Direct Visualization of Molecular Stacking in Quasi-2D Hexagonal Ice

Understanding ice nucleation and growth is of great interest to researchers due to its importance in the biological, cryopreservation, and environmental fields. However, microstructural investigations of ice on the molecular scale are still lacking. In this paper, a simple method is proposed to prepare quasi-2-dimensional ice Ih films, which have been characterized via cryogenic transmission electron microscope. The intersecting stacking faults of basal (BSF) and prismatic (PSF) types have been directly visualized and resolved with a notable first-time report of PSF in ice Ih. Moreover, the possible growth pathways of BSF, namely, the Ic phase, were elucidated by the theoretical calculations and the chair conformation of H2O molecules. This study offers valuable insights that can enhance researchers' understanding of the growth kinetics of crystalline ice.

Phase Transition between Crystalline Variants of Ordinary Ice

Water is one of the most abundant molecules on Earth. However, this common and "simple" material has more than 18 different phases, which poses a great challenge to theoretically study the nature of water and ice. We designed two reaction coordinates that can distinguish between water and various ice states and used them to efficiently sample all possible states of the system in all-atom molecular dynamics simulation at ambient temperature and pressure. Various structural and thermodynamics properties, including the water-ice phase diagrams, can thus be calculated. We also present a simple model that successfully explains the thermodynamic stability of different ice states. Our work provides effective methods and data for theoretical studies of different phases of water and ice.

Proton strings and rings in atypical nucleation of ferroelectricity in ice

Ordinary ice has a proton-disordered phase which is kinetically metastable, unable to reach, spontaneously, the ferroelectric (FE) ground state at low temperature where a residual Pauling entropy persists. Upon light doping with KOH at low temperature, the transition to FE ice takes place, but its microscopic mechanism still needs clarification. We introduce a lattice model based on dipolar interactions plus a competing, frustrating term that enforces the ice rule (IR). In the absence of IR-breaking defects, standard Monte Carlo (MC) simulation leaves this ice model stuck in a state of disordered proton ring configurations with the correct Pauling entropy. A replica exchange accelerated MC sampling strategy succeeds, without open path moves, interfaces, or off-lattice configurations, in equilibrating this defect-free ice, reaching its low-temperature FE order through a well-defined first-order phase transition. When proton vacancies mimicking the KOH impurities are planted into the IR-conserving lattice, they enable standard MC simulation to work, revealing the kinetics of evolution of ice from proton disorder to partial FE order below the transition temperature. Replacing ordinary nucleation, each impurity opens up a proton ring generating a linear string, an actual FE hydrogen bond wire that expands with time. Reminiscent of those described for spin ice, these impurity-induced strings are proposed to exist in doped water ice too, where IRs are even stronger. The emerging mechanism yields a dependence of the long-time FE order fraction upon dopant concentration, and upon quenching temperature, that compares favorably with that known in real-life KOH doped ice.

Identification of synthesisable crystalline phases of water – a prototype for the challenges of computational materials design

We discuss the identification of experimentally realisable crystalline phases of water to outline and contextualise some of the diverse building blocks of a computational materials design process.

Computational Prediction of Novel Ice Phases: A Perspective

Although computational prediction of new ice phases is a niche field in water science, the scientific subject itself is representative of two important areas in physical chemistry, namely, statistical thermodynamics and molecular simulations. The prediction of a variety of novel ice phases has also attracted general public interest since the 1980s. In particular, the prediction of low-dimensional ice phases has gained momentum since the confirmation of a number of low-dimensional "computer ice" phases in the laboratory over the past decade. In this Perspective, the research advancements in computational prediction of novel ice phases over the past few years are reviewed. Particular attention is placed on new ice phases whose physical properties or dimensional structures are distinctly different from conventional bulk ices. Specific topics include the (i) formation of superionic ices, (ii) electrofreezing of water under high pressure and in a high external electric field, (iii) prediction of low-density porous ice at strongly negative pressure, (iv) ab initio computational study of two-dimensional (2D) ice under nanoscale confinement, and (v) 2D ices formed on a solid surface near ambient temperature without nanoscale confinement. Clearly, the formation of most of these novel ice phases demands certain extreme conditions. Ongoing challenges and new opportunities for predicting new ice phases from either classical molecular dynamics simulation or high-level ab initio computation are discussed.

