Quasi-harmonic approximation of thermodynamic properties of ice Ih, II, and III

Thermophysical properties of H2O and D2O ice Ih with contributions from proton disorder, quenching, relaxation, and extended defects: A model case for solids with quenching and relaxation

Application of the coherent thermodynamic model [W. Holzapfel and S. Klotz, J. Chem. Phys. 155, 024506 (2021)] for H2O ice Ih to the more detailed data for D2O ice Ih provides better insight into the contributions from quenched proton disorder and offers a new basis for understanding the apparent differences between the data for thermal expansion measured with neutron diffraction on polycrystalline samples [A. Fortes, Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater. 74, 196 (2018) and A. Fortes, Phys. Chem. Chem. Phys 21, 8264 (2019)] and macroscopic dilatation measurements on single crystals [D. Buckingham et al., Phys. Rev. Lett. 121, 185505 (2018)]. The comparison points to contributions from defects effecting the two techniques in different ways. The uncertainties in thermodynamic data due to the contributions from proton disorder and additional defects are compared with the "reference data" [R. Feistel and W. Wagner, J. Phys. Chem. Ref. Data 35, 1021 (2006)] for H2O ice Ih.

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.

Superconductivity Above 100 K Predicted in Carbon-Cage Network

To explore carbide superconductors with higher transition temperature, two novel carbon structures of cage-network are designed and their superconductivity is studied by doping metals. MC6 and MC10 are respectively identified as C24 and C32 cage-network structures. This study finds that both carbon structures drive strong electron-phonon interaction and can exhibit superconductivity above liquid nitrogen temperature. Importantly, the superconducting transition temperatures above 100 K are predicted to be achieved in C24 -cage-network systems doped by Na, Mg, Al, In, and Tl at ambient pressure, which is far higher than those in graphite, fullerene, and other carbides. Meanwhile, the superconductivity of cage-network carbides is also found to be sensitive to the electronegativity and concentration of dopant M. The result indicates that the higher transition temperatures can be obtained by optimizing the carbon-cage-network structures and the doping conditions. The study suggests that the carbon-cage-network structure is a direction to explore high-temperature superconducting carbides.

Computational Materials Design for Ceramic Nuclear Waste Forms Using Machine Learning, First-Principles Calculations, and Kinetics Rate Theory

Ceramic waste forms are designed to immobilize radionuclides for permanent disposal in geological repositories. One of the principal criteria for the effective incorporation of waste elements is their compatibility with the host material. In terms of performance under environmental conditions, the resistance of the waste forms to degradation over long periods of time is a critical concern when they are exposed to natural environments. Due to their unique crystallographic features and behavior in nature environment as exemplified by their natural analogues, ceramic waste forms are capable of incorporating problematic nuclear waste elements while showing promising chemical durability in aqueous environments. Recent studies of apatite- and hollandite-structured waste forms demonstrated an approach that can predict the compositions of ceramic waste forms and their long-term dissolution rate by a combination of computational techniques including machine learning, first-principles thermodynamics calculations, and modeling using kinetic rate equations based on critical laboratory experiments. By integrating the predictions of elemental incorporation and degradation kinetics in a holistic framework, the approach could be promising for the design of advanced ceramic waste forms with optimized incorporation capacity and environmental degradation performance. Such an approach could provide a path for accelerated ceramic waste form development and performance prediction for problematic nuclear waste elements.

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 (I_h) 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 I_h. While MD simulations (no NQE) predict that the density ρ(T) of LDA and ice I_h increases monotonically upon cooling, PIMD simulations indicate the presence of a density maximum in LDA and ice I_h. MD and PIMD simulations also predict a qualitatively different T-dependence for the thermal expansion coefficient α_P(T) and bulk modulus B(T) of both LDA and ice I_h. Remarkably, the ρ(T), α_P(T), and B(T) of LDA are practically identical to those of ice I_h. The origin of the observed NQE is due to the delocalization of the H atoms, which is identical in LDA and ice I_h. 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.

New Insights into the Volume Isotope Effect of Ice Ih from Polarizable Many-Body Potentials

The anomalous volume isotope effect (VIE) of ice Ih is calculated and analyzed based on the quasi-harmonic approximation to account for nuclear quantum effects in the Helmholtz free energy. While a lot of recently developed polarizable many-body potential functions give a normal VIE contrary to experimental results, we find that one of them, MB-pol, yields the anomalous VIE in good agreement with the most recent high-resolution neutron diffraction measurements─better than DFT calculations. The short-range three-body terms in the MB-pol function, which are fitted to CCSD(T) calculations, are found to have a surprisingly large influence. A vibrational mode group decomposition of the zero-point pressure together with a hitherto unconsidered benchmark value for the intramolecular stretching modes of H₂O ice Ih obtained from Raman spectroscopy data unveils the reason for the VIE: a delicate competition between the latter and the librations.

