Novel Algorithm to Generate Hydrogen-Disordered Ice Structures

Observation of plastic ice VII by quasi-elastic neutron scattering

Water is the third most abundant molecule in the universe and a key component in the interiors of icy moons, giant planets and Uranus- and Neptune-like exoplanets1-3. Owing to its distinct molecular structure and flexible hydrogen bonds that readily adapt to a wide range of pressures and temperatures, water forms numerous crystalline and amorphous phases4-6. Most relevant for the high pressures and temperatures of planetary interiors is ice VII (ref. 4), and simulations have identified along its melting curve the existence of a so-called plastic phase7-12 in which individual molecules occupy fixed positions as in a solid yet are able to rotate as in a liquid. Such plastic ice has not yet been directly observed in experiments. Here we present quasi-elastic neutron scattering measurements, conducted at temperatures between 450 and 600 K and pressures up to 6 GPa, that reveal the existence of a body-centred cubic structure, as found in ice VII, with water molecules showing picosecond rotational dynamics typical for liquid water. Comparison with molecular dynamics simulations indicates that this plastic ice VII does not conform to a free rotor phase but rather shows rapid orientational jumps, as observed in jump-rotor plastic crystals13,14. We anticipate that our observation of plastic ice VII will affect our understanding of the geodynamics of icy planets and the differentiation processes of large icy moons.

Efficient Parametrization of Transferable Atomic Cluster Expansion for Water

We present a highly accurate and transferable parametrization of water using the atomic cluster expansion (ACE). To efficiently sample liquid water, we propose a novel approach that involves sampling static calculations of various ice phases and utilizing the active learning (AL) feature of the ACE-based D-optimality algorithm to select relevant liquid water configurations, bypassing computationally intensive ab initio molecular dynamics simulations. Our results demonstrate that the ACE descriptors enable a potential initially fitted solely on ice structures, which is later upfitted with few configurations of liquid, identified with AL to provide an excellent description of liquid water. The developed potential exhibits remarkable agreement with first-principles reference, accurately capturing various properties of liquid water, including structural characteristics such as pair correlation functions, covalent bonding profiles, and hydrogen bonding profiles, as well as dynamic properties like the vibrational density of states, diffusion coefficient, and thermodynamic properties such as the melting point of the ice Ih. Our research introduces a new and efficient sampling technique for machine learning potentials in water simulations while also presenting a transferable interatomic potential for water that reveals the accuracy of first-principles reference. This advancement not only enhances our understanding of the relationship between ice and liquid water at the atomic level but also opens up new avenues for studying complex aqueous systems.

Stability mechanism of crystalline CO2 and Xe

We explore the phase behaviors of simple molecular crystals in order to investigate the molecular basis of the stability mechanism relative to their liquid counterparts. The free energies of the face centered cubic crystals of Xe and CO2 are calculated as a collection of oscillators, and those of the liquids are from an equation of state via molecular dynamics simulations. The vibrational free energy in the solid is separated into the harmonic and anharmonic terms. The harmonic free energies decrease harshly with the expansion of the volume manifested as the large positive Grüneisen parameters, but the anharmonic free energies are positive and increase with volume, both of which originate from the deviation of the potential surface from the parabolic curve. The anharmonic free energies, though less significant in magnitude and destabilize the solids thermodynamically, serve to enhance their mechanical stability. The solid-liquid phase boundaries cannot be settled correctly without the exquisite balance between the two opposing contributions. A sharp contrast regarding the solid free energy is found in low-pressure ice, where the harmonic free energy does not decrease monotonically with volume and its anharmonic free energy is negative.

Theoretical Studies of Anisotropic Melting of Ice Induced by Ultrafast Nonthermal Heating

Water and ice are routinely studied with X-rays to reveal their diverse structures and anomalous properties. We employ a hybrid collisional-radiative/molecular-dynamics method to explore how femtosecond X-ray pulses interact with hexagonal ice. We find that ice makes a phase transition into a crystalline plasma where its initial structure is maintained up to tens of femtoseconds. The ultrafast melting process occurs anisotropically, where different geometric configurations of the structure melt on different time scales. The transient state and anisotropic melting of crystals can be captured by X-ray diffraction, which impacts any study of crystalline structures probed by femtosecond X-ray lasers.