Cubic ice Ic without stacking defects obtained from ice XVII

Amongst the more than 18 different forms of water ice, only the common hexagonal phase and the cubic phase are present in nature on Earth. Nonetheless, it is now widely recognized that all samples of 'cubic ice' discovered so far do not have a fully cubic crystal structure but instead are stacking-disordered forms of ice I (namely, ice Isd), which contain both hexagonal and cubic stacking sequences of hydrogen-bonded water molecules. Here, we describe a method to obtain large quantities of cubic ice Ic with high structural purity. Cubic ice Ic is formed by heating a powder of D₂O ice XVII obtained from annealing of pristine C₀ hydrate samples under dynamic vacuum. Neutron diffraction experiments performed on two different instruments and Raman spectroscopy measurements confirm the structural purity of the cubic ice, Ic. These findings contribute to a better understanding of ice I polymorphism and the existence of the two natural ice forms.

Hydrogen polarity of interfacial water regulates heterogeneous ice nucleation

Using all-atomic molecular dynamics (MD) simulations, we show that the structure of interfacial water (IW) induced by substrates characterizes the ability of a substrate to nucleate ice. We probe the shape and structure of ice nuclei and the corresponding supercooling temperatures to measure the ability of IW with various hydrogen polarities for ice nucleation, and find that the hydrogen polarization of IW even with the ice-like oxygen lattice increases the contact angle of the ice nucleus on IW, thus lifting the free energy barrier of heterogeneous ice nucleation. The results show that not only the oxygen lattice order but the hydrogen disorder of IW on substrates are required to effectively facilitate the freezing of top water.

A new theoretical model for hexagonal ice, Ih(d), from first principles investigations

Due to their great importance in science, technology, and the life sciences, water and ice have been extensively investigated over many years. In particular, hexagonal ice Ih has been of great interest since it is the most common form of ice, and several modifications, Ih(a), Ih(b) and Ih(c) are known, whose structural details are still under discussion. In this study, we present an alternative theoretical model, called Ih(d), for the hexagonal ice modification in space group P63/mmc (no. 194), based on first-principles calculations that have been performed using DFT-LDA, GGA-PBE, and hybrid B3LYP and PBE0 functionals.

The role of nuclear quantum effects in the relative stability of hexagonal and cubic ice

At atmospheric pressure, hexagonal ice (I_h) is thermodynamically stable relative to cubic ice (I_c), although the magnitude and underlying physical origin of this stability difference are not well defined. Pure I_c crystals are not accessible experimentally, and hence computer simulations have often been used to interrogate the relative stabilities of I_h and I_c; however, these simulations are dominated by molecular interaction models that ignore the intramolecular flexibility of individual water molecules, do not describe intermolecular hydrogen-bonding with sufficient accuracy, or ignore the role of nuclear quantum effects (NQEs) such as zero-point energy. Here, we show that when comparing the relative stability of I_h and I_c using a flexible, anharmonic molecular interaction model, while also accurately accounting for NQEs, a new picture emerges: I_h is stabilized relative to I_c as a result of subtle differences in the intramolecular geometries and intermolecular interactions of water molecules which are modulated by NQEs. Our simulations hence suggest that NQEs are a major contributor to the stabilization of I_h under terrestrial conditions and thus contribute to the well-known hexagonal (sixfold) symmetry of ice crystals.

An ultralow-density porous ice with the largest internal cavity identified in the water phase diagram

The recent back-to-back findings of low-density porous ice XVI and XVII have rekindled the century-old field of the solid-state physics and chemistry of water. Experimentally, both ice XVI and XVII crystals can be produced by extracting guest atoms or molecules enclosed in the cavities of preformed ice clathrate hydrates. Herein, we examine more than 200 hypothetical low-density porous ices whose structures were generated according to a database of zeolite structures. Hitherto unreported porous EMT ice, named according to zeolite nomenclature, is identified to have an extremely low density of 0.5 g/cm3 and the largest internal cavity (7.88 Å in average radius). The EMT ice can be viewed as dumbbell-shaped motifs in a hexagonal close-packed structure. Our first-principles computations and molecular dynamics simulations confirm that the EMT ice is stable under negative pressures and exhibits higher thermal stability than other ultralow-density ices. If all cavities are fully occupied by hydrogen molecules, the EMT ice hydrate can easily outperform the record hydrogen storage capacity of 5.3 wt % achieved with sII hydrogen hydrate. Most importantly, in the reconstructed temperature-pressure (T-P) phase diagram of water, the EMT ice is located at deeply negative pressure regions below ice XVI and at higher temperature regions next to FAU. Last, the phonon spectra of empty-sII, FAU, EMT, and other zeolite-like ice structures are computed by using the dispersion corrected vdW-DF2 functional. Compared with those of ice XI (0.93 g/cm3), both the bending and stretching vibrational modes of the EMT ice are blue-shifted due to their weaker hydrogen bonds.

