Anomalous proton dynamics in ice at low temperatures

Systematic analysis of electronic barrier heights and widths for concerted proton transfer in cyclic hydrogen bonded clusters: (HF)n, (HCl)n and (H2O)n where n = 3, 4, 5

The MP2 and CCSD(T) methods are paired with correlation consistent basis sets as large as aug-cc-pVQZ to optimize the structures of the cyclic minima for (HF)n, (HCl)n and (H2O)n where n = 3-5, as well as the corresponding transition states (TSs) for concerted proton transfer (CPT). MP2 and CCSD(T) harmonic vibrational frequencies confirm the nature of each minimum and TS. Both conventional and explicitly correlated CCSD(T) computations are employed to assess the electronic dissociation energies and barrier heights for CPT near the complete basis (CBS) limit for all 9 clusters. Results for (HF)n are consistent with prior studies identifying Cnh and Dnh point group symmetry for the minima and TSs, respectively. Our computations also confirm that CPT proceeds through Cs TS structures for the C1 minima of (H2O)3 and (H2O)5, whereas the process goes through a TS with D2d symmetry for the S4 global minimum of (H2O)4. This work corroborates earlier findings that the minima for (HCl)3, (HCl)4 and (HCl)5 have C3h, S4 and C1 point group symmetry, respectively, and that the Cnh structures are not minima for n = 4 and 5. Moreover, our computations show the TSs for CPT in (HCl)3, (HCl)4 and (HCl)5 have D3h, D2d, and C2 point group symmetry, respectively. At the CCSD(T) CBS limit, (HF)4 and (HF)5 have the smallest electronic barrier heights for CPT (≈15 kcal mol-1 for both), followed by the HF trimer (≈21 kcal mol-1). The barriers are appreciably higher for the other clusters (around 27 kcal mol-1 for (H2O)4 and (HCl)3; roughly 30 kcal mol-1 for (H2O)3, (H2O)5 and (HCl)4; up to 38 kcal mol-1 for (HCl)5). At the CBS limit, MP2 significantly underestimates the CCSD(T) barrier heights (e.g., by ca. 2, 4 and 7 kcal mol-1 for the pentamers of HF, H2O and HCl, respectively), whereas CCSD overestimates these barriers by roughly the same magnitude. Scaling the barrier heights and dissociation energies by the number of fragments in the cluster reveals strong linear relationships between the two quantities and with the magnitudes of the imaginary vibrational frequency for the TSs.

Networks of Hydrogen Bond Networks in Water Clusters

Water clusters play a prominent role in atmospheric and solution chemistry. Numerous arrangements of protons, H-bond configurations or networks, shape the cluster properties. Studies of small water clusters by cryogenic scanning tunneling microscopy and high-resolution rovibrational spectroscopy have established proton rearrangement mechanisms forming pathways between H-bond networks. The mechanisms, concerted tunneling in particular, describe the local processes connecting pairs of configurations. Here, proton rearrangement networks mapping these transformations are defined and explored to provide a global view of the H-bond configurations in clusters. The networks are constructed for clusters of different sizes and structures. Their analysis reveals an odd-even effect with respect to the number of water molecules, exponential growth of the small-world character, bimodality of the degree distributions, and gapped assortativity of the networks. The last two properties signify the unexpected division of H-bond configurations into two classes according to their network connectivity. The results demonstrate qualitative differences between proton rearrangement mechanisms, suggest a strong influence of the cluster structure. The generated networks are of interest as real-world models for network rewiring; they establish an alternative platform for studies of proton rearrangements in H-bonded systems.

Accurate calculation of tunneling splittings in water clusters using path-integral based methods

Tunneling splittings observed in molecular rovibrational spectra are significant evidence for tunneling motion of hydrogen nuclei in water clusters. Accurate calculations of the splitting sizes from first principles require a combination of high-quality inter-atomic interactions and rigorous methods to treat the nuclei with quantum mechanics. Many theoretical efforts have been made in recent decades. This Perspective focuses on two path-integral based tunneling splitting methods whose computational cost scales well with the system size, namely, the ring-polymer instanton method and the path-integral molecular dynamics (PIMD) method. From a simple derivation, we show that the former is a semiclassical approximation to the latter, despite that the two methods are derived very differently. Currently, the PIMD method is considered to be an ideal route to rigorously compute the ground-state tunneling splitting, while the instanton method sacrifices some accuracy for a significantly smaller computational cost. An application scenario of such a quantitatively rigorous calculation is to test and calibrate the potential energy surfaces of molecular systems by spectroscopic accuracy. Recent progress in water clusters is reviewed, and the current challenges are discussed.

