Simultaneous Deep Tunneling and Classical Hopping for Hydrogen Diffusion on Metals

Deciphering the Factors Controlling Hydrogen and Methyl Spillover upon Methane Dissociation on Rh/Cu(111) Single-Atom Alloy

Spillover of adsorbed species from one active site to another is a key step in heterogeneous catalysis. However, the factors controlling this step, particularly the spillover of polyatomic species, have rarely been studied. Herein, we investigate the spillover dynamics of H* and CH3* species on a single-atom alloy surface (Rh/Cu(111)) upon the dissociative chemisorption of methane (CH4), using molecular dynamics that considers both surface phonons and electron-hole pairs. These dynamical calculations are made possible by a high-dimensional potential energy surface machine learned from density functional theory data. Our results provide compelling evidence that the H* and CH3* can spill over on the metal surface at experimental temperatures and reveal novel dynamical features involving an internal motion during diffusion for CH3*. Increasing surface temperature has a minor effect on promoting spillover, as geminate recombinative desorption becomes more prevalent. However, the poisoning of the active site can be mitigated by the frequent gaseous molecular collisions that occur under ambient pressure in real-world catalysis, which transfer energy to the trapped adsorbates. Interestingly, the bulky CH3* exhibits a significant spillover advantage over the light H* due to its larger size, which facilitates energy acquisition. These insights help to advance our understanding of spillover in heterogeneous catalysis.

Quantum rates in dissipative systems with spatially varying friction

We investigate whether making the friction spatially dependent on the reaction coordinate introduces quantum effects into the thermal reaction rates for dissipative reactions. Quantum rates are calculated using the numerically exact multi-configuration time-dependent Hartree method, as well as the approximate ring-polymer molecular dynamics (RPMD), ring-polymer instanton methods, and classical molecular dynamics. By conducting simulations across a wide range of temperatures and friction strengths, we can identify the various regimes that govern the reactive dynamics. At high temperatures, in addition to the spatial-diffusion and energy-diffusion regimes predicted by Kramer's rate theory, a (coherent) tunneling-dominated regime is identified at low friction. At low temperatures, incoherent tunneling dominates most of Kramer's curve, except at very low friction, when coherent tunneling becomes dominant. Unlike in classical mechanics, the bath's influence changes the equilibrium time-independent properties of the system, leading to a complex interplay between spatially dependent friction and nuclear quantum effects even at high temperatures. More specifically, a realistic friction profile can lead to an increase (or decrease) of the quantum (classical) rates with friction within the spatial-diffusion regime, showing that classical and quantum rates display qualitatively different behaviors. Except at very low frictions, we find that RPMD captures most of the quantum effects in the thermal reaction rates.

Robust Gaussian Process Regression Method for Efficient Tunneling Pathway Optimization: Application to Surface Processes

Simulation of surface processes is a key part of computational chemistry that offers atomic-scale insights into mechanisms of heterogeneous catalysis, diffusion dynamics, and quantum tunneling phenomena. The most common theoretical approaches involve optimization of reaction pathways, including semiclassical tunneling pathways (called instantons). The computational effort can be demanding, especially for instanton optimizations with an ab initio electronic structure. Recently, machine learning has been applied to accelerate reaction-pathway optimization, showing great potential for a wide range of applications. However, previous methods still suffer from numerical and efficiency issues and were not designed for condensed-phase reactions. We propose an improved framework based on Gaussian process regression for general transformed coordinates, which has improved efficiency and numerical stability, and we propose a descriptor that combines internal and Cartesian coordinates suitable for modeling surface processes. We demonstrate with 11 instanton optimizations in three representative systems that the improved approach makes ab initio instanton optimization significantly cheaper, such that it becomes not much more expensive than a classical transition-state theory rate calculation.

