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We perform classical molecular dynamics (MD) and path-integral MD (PIMD) simulations of H2O and D2O using the q-TIP4P/F model over a wide range of temperatures and pressures to study the nuclear quantum effects (NQEs) on (i) the vitrification of liquid water upon isobaric cooling at different pressures and (ii) pressure-induced transformations at constant temperature between low-density amorphous and high-density amorphous ice (LDA and HDA) and hexagonal ice Ih and HDA. Upon isobaric cooling, classical and quantum H2O and D2O vitrify into a continuum of intermediate amorphous ices (IA), with densities in-between those of LDA and HDA (depending on pressure). Importantly, the density of the IA varies considerably if NQEs are included (similar conclusions hold for ice Ih at all pressures studied). While the structure of the IA is not very sensitive to NQE, the geometry of the hydrogen-bond (HB) is. NQE leads to longer and less linear HB in LDA, HDA, and ice Ih than found in the classical case. Interestingly, the delocalization of the H/D atoms is non-negligible and identical in LDA, HDA, and ice Ih at all pressures studied. Our isothermal compression/decompression MD/PIMD simulations show that classical and quantum H2O and D2O all exhibit LDA–HDA and ice Ih-HDA transformations, consistent with experiments. The inclusion of NQE leads to a softer HB-network, which lowers slightly the LDA/ice Ih-to-HDA transformation pressures. Interestingly, the HB in HDA is longer and less linear than in LDA, which is counterintuitive given that HDA is ≈25% denser than LDA. Overall, our results show that, while classical computer simulations provide the correct qualitative phenomenology of ice and glassy water, NQEs are necessary for a quantitative description. 

Abstract The potential energy landscape (PEL) formalism is a powerful tool within statistical mechanics to study the thermodynamic properties of classical low-temperature liquids and glasses. Recently, the PEL formalism has been extended to liquids/glasses that obey quantum mechanics, but applications have been limited to atomistic model liquids. In this work, we extend the PEL formalism to liquid/glassy water using path-integral molecular dynamics (PIMD) simulations, where nuclear quantum effects (NQE) are included. Our PIMD simulations, based on the q-TIP4P/F water model, show that the PEL of quantum water is both Gaussian and anharmonic. Importantly, the ring-polymers associated to the O/H atoms in the PIMD simulations, collapse at the local minima of the PEL (inherent structures, IS) for both liquid and glassy states. This allows us to calculate, analytically, the IS vibrational density of states (IS-VDOS) of the ring-polymer system using the IS-VDOS of classical water (obtained from classical MD simulations). The role of NQE on the structural properties of liquid/glassy water at various pressures are discussed in detail. Overall, our results demonstrate that the PEL formalism can effectively describe the behavior of molecular liquids at low temperatures and in the glass states, regardless of whether the liquid/glass obeys classical or quantum mechanics. 

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). 

Abstract Amorphous ices are usually classified as belonging to low-density or high-density amorphous ice (LDA and HDA) with densitiesρ_LDA ≈ 0.94 g/cm³andρ_HDA ≈ 1.15−1.17 g/cm³. However, a recent experiment crushing hexagonal ice (ball-milling) produced amedium-density amorphous ice (MDA,ρ_MDA ≈ 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 atP ≈ 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 atP = 125 MPa is located in the intermediate region of the PEL that separates LDA and HDA. 

Water-mediated interactions (WMIs) are responsible for diverse processes in aqueous solutions, including protein folding and nanoparticle aggregation. WMI may be affected by changes in temperature and pressure, and hence, they can alter chemical/physical processes that occur in aqueous environments. Traditionally, attention has been focused on hydrophobic interactions while, in comparison, the role of hydrophilic and hybrid (hydrophobic–hydrophilic) interactions have been mostly overlooked. Here, we study the role of T and P on the WMI between nanoscale (i) hydrophobic–hydrophobic, (ii) hydrophilic–hydrophilic, and (iii) hydrophilic–hydrophobic pairs of (hydroxylated/non-hydroxylated) graphene-based surfaces. We find that hydrophobic, hydrophilic, and hybrid interactions are all sensitive to P. However, while hydrophobic interactions [case (i)] are considerably sensitive to T-variations, hydrophilic [case (ii)] and hybrid interactions [case (iii)] are practically T-independent. An analysis of the entropic and enthalpic contributions to the potential of mean force for cases (i)–(iii) is also presented. Our results are important in understanding T- and P-induced protein denaturation and the interactions of biomolecules in solution, including protein aggregation and phase separation processes. From the computational point of view, the results presented here are relevant in the design of implicit water models for the study of molecular and colloidal/nanoparticle systems at different thermodynamic conditions. 

As a liquid approaches the gas state, the properties of the potential energy landscape (PEL) sampled by the system become anomalous. Specifically, (i) the mechanically stable local minima of the PEL [inherent structures (IS)] can exhibit cavitation above the so-called Sastry volume, v S , before the liquid enters the gas phase. In addition, (ii) the pressure of the liquid at the sampled IS [i.e., the PEL equation of state, P IS ( v)] develops a spinodal-like minimum at v S . We perform molecular dynamics simulations of a monatomic water-like liquid and verify that points (i) and (ii) hold at high temperatures. However, at low temperatures, cavitation in the liquid and the corresponding IS occurs simultaneously and a Sastry volume cannot be defined. Remarkably, at intermediate/high temperatures, the IS of the liquid can exhibit crystallization, i.e., the liquid regularly visits the regions of the PEL that belong to the crystal state. The model liquid considered also exhibits a liquid–liquid phase transition (LLPT) between a low-density and a high-density liquid (LDL and HDL). By studying the behavior of P IS ( v) during the LLPT, we identify a Sastry volume for both LDL and HDL. The HDL Sastry volume marks the onset above which IS are heterogeneous (composed of LDL and HDL particles), analogous to points (i) and (ii) above. However, the relationship between the LDL Sastry volume and the onset of heterogeneous IS is less evident. We conclude by presenting a thermodynamic argument that can explain the behavior of the PEL equation of state P IS ( v) across both the liquid–gas phase transition and LLPT. 

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.