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.

Collective Proton Transfers in Cyclic Water-Ammonia Tetramers: A Path Integral Machine-Learning Study

We present results from machine-learning-based path integral molecular dynamics simulations that describe isomerization paths articulated via collective proton transfers along mixed, cyclic tetramers combining water and ammonia at cryogenic conditions. The net result of such isomerizations is a reverse of the chirality of the global hydrogen-bonding architecture along the different cyclic moieties. In monocomponent tetramers, the classical free energy profiles associated with these isomerizations present the usual symmetric double-well characteristics whereas the reactive paths exhibit full concertedness among the different intermolecular transfer processes. Contrastingly, in mixed water/ammonia tetramers, the incorporation of a second component introduces imbalances in the strengths of the different hydrogen bonds leading to a partial loss of concertedness, most notably at the vicinity of the transition state. As such, the highest and lowest degrees of progression are registered along OH···N and O···HN coordinations, respectively. These characteristics lead to polarized transition state scenarios akin to solvent-separated ion-pair configurations. The explicit incorporation of nuclear quantum effects promotes drastic depletions in the activation free energies and modifications in the overall shape of the profiles which include central plateau-like stages, indicating the prevalence of deep tunneling regimes. On the other hand, the quantum treatment of the nuclei partially restores the degree of concertedness among the evolutions of the individual transfers.

Determination of concerted or stepwise mechanism of hydrogen tunneling from isotope effects: Departure between experiment and theory

Isotope substitution is an important experimental technique that offers deep insight into reaction mechanisms, as the measured kinetic isotope effects (KIEs) can be directly compared with theory. For multiple proton transfer processes, there are two types of mechanisms: stepwise transfer and concerted transfer. The Bell-Limbach model provides a simple theory to determine whether the proton transfer mechanism is stepwise or concerted from KIEs. Recent STM experiments have studied the proton switching process in water tetramers on NaCl(001). Theoretical studies predict that this process occurs via a concerted mechanism, however, the experimental KIEs resemble the Bell-Limbach model for stepwise tunneling, raising question on the underlying mechanism or the validity of the model. We study this system using ab initio instanton theory, and in addition to thermal rates, we also considered microcanonical rates, as well as tunneling splittings. Instanton theory predicts a concerted mechanism, and the KIEs for tunneling rates (both thermal and microcanonical) upon deuteration are consistent with the Bell-Limbach model for concerted tunneling, but could not explain the experiments. For tunneling splittings, partial and full deuteration changes the size of it in a similar fashion to how it changes the rates. We further examined the Bell-Limbach model in another system, porphycene, which has both stepwise and concerted tunneling pathways. The KIEs predicted by instanton theory are again consistent with the Bell-Limbach model. This study highlights differences between KIEs in stepwise and concerted tunneling, and the discrepancy between theory and recent STM experiments. New theory/experiments are desired to settle this problem.

Proton Transport and Related Chemical Processes of Ice

Excess protons play a key role in the chemical reactions of ice because of their exceptional mobility, even when the diffusion of atoms and molecules is suppressed in ice at low temperatures. This article reviews the current state of knowledge on the properties of excess protons in ice, with a focus on the involvement of protons in chemical reactions. The mechanism of efficient proton transport in ice, which involves a proton-hopping relay along the hydrogen-bond ice network and the reorientation of water, is discussed and compared with the inefficient transport of hydroxide in ice. Distinctly different properties of protons residing in the ice interior and on the ice surface are emphasized. Recent observations of the spontaneous occurrence of reactions in ice at low temperatures, which include the dissociation of protic acids and the hydrolysis of acidic oxides, are discussed with regard to the kinetic and thermodynamic effects of mobile protons on the promotion of unique chemical processes of ice.

Significance Of Nuclear Quantum Effects In Hydrogen Bonded Molecular Chains

In hydrogen-bonded systems, nuclear quantum effects such as zero-point motion and tunneling can significantly affect their material properties through underlying physical and chemical processes. Presently, direct observation of the influence of nuclear quantum effects on the strength of hydrogen bonds with resulting structural and electronic implications remains elusive, leaving opportunities for deeper understanding to harness their fascinating properties. We studied hydrogen-bonded one-dimensional quinonediimine molecular networks which may adopt two isomeric electronic configurations via proton transfer. Herein, we demonstrate that concerted proton transfer promotes a delocalization of π-electrons along the molecular chain, which enhances the cohesive energy between molecular units, increasing the mechanical stability of the chain and giving rise to distinctive electronic in-gap states localized at the ends. These findings demonstrate the identification of a class of isomeric hydrogen-bonded molecular systems where nuclear quantum effects play a dominant role in establishing their chemical and physical properties. This identification is a step toward the control of mechanical and electronic properties of low-dimensional molecular materials via concerted proton tunneling.