Room temperature electrofreezing of water yields a missing dense ice phase in the phase diagram

Water can freeze into diverse ice polymorphs depending on the external conditions such as temperature (T) and pressure (P). Herein, molecular dynamics simulations show evidence of a high-density orthorhombic phase, termed ice χ, forming spontaneously from liquid water at room temperature under high-pressure and high external electric field. Using free-energy computations based on the Einstein molecule approach, we show that ice χ is an additional phase introduced to the state-of-the-art T–P phase diagram. The χ phase is the most stable structure in the high-pressure/low-temperature region, located between ice II and ice VI, and next to ice V exhibiting two triple points at 6.06 kbar/131.23 K and 9.45 kbar/144.24 K, respectively. A possible explanation for the missing ice phase in the T–P phase diagram is that ice χ is a rare polarized ferroelectric phase, whose nucleation/growth occurs only under very high electric fields.

Water can crystallize in different ice polymorphs according to temperature and pressure conditions. Here the authors predict by molecular dynamics simulations a new ice phase spontaneously forming at room temperature under high pressure and high electric field.

Ab initio thermodynamics of liquid and solid water

Thermodynamic properties of liquid water as well as hexagonal (Ih) and cubic (Ic) ice are predicted based on density functional theory at the hybrid-functional level, rigorously taking into account quantum nuclear motion, anharmonic fluctuations, and proton disorder. This is made possible by combining advanced free-energy methods and state-of-the-art machine-learning techniques. The ab initio description leads to structural properties in excellent agreement with experiments and reliable estimates of the melting points of light and heavy water. We observe that nuclear-quantum effects contribute a crucial [Formula: see text] to the stability of ice Ih, making it more stable than ice Ic. Our computational approach is general and transferable, providing a comprehensive framework for quantitative predictions of ab initio thermodynamic properties using machine-learning potentials as an intermediate step.

Is High-Density Amorphous Ice Simply a "Derailed" State along the Ice I to Ice IV Pathway?

The structural nature of high-density amorphous ice (HDA), which forms through low-temperature pressure-induced amorphization of the "ordinary" ice I, is heavily debated. Clarifying this question is important for understanding not only the complex condensed states of H₂O but also in the wider context of pressure-induced amorphization processes, which are encountered across the entire materials spectrum. We first show that ammonium fluoride (NH₄F), which has a similar hydrogen-bonded network to ice I, also undergoes a pressure collapse upon compression at 77 K. However, the product material is not amorphous but NH₄F II, a high-pressure phase isostructural with ice IV. This collapse can be rationalized in terms of a highly effective mechanism. In the case of ice I, the orientational disorder of the water molecules leads to a deviation from this mechanism, and we therefore classify HDA as a "derailed" state along the ice I to ice IV pathway.

Orbital Dimer Model for the Spin-Glass State in Y_{2}Mo_{2}O_{7}

The formation of a spin glass generally requires that magnetic exchange interactions are both frustrated and disordered. Consequently, the origin of spin-glass behavior in Y_{2}Mo_{2}O_{7}-in which magnetic Mo^{4+} ions occupy a frustrated pyrochlore lattice with minimal compositional disorder-has been a longstanding question. Here, we use neutron and x-ray pair-distribution function (PDF) analysis to develop a disorder model that resolves apparent incompatibilities between previously reported PDF, extended x-ray-absorption fine structure spectroscopy, and NMR studies, and provides a new and physical explanation of the exchange disorder responsible for spin-glass formation. We show that Mo^{4+} ions displace according to a local "two-in-two-out" rule on each Mo_{4} tetrahedron, driven by orbital dimerization of Jahn-Teller active Mo^{4+} ions. Long-range orbital order is prevented by the macroscopic degeneracy of dimer coverings permitted by the pyrochlore lattice. Cooperative O^{2-} displacements yield a distribution of Mo-O-Mo angles, which in turn introduces disorder into magnetic interactions. Our study demonstrates experimentally how frustration of atomic displacements can assume the role of compositional disorder in driving a spin-glass transition.

