclear quantum effects on the dynamics and glass behavior of a monatomic liquid with two liquid states.

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., Tg LDL(P) decreases upon compression. Instead, (ii) the glass transition temperature of the high-density liquid (HDL) is normal, i.e., Tg HDL(P) increases upon compression. (iii) NQE shift both Tg LDL(P) and Tg HDL(P) 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.

Evidence of a liquid-liquid phase transition in H[Formula: see text]O and D[Formula: see text]O from path-integral molecular dynamics simulations.

We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H[Formula: see text]O and D[Formula: see text]O 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 H[Formula: see text]O and D[Formula: see text]O 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 H[Formula: see text]O and D[Formula: see text]O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H[Formula: see text]O and D[Formula: see text]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[Formula: see text]O, from PIMD simulations, is located at [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: see text]. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D[Formula: see text]O is estimated to be [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: 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/cm[Formula: 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 D[Formula: see text]O and, particularly, H[Formula: see text]O suggest that improved water models are needed for the study of supercooled water.

The role of high-density and low-density amorphous ice on biomolecules at cryogenic temperatures: a case study with polyalanine.

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).

Nuclear quantum effects on the thermodynamic, structural, and dynamical properties of water.

We perform path-integral molecular dynamics (PIMD) simulations of H2O and D2O using the q-TIP4P/F model. Simulations are performed at P = 1 bar and over a wide range of temperatures that include the equilibrium (T≥ 273 K) and supercooled (210 ≤T < 273 K) liquid states of water. The densities of both H2O and D2O calculated from PIMD simulations are in excellent agreement with experiments in the equilibrium and supercooled regimes. We also evaluate important thermodynamic response functions, specifically, the thermal expansion coefficient αP(T), isothermal compressibility κT(T), isobaric heat capacity CP(T), and static dielectric constant ε(T). While these properties are in excellent [αP(T) and κT(T)] or semi-quantitative agreement [CP(T) and ε(T)] with experiments in the equilibrium regime, they are increasingly underestimated upon further cooling. It follows that the inclusion of nuclear quantum effects in PIMD simulations of (q-TIP4P/F) water is not sufficient to reproduce the anomalous large fluctuations in density, entropy, and electric dipole moment characteristic of supercooled water. It has been hypothesized that water may exhibit a liquid-liquid critical point (LLCP) in the supercooled regime at P > 1 bar and that such a LLCP generates a maximum in CP(T) and κT(T) at 1 bar. Consistent with this hypothesis and in particular, with experiments, we find a maximum in the κT(T) of q-TIP4P/F light and heavy water at T≈ 230-235 K. No maximum in CP(T) could be detected down to T≥ 210 K. We also calculate the diffusion coefficient D(T) of H2O and D2O using the ring-polymer molecular dynamics (RPMD) technique and find that computer simulations are in remarkable good agreement with experiments at all temperatures studied. The results from RPMD/PIMD simulations are also compared with the corresponding results obtained from classical MD simulations of q-TIP4P/F water where atoms are represented by single interacting sites. Surprisingly, we find minor differences in most of the properties studied, with CP(T), D(T), and structural properties being the only (expected) exceptions.