Proton ordering energetics in ice phases

Imaging Low-Temperature Phases of Ice with Polarization-Resolved Hyperspectral Stimulated Raman Scattering Microscopy

Water freezes into various phases of ice under different cryogenic temperatures and pressure conditions, such as ice I_h and ice XI at normal pressure. Vibrational imaging with high spectral, spatial, and polarization resolutions could provide detailed information on ice, including the phases and crystal orientations at the microscopic level. Here, we report in situ stimulated Raman scattering (SRS) imaging of ice to analyze the vibrational spectral changes of the OH stretching modes associated with the phase transition between ice I_h and ice XI. In addition, polarization-resolved measurements were performed to reveal the microcrystal orientations of the two phases of ice, with the spatial-dependent anisotropy pattern indicating the inhomogeneous distribution of their orientations. Furthermore, the angular patterns were theoretically explained by third-order nonlinear optics with the known crystal symmetries of the ice phases. Our work may provide new opportunities to investigate many intriguing physical chemistry properties of ice under low-temperature conditions.

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.

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.

Prediction of properties from first principles with quantitative accuracy: six representative ice phases

Based on a high-level MP2 theory with the fragment approach, the crystal structure, vibration spectra and phase transitions of six representative ice phases (II, VI, VII, VIII, IX, and XV) are predicted.

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.

Modeling Molecular Interactions in Water: From Pairwise to Many-Body Potential Energy Functions

Almost 50 years have passed from the first computer simulations of water, and a large number of molecular models have been proposed since then to elucidate the unique behavior of water across different phases. In this article, we review the recent progress in the development of analytical potential energy functions that aim at correctly representing many-body effects. Starting from the many-body expansion of the interaction energy, specific focus is on different classes of potential energy functions built upon a hierarchy of approximations and on their ability to accurately reproduce reference data obtained from state-of-the-art electronic structure calculations and experimental measurements. We show that most recent potential energy functions, which include explicit short-range representations of two-body and three-body effects along with a physically correct description of many-body effects at all distances, predict the properties of water from the gas to the condensed phase with unprecedented accuracy, thus opening the door to the long-sought "universal model" capable of describing the behavior of water under different conditions and in different environments.

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.

Probing the structural and dynamical properties of liquid water with models including non-local electron correlation

Water is a ubiquitous liquid that displays a wide range of anomalous properties and has a delicate structure that challenges experiment and simulation alike. The various intermolecular interactions that play an important role, such as repulsion, polarization, hydrogen bonding, and van der Waals interactions, are often difficult to reproduce faithfully in atomistic models. Here, electronic structure theories including all these interactions at equal footing, which requires the inclusion of non-local electron correlation, are used to describe structure and dynamics of bulk liquid water. Isobaric-isothermal (NpT) ensemble simulations based on the Random Phase Approximation (RPA) yield excellent density (0.994 g/ml) and fair radial distribution functions, while various other density functional approximations produce scattered results (0.8-1.2 g/ml). Molecular dynamics simulation in the microcanonical (NVE) ensemble based on Møller-Plesset perturbation theory (MP2) yields dynamical properties in the condensed phase, namely, the infrared spectrum and diffusion constant. At the MP2 and RPA levels of theory, ice is correctly predicted to float on water, resolving one of the anomalies as resulting from a delicate balance between van der Waals and hydrogen bonding interactions. For several properties, obtaining quantitative agreement with experiment requires correction for nuclear quantum effects (NQEs), highlighting their importance, for structure, dynamics, and electronic properties. A computed NQE shift of 0.6 eV for the band gap and absorption spectrum illustrates the latter. Giving access to both structure and dynamics of condensed phase systems, non-local electron correlation will increasingly be used to study systems where weak interactions are of paramount importance.

Ferroelectricity in high-density H2O ice

The origin of longstanding anomalies in experimental studies of the dense solid phases of H2O ices VII, VIII, and X is examined using a combination of first-principles theoretical methods. We find that a ferroelectric variant of ice VIII is energetically competitive with the established antiferroelectric form under pressure. The existence of domains of the ferroelectric form within anti-ferroelectric ice can explain previously observed splittings in x-ray diffraction data. The ferroelectric form is stabilized by density and is accompanied by the onset of spontaneous polarization. The presence of local electric fields triggers the preferential parallel orientation of the water molecules in the structure, which could be stabilized in bulk using new high-pressure techniques.