Accurate Reaction Probabilities for Translational Energies on Both Sides of the Barrier of Dissociative Chemisorption on Metal Surfaces

Molecular dynamics simulations are essential for a better understanding of dissociative chemisorption on metal surfaces, which is often the rate-controlling step in heterogeneous and plasma catalysis. The workhorse quasi-classical trajectory approach ubiquitous in molecular dynamics is able to accurately predict reactivity only for high translational and low vibrational energies. In contrast, catalytically relevant conditions generally involve low translational and elevated vibrational energies. Existing quantum dynamics approaches are intractable or approximate as a result of the large number of degrees of freedom present in molecule-metal surface reactions. Here, we extend a ring polymer molecular dynamics approach to fully include, for the first time, the degrees of freedom of a moving metal surface. With this approach, experimental sticking probabilities for the dissociative chemisorption of methane on Pt(111) are reproduced for a large range of translational and vibrational energies by including nuclear quantum effects and employing full-dimensional simulations.

Electronic friction near metal surface: Incorporating nuclear quantum effect with ring polymer molecular dynamics

The molecular dynamics with electronic friction (MDEF) approach can accurately describe nonadiabatic effects at metal surfaces in the weakly nonadiabatic limit. That being said, the MDEF approach treats nuclear motion classically such that the nuclear quantum effects are completely missing in the approach. To address this limitation, we combine Electronic Friction with Ring Polymer Molecular Dynamics (EF-RPMD). In particular, we apply the averaged electronic friction from the metal surface to the centroid mode of the ring polymer. We benchmark our approach against quantum dynamics to show that EF-RPMD can accurately capture zero-point energy as well as transition dynamics. In addition, we show that EF-RPMD can correctly predict the electronic transfer rate near metal surfaces in the tunneling limit as well as the barrier crossing limit. We expect that our approach will be very useful to study nonadiabatic dynamics near metal surfaces when nuclear quantum effects become essential.

Sustained Hydrogen Spillover on Pt/Cu(111) Single-Atom Alloy: Dynamic Insights into Gas-Induced Chemical Processes

Hydrogen spillover, involving the surface migration of dissociated hydrogen atoms from active metal sites to the relatively inert catalyst support, plays a crucial role in hydrogen-involved catalytic processes. However, a comprehensive understanding of how H atoms are driven to spill over from active sites onto the catalyst support is still lacking. Here, we examine the atomic-scale perspective of the H spillover process on a Pt/Cu(111) single atom alloy surface using machine-learning accelerated molecular dynamics calculations based on density functional theory. Our results show that when an impinging H2 dissociates at an active Pt site, the Pt atom undergoes deactivation due to the dissociated hydrogen atoms that attach to it. Interestingly, collisions between H2 and sticking H atoms facilitate H spillover onto the host Cu, leading to the reactivation of the Pt atom and the realization of a continuous H spillover process. This work underscores the importance of the interaction between gas molecules and adsorbates as a driving force in elucidating chemical processes under a gaseous atmosphere, which has so far been underappreciated in thermodynamic studies.

Ring Polymer Molecular Dynamics Approach to Quantum Dissociative Chemisorption Rates

A ring polymer molecular dynamics (RPMD) method is proposed for the calculation of the dissociative chemisorption rate coefficient on surfaces. The RPMD rate theory is capable of handling quantum effects such as the zero-point energy and tunneling in dissociative chemisorption, while it relies on classical trajectories for the simulation. Applications to H2 dissociative chemisorption are demonstrated. For the highly activated process on Ag(111), strong deviations from Arrhenius behavior are found at low temperatures and attributed to tunneling. On Pt(111), where the dissociation has a barrierless pathway, the RPMD rate coefficient is found to agree with the experimentally derived thermal sticking coefficient within a factor of 2 over a large temperature range. Significant quantum effects are also found.

First-principles surface reaction rates by ring polymer molecular dynamics and neural network potential: role of anharmonicity and lattice motion

Elementary gas-surface processes are essential steps in heterogeneous catalysis. A predictive understanding of catalytic mechanisms remains challenging due largely to difficulties in accurately characterizing the kinetics of such steps. Experimentally, thermal rates for elementary surface reactions can now be measured using a novel velocity imaging technique, providing a stringent testing ground for ab initio rate theories. Here, we propose to combine ring polymer molecular dynamics (RPMD) rate theory with state-of-the-art first-principles-determined neural network potential to calculate surface reaction rates. Taking NO desorption from Pd(111) as an example, we show that the harmonic approximation and the neglect of lattice motion in the commonly-used transition state theory overestimates and underestimates the entropy change during the desorption process, respectively, leading to opposite errors in rate coefficient predictions and artificial error cancellations. Including anharmonicity and lattice motion, our results reveal a generally neglected surface entropy change due to significant local structural change during desorption and obtain the right answer for the right reasons. Although quantum effects are found to be less important in this system, the proposed approach establishes a more reliable theoretical benchmark for accurately predicting the kinetics of elementary gas-surface processes.

