Atomic imaging of the edge structure and growth of a two-dimensional hexagonal ice.

The formation and growth of water-ice layers on surfaces and of low-dimensional ice under confinement are frequent occurrences1-4. This is exemplified by the extensive reporting of two-dimensional (2D) ice on metals5-11, insulating surfaces12-16, graphite and graphene17,18 and under strong confinement14,19-22. Although structured water adlayers and 2D ice have been imaged, capturing the metastable or intermediate edge structures involved in the 2D ice growth, which could reveal the underlying growth mechanisms, is extremely challenging, owing to the fragility and short lifetime of those edge structures. Here we show that noncontact atomic-force microscopy with a CO-terminated tip (used previously to image interfacial water with minimal perturbation)12, enables real-space imaging of the edge structures of 2D bilayer hexagonal ice grown on a Au(111) surface. We find that armchair-type edges coexist with the zigzag edges usually observed in 2D hexagonal crystals, and freeze these samples during growth to identify the intermediate edge structures. Combined with simulations, these experiments enable us to reconstruct the growth processes that, in the case of the zigzag edge, involve the addition of water molecules to the existing edge and a collective bridging mechanism. Armchair edge growth, by contrast, involves local seeding and edge reconstruction and thus contrasts with conventional views regarding the growth of bilayer hexagonal ices and 2D hexagonal matter in general.

Crystal-Structure Matches in Solid-Solid Phase Transitions.

The exploration of solid-solid phase transition suffers from the uncertainty of how atoms in two crystal structures match. We devised a theoretical framework to describe and classify crystal-structure matches (CSM). Such description fully exploits the translational and rotational symmetries and is independent of the choice of supercells. This is enabled by the use of the Hermite normal form, an analog of reduced echelon form for integer matrices. With its help, exhausting all CSMs is made possible, which goes beyond the conventional optimization schemes. In an example study of the martensitic transformation of steel, our enumeration algorithm finds many candidate CSMs with lower strains than known mechanisms. Two long-sought CSMs accounting for the most commonly observed Kurdjumov-Sachs orientation relationship and the Nishiyama-Wassermann orientation relationship are unveiled. Given the comprehensiveness and efficiency, our enumeration scheme provide a promising strategy for solid-solid phase transition mechanism research.

Publisher Correction: The effect of hydration number on the interfacial transport of sodium ions.

In this Letter, the links to Supplementary Videos 5, 7, 9 and 10 were incorrect, and there were some formatting errors in the Supplementary Video legends. These errors have been corrected online.

The effect of hydration number on the interfacial transport of sodium ions.

Ion hydration and transport at interfaces are relevant to a wide range of applied fields and natural processes1-5. Interfacial effects are particularly profound in confined geometries such as nanometre-sized channels6-8, where the mechanisms of ion transport in bulk solutions may not apply9,10. To correlate atomic structure with the transport properties of hydrated ions, both the interfacial inhomogeneity and the complex competing interactions among ions, water and surfaces require detailed molecular-level characterization. Here we constructed individual sodium ion (Na+) hydrates on a NaCl(001) surface by progressively attaching single water molecules (one to five) to the Na+ ion using a combined scanning tunnelling microscopy and noncontact atomic force microscopy system. We found that the Na+ ion hydrated with three water molecules diffuses orders of magnitude more quickly than other ion hydrates. Ab initio calculations revealed that such high ion mobility arises from the existence of a metastable state, in which the three water molecules around the Na+ ion can rotate collectively with a rather small energy barrier. This scenario would apply even at room temperature according to our classical molecular dynamics simulations. Our work suggests that anomalously high diffusion rates for specific hydration numbers of ions are generally determined by the degree of symmetry match between the hydrates and the surface lattice.

Semiclassical Vibrational Spectroscopy of Real Molecular Systems by Means of Cross-Correlation Filter Diagonalization.