GenIce-core: Efficient algorithm for generation of hydrogen-disordered ice structures

Ice is different from ordinary crystals because it contains randomness, which means that statistical treatment based on ensemble averaging is essential. Ice structures are constrained by topological rules known as the ice rules, which give them unique anomalous properties. These properties become more apparent when the system size is large. For this reason, there is a need to produce a large number of sufficiently large crystals that are homogeneously random and satisfy the ice rules. We have developed an algorithm to quickly generate ice structures containing ions and defects. This algorithm is provided as an independent software module that can be incorporated into crystal structure generation software. By doing so, it becomes possible to simulate ice crystals on a previously impossible scale.

The limit of macroscopic homogeneous ice nucleation at the nanoscale

Nucleation in small volumes of water has garnered renewed interest due to the relevance of pore condensation and freezing under conditions of low partial pressures of water, such as in the upper troposphere. Molecular simulations can in principle provide insight on this process at the molecular scale that is challenging to achieve experimentally. However, there are discrepancies in the literature as to whether the rate in confined systems is enhanced or suppressed relative to bulk water at the same temperature and pressure. In this study, we investigate the extent to which the size of the critical nucleus and the rate at which it grows in thin films of water are affected by the thickness of the film. Our results suggest that nucleation remains bulk-like in films that are barely large enough accommodate a critical nucleus. This conclusion seems robust to the presence of physical confining boundaries. We also discuss the difficulties in unambiguously determining homogeneous nucleation rates in nanoscale systems, owing to the challenges in defining the volume. Our results suggest any impact on a film's thickness on the rate is largely inconsequential for present day experiments.

Cage occupancies of CH4, CO2, and Xe hydrates: Mean field theory and grandcanonical Monte Carlo simulations

We propose a statistical mechanical theory for the thermodynamic stability of clathrate hydrates, considering the influence of the guest-guest interaction on the occupancies of the cages. A mean field approximation is developed to examine the magnitude of the influence. Our new method works remarkably well, which is manifested by two sorts of grandcanonical Monte Carlo (GCMC) simulations. One is full GCMC, and the other is designed in the present study for clathrate hydrates, called lattice-GCMC, in which each guest can be adsorbed at one of the centers of the cage. In the latter simulation, only the guest-guest interaction is explicitly treated, incorporating the host-guest interaction into the free energy of the cage occupation without other guests. Critical phenomena for guest species, such as large density fluctuations, are observed when the temperature is low or the guest-guest interaction is strong.

Efficiency and energy balance for substitution of CH4 in clathrate hydrates with CO2 under multiple-phase coexisting conditions

Many experimental and theoretical studies on CH4-CO2 hydrates have been performed aiming at the extraction of CH4 as a relatively clean energy resource and concurrent sequestration of CO2. However, vague or insufficient characterization of the environmental conditions prevents us from a comprehensive understanding of even equilibrium properties of CH4-CO2 hydrates for this substitution. We propose possible reaction schemes for the substitution, paying special attention to the coexisting phases, the aqueous and/or the fluid, where CO2 is supplied from and CH4 is transferred to. We address the two schemes for the substitution operating in three-phase and two-phase coexistence. Advantages and efficiencies of extracting CH4 in the individual scheme are estimated from the chemical potentials of all the components in all the phases involved in the substitution on the basis of a statistical mechanical theory developed recently. It is found that although substitution is feasible in the three-phase coexistence, its working window in temperature-pressure space is much narrower compared to the two-phase coexistence condition. Despite that the substitution normally generates only a small amount of heat, a large endothermic substitution is suggested in the medium pressure range, caused by the vaporization of liquid CO2 due to mixing with a small amount of the released CH4. This study provides the first theoretical framework toward the practical use of hydrates replacing CH4 with CO2 and serves as a basis for quantitative planning.