Computational assignments of lattice vibrations of ice Ic

Herein,viathe first-principles density functional theory, CASTEP code, we investigated the 15 vibrational normal modes of ferroelectric hydrogen-ordered phase of ice Ic and the two peaks of hydrogen bond are clarified.

Raman and IR Spectra of Ice Ih and Ice XI with an Assessment of DFT Methods

IR and Raman spectroscopic technology can be directly used to identify the occurrence of ferroelectric ice XI in laboratory or extraterrestrial settings. The performance of 16 different DFT methods applied on the ice Ih, VIII, IX, and XI crystal phases is evaluated. Based on a selected DFT computational scheme, the IR and Raman spectra of ice Ih and XI are derived and compared. When the spectra, both IR and Raman, of ice Ih and ice XI are compared, the librational vibrations are found to be the most affected by the proton ordering. The spectroscopic fingerprint of ice XI can be used to distinguish ferroelectric ice XI from ice Ih in the universe. Furthermore, the existence of only one kind of H-bond in ice Ih is demonstrated from the overlapping subspectra for different types of H-bonded pair configurations in 16 isomers of ice Ih, which provides an illustration to the historic debate on whether one or two kinds of H-bonds existed in ice.

Incipient ferroelectricity of water molecules confined to nano-channels of beryl

Water is characterized by large molecular electric dipole moments and strong interactions between molecules; however, hydrogen bonds screen the dipole–dipole coupling and suppress the ferroelectric order. The situation changes drastically when water is confined: in this case ordering of the molecular dipoles has been predicted, but never unambiguously detected experimentally. In the present study we place separate H₂O molecules in the structural channels of a beryl single crystal so that they are located far enough to prevent hydrogen bonding, but close enough to keep the dipole–dipole interaction, resulting in incipient ferroelectricity in the water molecular subsystem. We observe a ferroelectric soft mode that causes Curie–Weiss behaviour of the static permittivity, which saturates below 10 K due to quantum fluctuations. The ferroelectricity of water molecules may play a key role in the functioning of biological systems and find applications in fuel and memory cells, light emitters and other nanoscale electronic devices.

Ferroelectric orders hardly exist in liquid or ice state of water, despite its enormous molecular electrical polarizability. Here, Gorshunov et al. report incipient ferroelectricity in chains of interacting water molecules by placing them in the structural channels of a beryl crystal.

Effects of the CO₂ Guest Molecule on the sI Clathrate Hydrate Structure

This paper analyzes the structural, energetic and mechanical properties of carbon dioxide hydrate clathrates calculated using finite cluster and periodic ab initio density-functional theory methodologies. Intermolecular interactions are described by the exchange-hole dipole moment method. The stability, gas saturation energetics, guest–host interactions, cage deformations, vibrational frequencies, and equation of state parameters for the low-pressure sI cubic phase of the CO₂@H₂O clathrate hydrate are presented. Our results reveal that: (i) the gas saturation process energetically favors complete filling; (ii) carbon dioxide molecules prefer to occupy the larger of the two cages in the sI structure; (iii) blue shifts occur in both the symmetric and antisymmetric stretching frequencies of CO₂ upon encapsulation; and (iv) free rotation of guest molecules is restricted to a plane parallel to the hexagonal faces of the large cages. In addition, we calculate the librational frequency of the hindered rotation of the guest molecule in the plane perpendicular to the hexagonal faces. Our calculated spectroscopic data can be used as signatures for the detection of clathrate hydrates in planetary environments.

Effect of salt on the H-bond symmetrization in ice

The richness of the phase diagram of water reduces drastically at very high pressures where only two molecular phases, proton-disordered ice VII and proton-ordered ice VIII, are known. Both phases transform to the centered hydrogen bond atomic phase ice X above about 60 GPa, i.e., at pressures experienced in the interior of large ice bodies in the universe, such as Saturn and Neptune, where nonmolecular ice is thought to be the most abundant phase of water. In this work, we investigate, by Raman spectroscopy up to megabar pressures and ab initio simulations, how the transformation of ice VII in ice X is affected by the presence of salt inclusions in the ice lattice. Considerable amounts of salt can be included in ice VII structure under pressure via rock-ice interaction at depth and processes occurring during planetary accretion. Our study reveals that the presence of salt hinders proton order and hydrogen bond symmetrization, and pushes ice VII to ice X transformation to higher and higher pressures as the concentration of salt is increased.