Molecular dynamics analysis of elastic properties and new phase formation during amorphous ices transformations

Unlike conventional first-order phase transitions, the kinetics of amorphous-amorphous transitions has been much less studied. The ultrasonic experiments on the transformations between low-density and high-density amorphous ice induced by pressure or heating provided the pressure and temperature dependencies of elastic moduli. In this article, we make an attempt to build a microscopic picture of these experimentally studied transformations using the molecular dynamics method with the TIP4P/Ice water model. We study carefully the dependence of the results of elastic constants calculations on the deformation rates. The system size effects are considered as well. The comparison with the experimental data enriches our understanding of the transitions observed. Our modeling gives new information about the formation mechanisms of new phase clusters during the transition between low-density and high-density amorphous ices. We analyse the applicability of the term “nucleation” for these processes.

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.

The microscopic origin of the anomalous isotopic properties of ice relies on the strong quantum anharmonic regime of atomic vibration

Water ice is a unique material presenting intriguing physical properties, such as negative thermal expansion and anomalous volume isotope effect (VIE). They arise from the interplay between weak hydrogen bonds and nuclear quantum fluctuations, making theoretical calculations challenging. Here, we employ the stochastic self-consistent harmonic approximation to investigate how thermal and quantum fluctuations affect the physical properties of ice XI with ab initio accuracy. Regarding the anomalous VIE, our work reveals that quantum effects on hydrogen are so strong to be in a nonlinear regime: When progressively increasing the mass of hydrogen from protium to infinity (classical limit), the volume first expands and then contracts, with a maximum slightly above the mass of tritium. We observe an anharmonic renormalization of about 10% in the bending and stretching phonon frequencies probed in IR and Raman experiments. For the first time, we report an accurate comparison of the low-energy phonon dispersion with the experimental data, possible only thanks to high-level accuracy in the electronic correlation and nuclear quantum and thermal fluctuations, paving the way for the study of thermal transport in ice from first-principles and the simulation of ice under pressure.

Coherent thermodynamic model for ice Ih-A model case for complex behavior

New data on the variation of the thermal expansion of ice Ih with temperature at ambient pressure together with new evaluations of the bulk modulus and earlier data for the heat capacity provide the basis for a coherent thermodynamic modeling of the main thermophysical properties of ice Ih over its whole range of stability. The quasi-harmonic approximation with one Debye term and seven Einstein terms, together with explicit anharmonicity, represents the dominant contribution next to minor "anomalies" from hydrogen ordering and lattice defects. The model accurately fits the main features of all experimental data and provides a basis for the comparison with earlier determinations of the phonon density of states and the Grüneisen parameters.

Progress and challenges in ab initio simulations of quantum nuclei in weakly bonded systems

Atomistic simulations based on the first-principles of quantum mechanics are reaching unprecedented length scales. This progress is due to the growth in computational power allied with the development of new methodologies that allow the treatment of electrons and nuclei as quantum particles. In the realm of materials science, where the quest for desirable emergent properties relies increasingly on soft weakly bonded materials, such methods have become indispensable. In this Perspective, an overview of simulation methods that are applicable for large system sizes and that can capture the quantum nature of electrons and nuclei in the adiabatic approximation is given. In addition, the remaining challenges are discussed, especially regarding the inclusion of nuclear quantum effects (NQEs) beyond a harmonic or perturbative treatment, the impact of NQEs on electronic properties of weakly bonded systems, and how different first-principles potential energy surfaces can change the impact of NQEs on the atomic structure and dynamics of weakly bonded systems.

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 α_P(T), isothermal compressibility κ_T(T), isobaric heat capacity C_P(T), and static dielectric constant ε(T). While these properties are in excellent [α_P(T) and κ_T(T)] or semi-quantitative agreement [C_P(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 C_P(T) and κ_T(T) at 1 bar. Consistent with this hypothesis and in particular, with experiments, we find a maximum in the κ_T(T) of q-TIP4P/F light and heavy water at T≈ 230-235 K. No maximum in C_P(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 C_P(T), D(T), and structural properties being the only (expected) exceptions.

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.

Calorimetric Signature of Deuterated Ice II: Turning an Endotherm to an Exotherm

Calorimetric studies on ice II reveal a surprising H₂O/D₂O isotope effect. While the ice II to ice Ic transition is endothermic for H₂O, it is exothermic for D₂O samples. The transition enthalpies are +40 and -140 J/mol, respectively, where such a sign change upon isotope substitution is unprecedented in ice research. To understand the observations we employ force field calculations using two water models known to perform well for H₂O ice phases and their vibrational properties. These simulations reveal that the isotope effect can be traced back to zero-point energy. q-TIP4P/F fares better and is able to account for approximately three-fourths of the isotope effect, while MB-pol only catches approximately one-third. Phonon and configurational entropy contributions are necessary to predict reasonable transition enthalpies, but they do not have an impact on the isotope effect. We suggest to use these calorimetric isotope data as a benchmark for water models.