On the phase behaviors of CH4-CO2 binary clathrate hydrates: Two-phase and three-phase coexistences

We develop a statistical mechanical theory on clathrate hydrates in order to explore the phase behaviors of clathrate hydrates containing two kinds of guest species and apply it to CH4-CO2 binary hydrates. The two boundaries separating water and hydrate and hydrate and guest fluid mixtures are estimated, which are extended to the lower temperature and the higher pressure region far distant from the three-phase coexisting conditions. The chemical potentials of individual guest components can be calculated from free energies of cage occupations, which are available from intermolecular interactions between host water and guest molecules. This allows us to derive all thermodynamic properties pertinent to the phase behaviors in the whole space of thermodynamic variables of temperature, pressure, and guest compositions. It is found that the phase boundaries of CH4-CO2 binary hydrates with water and with fluid mixtures locate between simple CH4 and CO2 hydrates, but the composition ratios of CH4 guests in hydrates are disproportional to those in fluid mixtures. Such differences arise from the affinities of each guest species to the large and small cages of CS-I hydrates and significantly affect occupation of each cage type, which results in a deviation of the guest composition in hydrates from that in fluid on the two-phase equilibrium conditions. The present method provides a basis for the evaluation of the efficiency of the guest CH4 replacement to CO2 at the thermodynamic limit.

Medium-density amorphous ice

Amorphous ices govern a range of cosmological processes and are potentially key materials for explaining the anomalies of liquid water. A substantial density gap between low-density and high-density amorphous ice with liquid water in the middle is a cornerstone of our current understanding of water. However, we show that ball milling "ordinary" ice Ih at low temperature gives a structurally distinct medium-density amorphous ice (MDA) within this density gap. These results raise the possibility that MDA is the true glassy state of liquid water or alternatively a heavily sheared crystalline state. Notably, the compression of MDA at low temperature leads to a sharp increase of its recrystallization enthalpy, highlighting that H2O can be a high-energy geophysical material.

A Formulation of the Many-Body Expansion (MBE) for Periodic Systems: Application to Several Ice Phases

We introduce a new formulation of the many-body expansion (MBE) for periodic systems and apply it to 7 ice polymorphs (Ih, II, VIII, IX, XIII, XIV, and XV). This new formulation is built via a hierarchical procedure that connects gas-phase clusters that mimic unit cells over finite supercells to infinite solids. For periodic systems, the method is validated by showing that the lattice energies computed up to the 4-body in the MBE reproduce the lattice energies obtained using periodic boundary conditions with an Ewald summation for the 7 ice polymorphs. This development makes it possible to quantify, for the first time, the many-body contributions to the lattice energy of various ice polymorphs, which vary significantly among the 7 ice phases, amounting to between 7 and 24% of the total lattice energies. This development opens the door for obtaining insights into solid-state properties, while leveraging the computational benefits of the MBE.

Accurate crystal structure of ice VI from X-ray diffraction with Hirshfeld atom refinement

Water is an essential chemical compound for living organisms, and twenty of its different crystal solid forms (ices) are known. Still, there are many fundamental problems with these structures such as establishing the correct positions and thermal motions of hydrogen atoms. The list of ice structures is not yet complete as DFT calculations have suggested the existence of additional and - to date - unknown phases. In many ice structures, neither neutron diffraction nor DFT calculations nor X-ray diffraction methods can easily solve the problem of hydrogen atom disorder or accurately determine their anisotropic displacement parameters (ADPs). Here, accurate crystal structures of H2O, D2O and mixed (50%H2O/50%D2O) ice VI obtained by Hirshfeld atom refinement (HAR) of high-pressure single-crystal synchrotron and laboratory X-ray diffraction data are presented. It was possible to obtain O-H/D bond lengths and ADPs for disordered hydrogen atoms which are in good agreement with the corresponding single-crystal neutron diffraction data. These results show that HAR combined with X-ray diffraction can compete with neutron diffraction in detailed studies of polymorphic forms of ice and crystals of other hydrogen-rich compounds. As neutron diffraction is relatively expensive, requires larger crystals which can be difficult to obtain and access to neutron facilities is restricted, cheaper and more accessible X-ray measurements combined with HAR can facilitate the verification of the existing ice polymorphs and the quest for new ones.