Communication: On the stability of ice 0, ice i, and I(h)

Using ab initio methods, we examine the stability of ice 0, a recently proposed tetragonal form of ice implicated in the homogeneous freezing of water [J. Russo, F. Romano, and H. Tanaka, Nat. Mater. 13, 670 (2014)]. Vibrational frequencies are computed across the complete Brillouin Zone using Density Functional Theory (DFT), to confirm mechanical stability and quantify the free energy of ice 0 relative to ice I(h). The robustness of this result is tested via dispersion corrected semi-local and hybrid DFT, and Quantum Monte-Carlo calculation of lattice energies. Results indicate that popular molecular models only slightly overestimate the stability of ice zero. In addition, we study all possible realisations of proton disorder within the ice zero unit cell, and identify the ground state as ferroelectric. Comparisons are made to other low density metastable forms of ice, suggesting that the ice i structure [C. J. Fennel and J. D. Gezelter, J. Chem. Theory Comput. 1, 662 (2005)] may be equally relevant to ice formation.

Periodic MP2, RPA, and Boundary Condition Assessment of Hydrogen Ordering in Ice XV

Ice XV is the hydrogen-ordered form of the ice VI phase whose structure was predicted to be Cc and ferroelectric using periodic DFT approaches. However, neutron diffraction and Raman spectroscopy data show the structure to have P1̅ symmetry and to be antiferroelectric. Recent work1 using fragment-based MP2 and CCSD(T) approaches predicts the experimental structure as the ground state. We have reconsidered this problem using fully periodic MP2 and RPA approaches and find that the ferroelectric Cc structure is the lowest energy configuration. However, ubiquitously employed tinfoil boundary conditions stabilize polar structures. We suggest that ferroelectric Cc crystals can grow within a paraelectric ice VI matrix but may become unstable once a fraction of the matrix has become hydrogen-ordered. The reduction in dielectric constant causes P1̅ and other structures with small polarization to become favored, providing a possible resolution between observation and theoretical predictions.

Hidden asymmetry of ice

Ice is a very complex and fundamentally important solid. In the present article, we review a new property of the hydrogen-bonded network in ice structures: an explicit nonequivalence of some antipodal configurations with the opposite direction of all hydrogen bonds (H-bonds). This asymmetry is most pronounced for the structures with considerable deviation of the H-bond network from the tetrahedral coordination. That is why we have investigated in detail four-coordinated ice nanostructures with no outer "dangling" hydrogen atoms, namely, ice bilayers and ice nanotubes consisting of stacked n-membered rings. The reason for this H-bonding asymmetry is a fundamental nonequivalence of the arrangements of water molecules in some antipodal configurations with the opposite direction of all H-bonds. For these configurations, the overall pictures of deviations of the hydrogen bonds from linearity are qualitatively different. We consider the reversal of all H-bonds as an additional nongeometric operation of symmetry, more precisely antisymmetry. It is not easy to find the explicit breaking of the symmetry of hydrogen bonding (H-symmetry) in the variety of all configurations. Therefore, this asymmetry may be named hidden.

Proton Ordering of Cubic Ice Ic: Spectroscopy and Computer Simulations

Several proton-disordered crystalline ice structures are known to proton order at sufficiently low temperatures, provided that the right preparation procedure is used. For cubic ice, ice Ic, however, no proton ordering has been observed so far. Here, we subject ice Ic to an experimental protocol similar to that used to proton order hexagonal ice. In situ FT-IR spectroscopy carried out during this procedure reveals that the librational band of the spectrum narrows and acquires a structure that is observed neither in proton-disordered ice Ic nor in ice XI, the proton-ordered variant of hexagonal ice. On the basis of vibrational spectra computed for ice Ic and four of its proton-ordered variants using classical molecular dynamics and ab initio simulations, we conclude that the features of our experimental spectra are due to partial proton ordering, providing the first evidence of proton ordering in cubic ice. We further find that the proton-ordered structure with the lowest energy is ferroelectric, while the structure with the second lowest energy is weakly ferroelectric. Both structures fit the experimental spectral similarly well such that no unique assignment of proton order is possible based on our results.