We applied the harmonic inversion technique to extract vibrational eigenvalues from the semiclassical initial value representation (SC-IVR) propagator of molecular systems described by explicit potential surfaces. The cross-correlation filter-diagonalization (CCFD) method is used for the inversion problem instead of the Fourier transformation, which allows much shorter propagation time and is thus capable of avoiding numerical divergence issues while getting rid of approximations like the separable one to the pre-exponential factor. We also used the "Divide-and-Conquer" technique to control the total dimensions under consideration, which helps to further enhance the numerical behavior of SC-IVR calculations and the stability of harmonic inversion methods. The technique is tested on small molecules and water trimer to justify its applicability and reliability. Results show that the CCFD method can effectively extract the vibrational eigenvalues from short trajectories and reproduce the original spectra conventionally obtained from long-time ones, with no loss on accuracy while the numerical behavior is much better. This work demonstrates the possibility to apply the combined method of CCFD and SC-IVR to real molecular potential surfaces, which might be a new way to overcome the numerical instabilities caused by the increase of dimensions.

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.

Engineering Interlayer Electron-Phonon Coupling in WS2/BN Heterostructures.

In van der Waals (vdW) heterostructures, the interlayer electron-phonon coupling (EPC) provides one unique channel to nonlocally engineer these elementary particles. However, limited by the stringent occurrence conditions, the efficient engineering of interlayer EPC remains elusive. Here we report a multitier engineering of interlayer EPC in WS2/boron nitride (BN) heterostructures, including isotope enrichments of BN substrates, temperature, and high-pressure tuning. The hyperfine isotope dependence of Raman intensities was unambiguously revealed. In combination with theoretical calculations, we anticipate that WS2/BN supercells could induce Brillouin-zone-folded phonons that contribute to the interlayer coupling, leading to a complex nature of broad Raman peaks. We further demonstrate the significance of a previously unexplored parameter, the interlayer spacing. By varying the temperature and high pressure, we effectively manipulated the strengths of EPC with on/off capabilities, indicating critical thresholds of the layer-layer spacing for activating and strengthening interlayer EPC. Our findings provide new opportunities to engineer vdW heterostructures with controlled interlayer coupling.

Torsional Tunneling Splitting in a Water Trimer.

Using a full-dimensional quantum method for nuclei and a new first-principles water potential, we show that the torsional tunneling splitting in a water trimer can be reproduced with accuracy up to ∼1 cm-1. We quantify the coupling constants of the nuclear quantum states between nonadjacent wells and show that they are the main reason for shifting the quartet-split levels in spectra from a 1:2:1 spacing. This demonstrates the limitation of treatments using simplified models such as the Hückel model and emphasizes the nonlocal nature of the quantum interactions in this system. With such an ab initio endeavor, we examine the quality of the water potential developed and provide a rigorous scheme to decipher the experimental spectra with unprecedented accuracy, which is applicable to more general systems.

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 scanning tunneling microscopy (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 questions 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. The 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 change the size of it in a similar fashion to how they change 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.

Dynamic Nature of High-Pressure Ice VII.

Starting from Shannon's definition of dynamic entropy, we propose a theory to describe the rare-event-determined dynamic states in condensed matter and their transitions and apply it to high-pressure ice VII. A dynamic intensive quantity named dynamic field, rather than the conventional thermodynamic intensive quantities such as temperature and pressure, is taken as the controlling variable. The dynamic entropy versus dynamic field curve demonstrates two dynamic states in the stability region of ice VII and dynamic ice VII. Their microscopic differences were assigned to the dynamic patterns of proton transfer. This study puts a similar dynamical theory used in earlier studies of glass models on a simpler and more fundamental basis, which could be applied to describe the dynamic states of more realistic condensed matter systems.

Ferroelectric Problem beyond the Conventional Scaling Law.