Phase diagram of the TIP4P/Ice water model by enhanced sampling simulations

We studied the phase diagram for the TIP4P/Ice water model using enhanced sampling molecular dynamics simulations. Our approach is based on the calculation of ice-liquid free energy differences from biased coexistence simulations that sample reversibly the melting and growth of layers of ice. We computed a total of 19 melting points for five different ice polymorphs which are in excellent agreement with the melting lines obtained from the integration of the Clausius-Clapeyron equation. For proton-ordered and fully proton-disordered ice phases, the results are in very good agreement with previous calculations based on thermodynamic integration. For the partially-proton-disordered ice III, we find a large increase in stability that is in line with previous observations using direct coexistence simulations for the TIP4P/2005 model. This issue highlights the robustness of the approach employed here for ice polymorphs with diverse degrees of proton disorder. Our approach is general and can be applied to the calculation of other complex phase diagrams.

Capturing Individual Hydrogen Bond Strengths in Ices via Periodic Local Vibrational Mode Theory: Beyond the Lattice Energy Picture

Local stretching force constants derived from periodic local vibrational modes at the vdW-DF2 density functional level have been employed to quantify the intrinsic hydrogen bond strength of 16 ice polymorphs, ices Ih, II, III, IV, V, VI, VII, VIII, IX, XI, XII, XIII, XIV, XV, XVII, and XIX, that are stable under ambient to elevated pressures. Based on this characterization on 1820 hydrogen bonds, relationships between local stretching force constants and structural parameters such as hydrogen bond length and angle were identified. Moreover, different bond strength distributions, from uniform to inhomogeneous, were observed for the 16 ices and could be explained in relation to different local structural elements within ices, that is, rings, that consist of different hydrogen bond types. In addition, criteria for the classification of hydrogen bonds as strong, intermediate, and weak were introduced. The latter was used to explore a different dimension of the water-ice phase diagram. These findings will provide important guidelines for assessing the credibility of new ice structures.

On the role of intermolecular vibrational motions for ice polymorphs. III. Mode characteristics associated with negative thermal expansion

Low-pressure ice forms, such as hexagonal and cubic ice, expand on cooling below temperature 60 K. This negative thermal expansivity has been explored in terms of phonon frequency modulation with varying volume and attributed to the negative Grüneisen parameters unique mostly to tetrahedrally coordinated substances. However, an underlying mechanism for the negative Grüneisen parameters has not been known except some schematic analyses. We investigate in this study the characteristics of the intermolecular vibrational modes whose Grüneisen parameters are negative by examining the individual vibrational modes rigorously. It is found that the low frequency modes below 100 cm^-1, which we explicitly show are mostly bending motions of three hydrogen-bonded molecules, necessarily accompany elongation of the hydrogen bond length at peak amplitudes compared with that at the equilibrium position in executing the vibrational motions. The elongation gives rise to a decrease in the repulsive interaction while an increase in the Coulombic one. The decrease in the repulsive interaction is relaxed substantially by expansion due to its steep slope against molecular separation compared with the sluggish increase in the Coulombic one, and therefore, the negative Grüneisen parameters are obtainable. This scenario is tested against some variants of cubic ice with various water potential models. It is demonstrated that four interaction-site models are suitable to describe the intermolecular vibrations and the thermal expansivity because of the moderate tendency to favor the tetrahedral coordination.

On the anomalous homogeneity of hydrogen-disordered ice and its origin

Pauling's successful estimation of the residual entropy of hydrogen-disordered ice was based on the homogeneity of the binding energy of individual water molecules in ice. However, it has not been explained why the binding energies are homogeneous although the pair interaction energy of hydrogen-bonded dimers distributes widely. Here, we provide a rationale for this phenomenon. The topological constraints imposed by the ice rules, in which water molecules form directed cyclic paths of hydrogen bonds, cancel out the variability of local interactions. We also show that the cancellation mechanism does not work due to some imperfect cyclic paths on the surface of ice. Such water molecules do not enjoy homogeneity in the bulk state and suffer from a wide spectrum in the binding energy.