Ice Ih anomalies: Thermal contraction, anomalous volume isotope effect, and pressure-induced amorphization

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.

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose-Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh-Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born-Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick's theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn-Luttinger-type nonconvergence.

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.

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.

Reduced-cost supercell approach for computing accurate phonon density of states in organic crystals

Phonon contributions to organic crystal structures and thermochemical properties can be significant, but computing a well-converged phonon density of states with lattice dynamics and periodic density functional theory (DFT) is often computationally expensive due to the need for large supercells. Using semi-empirical methods like density functional tight binding (DFTB) instead of DFT can reduce the computational costs dramatically, albeit with noticeable reductions in accuracy. This work proposes approximating the phonon density of states via a relatively inexpensive DFTB supercell treatment of the phonon dispersion that is then corrected by shifting the individual phonon modes according to the difference between the DFT and DFTB phonon frequencies at the Γ-point. The acoustic modes are then computed at the DFT level from the elastic constants. In several small-molecule crystal test cases, this combined approach reproduces DFT thermochemistry with kJ/mol accuracy and 1-2 orders of magnitude less computational effort. Finally, this approach is applied to computing the free energy differences between the five crystal polymorphs of oxalyl dihydrazide.

Anharmonic Phonon Dispersion in Polyethylene

The second-order Green's function method for anharmonic crystals has been applied to an infinite, periodic chain of polyethylene taking into account up to quartic force constants. The frequency-independent approximation to the Dyson self-energy gives rise to numerous divergent resonances, which are fortuitous. Instead, solving the Dyson equation self-consistently with a frequency-dependent self-energy resists divergences from resonances or zero-frequency acoustic vibrations. The calculated anharmonic phonon dispersion, which nonetheless displays many true resonances, and anharmonic phonon density of states furnish hitherto unknown details that explain smaller features of observed vibrational spectra.

Fantasy versus reality in fragment-based quantum chemistry

Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersystem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and therefore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial "free lunch" in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective.

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.

Accurate and precise lattice parameters of H2O and D2O ice Ihbetween 1.6 and 270 K from high-resolution time-of-flight neutron powder diffraction data

Accurate and precise lattice parameters for D2O and H2O varieties of hexagonal ice (ice Ih, space groupP63/mmc) have been obtained in the range 1.6 to 270 K. Precision of the lattice parameters (∼0.0002% inaand 0.0004% incfor D2O, 0.0008% inaand 0.0015% incfor H2O) is ensured by use of the time-of-flight method on one of the longest primary neutron flight-path instruments in the world, the High-Resolution Powder Diffractometer at the ISIS neutron source. These data provide a more precise description of the negative thermal expansion of the material at low temperatures than the previous synchrotron `gold standard' [Röttgeret al.(1994).Acta Cryst.B50, 644–648], including the region below 10 K where the lattice parameters saturate. The volume expansivity of both isotopologues turns negative below 59–60 K, in excellent agreement with a recent dilatometry study. The axial expansivities are highly isotropic (differing by < 1% in D2O ice Ih). Furthermore, thec/aratio of different D2O ice samples exhibit a statistically significant dispersion of ∼0.015% below 150 K that appears to depend on the thermal history of the sample, which disappears on warming above 150 K. Similarly, H2O ice exhibits a `kink' in thec/aratio at ∼115 K. The most plausible explanation is a freezing-in of the molecular reorientation process on cooling and subsequent relaxation on warming.

H/D isotope effect on the molar volume and thermal expansion of benzene

Time-of-flight neutron powder diffraction data have been collected from C₆H₆ and C₆D₆ between 10 and 276 K, revealing no cross-over in their molar volumes and an almost temperature invariant volume-isotope-effect, in contrast with previously published work.

Identifying pragmatic quasi-harmonic electronic structure approaches for modeling molecular crystal thermal expansion

Quasi-harmonic approaches provide an economical route to modeling the temperature dependence of molecular crystal structures and properties. Several studies have demonstrated good performance of these models, at least for rigid molecules, when using fragment-based approaches with correlated wavefunction techniques. Many others have found success employing dispersion-corrected density functional theory (DFT). Here, a hierarchy of models in which the energies, geometries, and phonons are computed either with correlated methods or DFT are examined to identify which combinations produce useful predictions for properties such as the molar volume, enthalpy, and entropy as a function of temperature. The results demonstrate that refining DFT geometries and phonons with single-point energies based on dispersion-corrected second-order Møller-Plesset perturbation theory can provide clear improvements in the molar volumes and enthalpies compared to those obtained from DFT alone. Predicted entropies, which are governed by vibrational contributions, benefit less clearly from the hybrid schemes. Using these hybrid techniques, the room-temperature thermochemistry of acetaminophen (paracetamol) is predicted to address the discrepancy between two experimental sublimation enthalpy measurements.

Ab initio thermodynamic properties and their uncertainties for crystalline α-methanol

To investigate the performance of quasi-harmonic electronic structure methods for modeling molecular crystals at finite temperatures and pressures, thermodynamic properties are calculated for the low-temperature α polymorph of crystalline methanol and their computational uncertainties are analyzed.