The history of spin ice

This review is a study of how the idea of spin ice has evolved over the years, with a focus on the scientific questions that have come to define the subject. Since our initial discovery of spin ice in 1997, there have been well over five thousand papers that discuss it, and in the face of such detail, it must be difficult for the curious observer to 'see the wood for the trees'. To help in this task, we go in search of the biggest insight to have emerged from the study of spin ice. On the way, we identify highlights and outstanding puzzles, and celebrate the inspirational role that Roger Cowley played in the early years.

Raman spectra study hydrogen bonds network in ice Ih with cooling

The Raman spectra of ice Ih (H₂O and HDO) in the temperatures range from 253 to 83 K are measured. The results show that Raman peaks shift to low- or high-wavenumber due to the influence of temperature on hydrogen bonds dynamics. Importantly, Raman shifts are linear relationship with temperatures and its slope fully reflects the change of hydrogen bonds length. Finally, Raman intensity of ice Ih dependent on temperatures are also discussed.

Emergence of correlated proton tunnelling in water ice

Several experimental and theoretical studies report instances of concerted or correlated multiple proton tunnelling in solid phases of water. Here, we construct a pseudo-spin model for the quantum motion of protons in a hexameric H₂O ring and extend it to open system dynamics that takes environmental effects into account in the form of O-H stretch vibrations. We approach the problem of correlations in tunnelling using quantum information theory in a departure from previous studies. Our formalism enables us to quantify the coherent proton mobility around the hexagonal ring by one of the principal measures of coherence, the l ₁ norm of coherence. The nature of the pairwise pseudo-spin correlations underlying the overall mobility is further investigated within this formalism. We show that the classical correlations of the individual quantum tunnelling events in long-time limit is sufficient to capture the behaviour of coherent proton mobility observed in low-temperature experiments. We conclude that long-range intra-ring interactions do not appear to be a necessary condition for correlated proton tunnelling in water ice.

Thermal Expansion of Single-Crystal H_{2}O and D_{2}O Ice Ih

Thermal expansion of H_{2}O and D_{2}O ice Ih with relative resolution of 1 ppb is reported. A large transition in the thermal expansion coefficient at 101 K in H_{2}O moves to 125 K in D_{2}O, revealing one of the largest-known isotope effects. Rotational oscillatory modes that couple poorly to phonons, i.e., lattice solitons, may be responsible.

Ionization of Ammonia Nanoices with Adsorbed Methanol Molecules

Large ammonia clusters represent a model system of ices that are omnipresent throughout the space. The interaction of ammonia ices with other hydrogen-boding molecules such as methanol or water and their behavior upon an ionization are thus relevant in the astrochemical context. In this study, ammonia clusters (NH₃) _N with the mean size N̅ ≈ 230 were prepared in molecular beams and passed through a pickup cell in which methanol molecules were adsorbed. At the highest exploited pickup pressures, the average composition of (NH₃) _N(CH₃OH) _M clusters was estimated to be N: M ≈ 210:10. On the other hand, the electron ionization of these clusters yielded about 75% of methanol-containing fragments (NH₃) _n(CH₃OH) _mH⁺ compared to 25% contribution of pure ammonia (NH₃) _nH⁺ ions. On the basis of this substantial disproportion, we propose the following ionization mechanism: The prevailing ammonia is ionized in most cases, resulting in NH₄⁺ core solvated most likely with four ammonia molecules, yielding the well-known "magic number" structure (NH₃)₄NH₄⁺. The methanol molecules exhibit a strong propensity for sticking to the fragment ion. We have also considered mechanisms of intracluster reactions. In most cases, proton transfer between ammonia units take place. The theoretical calculations suggested the proton transfer either from the methyl group or from the hydroxyl group of the ionized methanol molecule to ammonia to be the energetically open channels. However, the experiments with selectively deuterated methanols did not show any evidence for the D⁺ transfer from the CD₃ group. The proton transfer from the hydroxyl group could not be excluded entirely or confirmed unambiguously by the experiment.