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.

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.

Six-site polarizable model of water based on the classical Drude oscillator

A polarizable water model, SWM6, was developed and optimized for liquid phase simulations under ambient conditions. Building upon the previously developed SWM4-NDP model, additional sites representing oxygen lone-pairs were introduced. The geometry of the sites is assumed to be rigid. Considering the large number of adjustable parameters, simulated annealing together with polynomial fitting was used to facilitate model optimization. The new water model was shown to yield the correct self-diffusion coefficient after taking the system size effect into account, and the dimer geometry is better reproduced than in the SWM4 models. Moreover, the experimental oxygen-oxygen radial distribution is better reproduced, indicating that the new model more accurately describes the local hydrogen bonding structure of bulk phase water. This was further validated by its ability to reproduce the experimental nuclear magnetic shielding and related chemical shift of the water hydrogen in the bulk phase, a property sensitive to the local hydrogen bonding structure. In addition, comparison of the liquid properties of the SWM6 model is made with those of a number of widely used additive and polarizable models. Overall, improved balance between the description of monomer, dimer, clustered, and bulk phase water is obtained with the new model compared to its SWM4-NDP polarizable predecessor, though application of the model requires an approximately twofold increase on computational resources.

Large variation of vacancy formation energies in the surface of crystalline ice

Resolving the atomic structure of the surface of ice particles within clouds, over the temperature range encountered in the atmosphere and relevant to understanding heterogeneous catalysis on ice, remains an experimental challenge. By using first-principles calculations, we show that the surface of crystalline ice exhibits a remarkable variance in vacancy formation energies, akin to an amorphous material. We find vacancy formation energies as low as ~0.1-0.2 eV, which leads to a higher than expected vacancy concentration. Because a vacancy's reactivity correlates with its formation energy, ice particles may be more reactive than previously thought. We also show that vacancies significantly reduce the formation energy of neighbouring vacancies, thus facilitating pitting and contributing to pre-melting and quasi-liquid layer formation. These surface properties arise from proton disorder and the relaxation of geometric constraints, which suggests that other frustrated materials may possess unusual surface characteristics.

Surface energy and surface proton order of the ice Ih basal and prism surfaces

Density-functional theory (DFT) is used to examine the basal and prism surfaces of ice Ih. Similar surface energies are obtained for the two surfaces; however, in each case a strong dependence of the surface energy on surface proton order is identified. This dependence, which can be as much as 50% of the absolute surface energy, is significantly larger than the bulk dependence (<1%) on proton order, suggesting that the thermodynamic ground state of the ice surface will remain proton ordered well above the bulk order-disorder temperature of about 72 K. On the basal surface this suggestion is supported by Monte Carlo simulations with an empirical potential and solution of a 2D Ising model with nearest neighbor interactions taken from DFT. Order parameters that define the surface energy of each surface in terms of nearest neighbor interactions between dangling OH bonds (those which point out of the surface into vacuum) have been identified and are discussed. Overall, these results suggest that proton order-disorder effects have a profound impact on the stability of ice surfaces and will most likely have an effect on ice surface reactivity as well as ice crystal growth and morphology.

Surface energy and surface proton order of ice Ih

Ice Ih is comprised of orientationally disordered water molecules giving rise to positional disorder of the hydrogen atoms in the hydrogen bonded network of the lattice. Here we arrive at a first principles determination of the surface energy of ice Ih and suggest that the surface of ice is significantly more proton ordered than the bulk. We predict that the proton order-disorder transition, which occurs in the bulk at approximately 72 K, will not occur at the surface at any temperature below surface melting. An order parameter which defines the surface energy of ice Ih surfaces is also identified.

The melting point of hexagonal ice (Ih) is strongly dependent on the quadrupole of the water models

It is shown that quadrupolar interactions play a determinant role in the melting temperatures of common water models and that there is a simple relationship between the strength of the quadrupolar forces and the position of the negative charge; our conclusion is that acceptable predictions for the melting temperature can only be obtained when the negatively charged site is shifted from the oxygen atom towards the hydrogens.

A Blind Structure Prediction of Ice XIV

Evidence points to several hydrogen ordered ice phases of ice XII that exhibit topologically distinct hydrogen networks from one another and which are formed under kinetically controlled conditions.