Ferroelectric (FE) size effects against the scaling law were reported recently in ultrathin group-IV monochalcogenides, and extrinsic effects (e.g., defects and lattice strains) were often resorted to. Via first-principles based finite-temperature (T) simulations, we reveal that these abnormalities are intrinsic to their unusual symmetry breaking from bulk to thin film. Changes of the electronic structures result in different order parameters characterizing the FE phase transition in bulk and in thin films, and invalidation of the scaling law. Beyond the scaling law T_{c} limit, this mechanism can help predict materials that are promising for room-T ultrathin FE devices of broad interest.

The strengths and limitations of effective centroid force models explored by studying isotopic effects in liquid water.

The development of effective centroid potentials (ECPs) is explored with both the constrained-centroid and quasi-adiabatic force matching using liquid water as a test system. A trajectory integrated with the ECP is free of statistical noises that would be introduced when the centroid potential is approximated on the fly with a finite number of beads. With the reduced cost of ECP, challenging experimental properties can be studied in the spirit of centroid molecular dynamics. The experimental number density of H2O is 0.38% higher than that of D2O. With the ECP, the H2O number density is predicted to be 0.42% higher, when the dispersion term is not refit. After correction of finite size effects, the diffusion constant of H2O is found to be 21% higher than that of D2O, which is in good agreement with the 29.9% higher diffusivity for H2O observed experimentally. Although the ECP is also able to capture the redshifts of both the OH and OD stretching modes in liquid water, there are a number of properties that a classical simulation with the ECP will not be able to recover. For example, the heat capacities of H2O and D2O are predicted to be almost identical and higher than the experimental values. Such a failure is simply a result of not properly treating quantized vibrational energy levels when the trajectory is propagated with classical mechanics. Several limitations of the ECP based approach without bead population reconstruction are discussed.

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.

Simultaneous Deep Tunneling and Classical Hopping for Hydrogen Diffusion on Metals.

Hydrogen diffusion on metals exhibits rich quantum behavior, which is not yet fully understood. Using simulations, we show that many hydrogen diffusion barriers can be categorized into those with parabolic tops and those with broad tops. With parabolic-top barriers, hydrogen diffusion evolves gradually from classical hopping, to shallow tunneling, to deep tunneling as the temperature (T) decreases, and noticeable quantum effects persist at moderate T. In contrast, with broad-top barriers quantum effects become important only at low T and the classical-to-quantum transition is sharp, at which classical hopping and deep tunneling both occur. This coexistence indicates that more than one mechanism contributes to the quantum reaction rate. The conventional definition of the classical-to-quantum crossover T is invalid for the broad tops, and we give a new definition. Extending this, we propose a model to predict the transition T for broad-top diffusion, providing a general guide for theory and experiment.

Hydrogen induced contrasting modes of initial nucleations of graphene on transition metal surfaces.

Our first-principles calculations reveal that there exist contrasting modes of initial nucleations of graphene on transition metal surfaces, in which hydrogen plays the role. On Cu(100) and Cu(111) surfaces, an sp2-type network of carbons can be automatically formed with the help of hydrogen under very low carbon coverages. Thus, by tuning the chemical potential of hydrogen, both of the nucleation process and the following growth can be finely controlled. In contrast, on the Ni(111) surface, instead of hydrogen, the carbon coverage is the critical factor for the nucleation and growth. These findings serve as new insights for further improving the poor quality of the grown graphene on transition metal substrates.

Direct observation of ordered configurations of hydrogen adatoms on graphene.

Ordered configurations of hydrogen adatoms on graphene have long been proposed, calculated, and searched for. Here, we report direct observation of several ordered configurations of H adatoms on graphene by scanning tunneling microscopy. On the top side of the graphene plane, H atoms in the configurations appear to stick to carbon atoms in the same sublattice. Scanning tunneling spectroscopy measurements revealed a substantial gap in the local density of states in H-contained regions as well as in-gap states below the conduction band due to the incompleteness of H ordering. These findings can be well explained by density functional theory calculations based on double-sided H configurations. In addition, factors that may influence H ordering are discussed.

Real-space imaging of interfacial water with submolecular resolution.