Thermodynamic and kinetic isotope effects on the order-disorder transition of ice XIV to ice XII

Isotope effects accompanying the order-disorder transition of ice XIV to ice XII are studied using calorimetry, X-ray diffraction, and dielectric spectroscopy. Particular emphasis is placed on the impact of the cooling rate applied during high-pressure production and during ambient-pressure recooling on the degree of hydrogen order in the low-temperature ice XIV phase. For specimens from D2O, ordering is harder to achieve in the sense that despite smaller cooling rates, the degree of order is less than in crystals produced from H2O. The degree of ordering can be quantified in terms of the Pauling entropy using calorimetry and manifests itself in structural and dynamical features that were examined using X-ray diffraction and dielectric spectroscopy, respectively. In hydrogen chloride doped samples, H/D substitution was found to slow down the dipolar dynamics up to about 30-fold and shifts the order-disorder transition by 4-6 K. By contrast to earlier assumptions it is possible to reach a high degree of ordering also at ambient pressure, provided the cooling rate is small enough. That is, at ambient pressure, orthorhombic stress slows down the dipolar reorientation near the ordering transition by a factor of 300-2000 for H2O and 30-100 for D2O samples. Furthermore, by long-term storage of our samples at 77 K we have reached surprisingly large increases in degree of order. For the D2O samples we observed an unprecedented high order, corresponding to more than 45% of the Pauling entropy.

The collective and quantum nature of proton transfer in the cyclic water tetramer on NaCl(001)

Proton tunneling is an elementary process in the dynamics of hydrogen-bonded systems. Collective tunneling is known to exist for a long time. Atomistic investigations of this mechanism in realistic systems, however, are scarce. Using a combination of ab initio theoretical and high-resolution experimental methods, we investigate the role played by the protons on the chirality switching of a water tetramer on NaCl(001). Our scanning tunneling spectroscopies show that partial deuteration of the H₂O tetramer with only one D₂O leads to a significant suppression of the chirality switching rate at a cryogenic temperature (T), indicating that the chirality switches by tunneling in a concerted manner. Theoretical simulations, in the meantime, support this picture by presenting a much smaller free-energy barrier for the translational collective proton tunneling mode than other chirality switching modes at low T. During this analysis, the virial energy provides a reasonable estimator for the description of the nuclear quantum effects when a traditional thermodynamic integration method cannot be used, which could be employed in future studies of similar problems. Given the high-dimensional nature of realistic systems and the topology of the hydrogen-bonded network, collective proton tunneling may exist more ubiquitously than expected. Systems of this kind can serve as ideal platforms for studies of this mechanism, easily accessible to high-resolution experimental measurements.

Molecular Dynamics of Hexamethylbenzene at Low Temperatures: Evidence of Unconventional Magnetism Based on Rotational Motion of Protons

The types of magnetism known to date are all mainly based on contributions from electron motion. We show how rotational motion of protons (H⁺ ) within the methyl groups in hexamethylbenzene (C₆ (CH₃ )₆ ) also contribute significantly to the magnetic susceptibility. Starting from below 118 K, as the rotational motion of the methyl groups set in, an associated magnetic moment positive in nature due to charge of the protons renders the susceptibility to become anomalously dependent on temperature. Starting from 20 K, the susceptibility diverges with decreasing temperature indicative of spin-spin interactions between methyl groups aligned in a previously unclassified type of anti-ferromagnetic configuration. Complementary dielectric constant measurements also show the existence of magneto-dielectric coupling. Our findings allow for the study of strongly correlated systems that are based on a species that possesses much slower dynamics.

Perspective: Structure and dynamics of water at surfaces probed by scanning tunneling microscopy and spectroscopy

The detailed and precise understanding of water-solid interaction largely relies on the development of atomic-scale experimental techniques, among which scanning tunneling microscopy (STM) has proven to be a noteworthy example. In this perspective, we review the recent advances of STM techniques in imaging, spectroscopy, and manipulation of water molecules. We discuss how those newly developed techniques are applied to probe the structure and dynamics of water at solid surfaces with single-molecule and even submolecular resolution, paying particular attention to the ability of accessing the degree of freedom of hydrogen. In the end, we present an outlook on the directions of future STM studies of water-solid interfaces as well as the challenges faced by this field. Some new scanning probe techniques beyond STM are also envisaged.

Collective proton transfer in ordinary ice: local environments, temperature dependence and deuteration effects

Ordinary ice at low temperature: what about collective nuclear quantum effects in its chiral six rings?

Proton Conductivity in Phosphoric Acid: The Role of Quantum Effects

Phosphoric acid has one of the highest intrinsic proton conductivities of any known liquids, and the mechanism of this exceptional conductivity remains a puzzle. Our detailed experimental studies discovered a strong isotope effect in the conductivity of phosphoric acids caused by (i) a strong isotope shift of the glass transition temperature and (ii) a significant reduction of the energy barrier by zero-point quantum fluctuations. These results suggest that the high conductivity in phosphoric acids is caused by a very efficient proton transfer mechanism, which is strongly assisted by quantum effects.