On the role of intermolecular vibrational motions for ice polymorphs I: Volumetric properties of crystalline and amorphous ices

Intermolecular vibrations and volumetric properties are investigated using the quasiharmonic approximation with the TIP4P/2005, TIP4P/Ice, and SPC/E potential models for most of the known crystalline and amorphous ice forms that have hydrogen-disordering. The ice forms examined here cover low pressure ices (hexagonal and cubic ice I, XVI, and hypothetical dtc ice), medium pressure ices (III, IV, V, VI, XII, hydrogen-disordered variant of ice II), and high pressure ice (VII) as well as the low density and the high density amorphous forms. We focus on the thermal expansivities and the isothermal compressibilities in the low temperature regime over a wide range of pressures calculated via the intermolecular vibrational free energies. Negative thermal expansivity appears only in the low pressure ice forms. The sign of the thermal expansivity is elucidated in terms of the mode Grüneisen parameters of the low frequency intermolecular vibrational motions. Although the band structure for the low frequency region of the vibrational density of state in the medium pressure ice has a close resemblance to that in the low pressure ice, its response against volume variation is opposite. We reveal that the mixing of translational and rotational motions in the low frequency modes plays a crucial role in the appearance of the negative thermal expansivity in the low pressure ice forms. The medium pressure ices can be further divided into two groups in terms of the hydrogen-bond network flexibility, which is manifested in the properties on the molecular rearrangement against volume variation, notably the isothermal compressibility.

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.

Thermal Gradient Approach for the Quasi-harmonic Approximation and Its Application to Improved Treatment of Anisotropic Expansion

We present a novel approach to efficiently implement thermal expansion in the quasi-harmonic approximation (QHA) for both isotropic and more importantly, anisotropic expansion. In this approach, we rapidly determine a crystal's equilibrium volume and shape at a given temperature by integrating along the gradient of expansion from 0 Kelvin up to the desired temperature. We compare our approach to previous isotropic methods that rely on a brute-force grid search to determine the free energy minimum, which is infeasible to carry out for anisotropic expansion, as well as quasi-anisotropic approaches that take into account the contributions to anisotropic expansion from the lattice energy. We compare these methods for experimentally known polymorphs of piracetam and resorcinol and show that both isotropic methods agree to within error up to 300 K. Using the Grüneisen parameter causes up to 0.04 kcal/mol deviation in the Gibbs free energy, but for polymorph free energy differences there is a cancellation in error with all isotropic methods within 0.025 kcal/mol at 300 K. Anisotropic expansion allows the crystals to relax into lattice geometries 0.01-0.23 kcal/mol lower in energy at 300 K relative to isotropic expansion. For polymorph free energy differences all QHA methods produced results within 0.02 kcal/mol of each other for resorcinol and 0.12 kcal/mol for piracetam, the two molecules tested here, demonstrating a cancellation of error for isotropic methods. We also find that with expansion in more than a single volume variable, there is a non-negligible rate of failure of the basic approximations of QHA. Specifically, while expanding into new harmonic modes as the box vectors are increased, the system often falls into alternate, structurally distinct harmonic modes unrelated by continuous deformation from the original harmonic mode.

Path-integral simulation of graphene monolayers under tensile stress

Finite-temperature properties of graphene monolayers under tensile stress have been studied by path-integral molecular dynamics (PIMD) simulations.

How important is thermal expansion for predicting molecular crystal structures and thermochemistry at finite temperatures?

Molecular crystals expand appreciably upon heating due to both zero-point and thermal vibrational motion, yet this expansion is often neglected in molecular crystal modeling studies. Here, a quasi-harmonic approximation is coupled with fragment-based hybrid many-body interaction calculations to predict thermal expansion and finite-temperature thermochemical properties in crystalline carbon dioxide, ice Ih, acetic acid and imidazole. Fragment-based second-order Möller-Plesset perturbation theory (MP2) and coupled cluster theory with singles, doubles and perturbative triples [CCSD(T)] predict the thermal expansion and the temperature dependence of the enthalpies, entropies and Gibbs free energies of sublimation in good agreement with experiment. The errors introduced by neglecting thermal expansion in the enthalpy and entropy cancel somewhat in the Gibbs free energy. The resulting ∼ 1-2 kJ mol(-1) errors in the free energy near room temperature are comparable to or smaller than the errors expected from the electronic structure treatment, but they may be sufficiently large to affect free-energy rankings among energetically close polymorphs.

Evolution of Hydrogen Dynamics in Amorphous Ice with Density

The single-particle dynamics of hydrogen atoms in several of the amorphous ices are reported using a combination of deep inelastic neutron scattering (DINS) and inelastic neutron scattering (INS). The mean kinetic energies of the hydrogen nuclei are found to increase with increasing density, indicating the weakening of hydrogen bonds as well as a trend toward steeper and more harmonic hydrogen vibrational potential energy surfaces. DINS shows much more pronounced changes in the O-H stretching component of the mean kinetic energy going from low- to high-density amorphous ices than indicated by INS and Raman spectroscopy. This highlights the power of the DINS technique to retrieve accurate ground-state kinetic energies beyond the harmonic approximation. In a novel approach, we use information from DINS and INS to determine the anharmonicity constants of the O-H stretching modes. Furthermore, our experimental kinetic energies will serve as important benchmark values for path-integral Monte Carlo simulations.