Water/solid interfaces are vital to our daily lives and are also a central theme across an incredibly wide range of scientific disciplines. Resolving the internal structure, that is, the O-H directionality, of water molecules adsorbed on solid surfaces has been one of the key issues of water science yet it remains challenging. Using a low-temperature scanning tunnelling microscope, we report submolecular-resolution imaging of individual water monomers and tetramers on NaCl(001) films supported by a Au(111) substrate at 5 K. The frontier molecular orbitals of adsorbed water were directly visualized, which allowed discrimination of the orientation of the monomers and the hydrogen-bond directionality of the tetramers in real space. Comparison with ab initio density functional theory calculations reveals that the ability to access the orbital structures of water stems from the electronic decoupling effect provided by the NaCl films and the precisely tunable tip-water coupling.

Nuclear quantum effects on the high pressure melting of dense lithium.

Using a self-developed combination of the thermodynamic integration and the ab initio path-integral molecular dynamics methods, we quantitatively studied the influence of nuclear quantum effects (NQEs) on the melting of dense lithium at 45 GPa. We find that although the NQEs significantly change the free-energies of the competing solid and liquid phases, the melting temperature (Tm) is lowered by only ∼15 K, with values obtained using both classical and quantum nuclei in close proximity to a new experiment. Besides this, a substantial narrowing of the solid/liquid free-energy differences close to Tm was observed, in alignment with a tendency that glassy states might form upon rapid cooling. This tendency was demonstrated by the dynamics of crystallization in the two-phase simulations, which helps to reconcile an important conflict between two recent experiments. This study presents a simple picture for the phase diagram of lithium under pressure. It also indicates that claims on the influence of NQEs on phase diagrams should be carefully made and the method adopted offers a robust solution for such quantitative analyses.

Systematic investigation on topological properties of layered GaS and GaSe under strain.

The topological properties of layered ß-GaS and ε-GaSe under strain are systematically investigated by ab initio calculations with the electronic exchange-correlation interactions treated beyond the generalized gradient approximation (GGA). Based on the GW method and the Tran-Blaha modified Becke-Johnson potential approach, we find that while ε-GaSe can be strain-engineered to become a topological insulator, ß-GaS remains a trivial one even under strong strain, which is different from the prediction based on GGA. The reliability of the fixed volume assumption rooted in nearly all the previous calculations is discussed. By comparing to strain calculations with optimized inter-layer distance, we find that the fixed volume assumption is qualitatively valid for ß-GaS and ε-GaSe, but there are quantitative differences between the results from the fixed volume treatment and those from more realistic treatments. This work indicates that it is risky to use theoretical approaches like GGA that suffer from the band gap problem to address physical properties, including, in particular, the topological nature of band structures, for which the band gap plays a crucial role. In the latter case, careful calibration against more reliable methods like the GW approach is strongly recommended.

On the room-temperature phase diagram of high pressure hydrogen: an ab initio molecular dynamics perspective and a diffusion Monte Carlo study.

The finite-temperature phase diagram of hydrogen in the region of phase IV and its neighborhood was studied using the ab initio molecular dynamics (MD) and the ab initio path-integral molecular dynamics (PIMD). The electronic structures were analyzed using the density-functional theory (DFT), the random-phase approximation, and the diffusion Monte Carlo (DMC) methods. Taking the state-of-the-art DMC results as benchmark, comparisons of the energy differences between structures generated from the MD and PIMD simulations, with molecular and dissociated hydrogens, respectively, in the weak molecular layers of phase IV, indicate that standard functionals in DFT tend to underestimate the dissociation barrier of the weak molecular layers in this mixed phase. Because of this underestimation, inclusion of the quantum nuclear effects (QNEs) in PIMD using electronic structures generated with these functionals leads to artificially dissociated hydrogen layers in phase IV and an error compensation between the neglect of QNEs and the deficiencies of these functionals in standard ab initio MD simulations exists. This analysis partly rationalizes why earlier ab initio MD simulations complement so well the experimental observations. The temperature and pressure dependencies for the stability of phase IV were also studied in the end and compared with earlier results.