Dielectric Anomaly in Ice near 20 K: Evidence of Macroscopic Quantum Phenomena

H2O is one of the most important substances needed in sustaining life; but not much is known about its ground state. Here a previously unidentified anomaly is identified in the form of a minimum in the imaginary part of the dielectric constant with respect to temperature near 20 K, while the real part remains monotonic. Isothermal dispersion and absorption measurements show coinciding results. For the case of heavy ice (D2O), no anomaly was identified, confirming an apparent isotope effect. Concerted quantum tunneling of protons is believed to be the main cause behind the reported anomaly. Our findings identify another system that exhibits macroscopic quantum phenomena that rarely occur in nature.

Anomalously large isotope effect in the glass transition of water

We present the discovery of an unusually large isotope effect in the structural relaxation and the glass transition temperature Tg of water. Dielectric relaxation spectroscopy of low-density as well as of vapor-deposited amorphous water reveal Tg differences of 10 ± 2 K between H2O and D2O, sharply contrasting with other hydrogen-bonded liquids for which H/D exchange increases Tg by typically less than 1 K. We show that the large isotope effect and the unusual variation of relaxation times in water at low temperatures can be explained in terms of quantum effects. Thus, our findings shed new light on water's peculiar low-temperature dynamics and the possible role of quantum effects in its structural relaxation, and possibly in dynamics of other low-molecular-weight liquids.

Exceptional isotopic-substitution effect: breakdown of collective proton tunneling in hexagonal ice due to partial deuteration

Multiple proton transfer controls many chemical reactions in hydrogen-bonded networks. However, in contrast to well-understood single proton transfer, the mechanisms of correlated proton transfer and of correlated proton tunneling in particular have remained largely elusive. Herein, fully quantized ab initio simulations are used to investigate H/D isotopic-substitution effects on the mechanism of the collective tunneling of six protons within proton-ordered cyclic water hexamers that are contained in proton-disordered ice, a prototypical hydrogen-bonded network. At the transition state, isotopic substitution leads to a Zundel-like complex, [HO⋅⋅⋅D⋅⋅⋅OH], which localizes ionic defects and thus inhibits perfectly correlated proton tunneling. These insights into fundamental aspects of collective proton tunneling not only rationalize recent neutron-scattering experiments, but also stimulate investigations into multiple proton transfer in hydrogen-bonded networks much beyond ice.

Quantum simulation of collective proton tunneling in hexagonal ice crystals

The effect of proton tunneling on many-body correlated proton transfer in hexagonal ice is investigated by quantum simulation. Classical single-particle hopping along individual hydrogen bonds leads to charge defects at high temperature, whereas six protons in ringlike topologies can move concertedly as a delocalized quasiparticle via collective tunneling at low temperature, thus preventing the creation of high-energy topological defects. Our findings rationalize many-body quantum tunneling in hydrogen-bonded networks and suggest that this phenomenon might be more widespread than previously thought.

Two-dimensional infrared spectroscopy of isotope-diluted ice Ih

We present experimental 2D IR spectra of isotope diluted ice Ih (i.e., the OH stretch mode of HOD in D(2)O and the OD stretch mode of HOD in H(2)O) at T = 80 K. The main spectral features are the extremely broad 1-2 excited state transition, much broader than the corresponding 0-1 groundstate transition, as well as the presence of quantum beats. We do not observe any inhomogeneous broadening that might be expected due to proton disorder in ice Ih. Complementary, we perform simulations in the framework of the Lippincott-Schroeder model, which qualitatively reproduce the experimental observations. We conclude that the origin of the observed line shape features is the coupling of the OH-vibrational coordinate with crystal phonons and explain the beatings as a coherent oscillation of the O···O hydrogen bond degree of freedom.

Infrared and Raman line shapes for ice Ih. II. H2O and D2O

We present a theoretical study of infrared and Raman line shapes of polycrystalline and single crystal ice Ih, for both water and heavy water, at 1, 125, and 245 K. Our calculations involve a mixed quantum/classical approach, a new water simulation model with explicit three-body interactions, transition frequency and dipole maps, and intramolecular and intermolecular vibrational coupling maps. Our theoretical spectra are in reasonable agreement with experimental spectra (available only near the two higher temperatures). We trace the origins of the different spectral peaks to weak and strong intermolecular couplings. We also discuss the delocalization of the vibrational eigenstates in terms of the competing effects of disorder and coupling.