Dissipative tunneling rates through the incorporation of first-principles electronic friction in instanton rate theory. I. Theory

Reactions involving adsorbates on metallic surfaces and impurities in bulk metals are ubiquitous in a wide range of technological applications. The theoretical modeling of such reactions presents a formidable challenge for theory because nuclear quantum effects (NQEs) can play a prominent role and the coupling of the atomic motion with the electrons in the metal gives rise to important non-adiabatic effects (NAEs) that alter atomic dynamics. In this work, we derive a theoretical framework that captures both NQEs and NAEs and, due to its high efficiency, can be applied to first-principles calculations of reaction rates in high-dimensional realistic systems. More specifically, we develop a method that we coin ring polymer instanton with explicit friction (RPI-EF), starting from the ring polymer instanton formalism applied to a system-bath model. We derive general equations that incorporate the spatial and frequency dependence of the friction tensor and then combine this method with the ab initio electronic friction formalism for the calculation of thermal reaction rates. We show that the connection between RPI-EF and the form of the electronic friction tensor presented in this work does not require any further approximations, and it is expected to be valid as long as the approximations of both underlying theories remain valid.

Debye Temperature and Quantum Diffusion of Hydrogen in Body-Centered Cubic Metals

Diffusion of deuterium in potassium is studied herein. Mass transfer is controlled predominantly by the mechanism of overbarrier atomic jumps at temperatures 120-260 K and by the tunneling mechanism at 90-120 K. These results together with literature data allowed us to determine conditions under which the quantum diffusion of hydrogen in metals can be observed, which is a fundamental problem. It is established that in metals with a body-centered cubic lattice tunneling can be observed only at temperatures below the Debye temperature θ_D solely for metals with θ_D < 350 K. Predictions are made for metals in which quantum diffusion of hydrogen can be experimentally registered. Metals for which such results cannot be obtained are specified as well. Among them are important engineering materials such as α-Fe, W, Mo, V, and Cr.

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.

The quantum mean square displacement of thermalized CO on Cu(100) in the short time approximation

The mean square displacement of a thermalized CO molecule moving on a copper substrate is evaluated on the basis of a new quantum dynamical approach (Mol. Phys. 119, e1971315, 2021); results at 190 K, the Cu(100) lattice constant a ≈ 256 pm.

Microcanonical Tunneling Rates from Density-of-States Instanton Theory

Semiclassical instanton theory is a form of quantum transition-state theory which can be applied to the computation of thermal reaction rates in complex molecular systems including quantum tunneling effects. There have been a number of attempts to extend the theory to treat microcanonical rates. However, the previous formulations are either computationally unfeasible for large systems due to an explicit sum over states or they involve extra approximations, which make them less reliable. We propose a robust and practical microcanonical formulation called density-of-states instanton theory, which avoids the sum over states altogether. In line with the semiclassical approximations inherent to the instanton approach, we employ the stationary-phase approximation to the inverse Laplace transform to obtain the densities of states. This can be evaluated using only post-processing of the data available from a small set of instanton calculations, such that our approach remains computationally efficient. We show that the new formulation predicts results that agree well with quantum scattering theory for an atom-diatom reaction and with experiments for a photoexcited unimolecular hydrogen transfer in a Criegee intermediate. When the thermal rate is evaluated from a Boltzmann average over our new microcanonical formalism, it can overcome some problems of conventional instanton theory. In particular, it predicts a smooth transition at the crossover temperature and is able to describe bimolecular reactions with pre-reactive complexes such as CH₃OH + OH.

Heavy-atom tunnelling in Cu(ii)N6 complexes: theoretical predictions and experimental manifestation

The degenerate rearrangement on Jahn-Teller distorted metal complexes is a promising reaction for the observation of significant heavy atom quantum mechanical tunnelling. Herein, a family of Cu(ii)-N₆ complexes are theoretically proven to exhibit rapid dynamical Jahn-Teller tunneling even close to the absolute zero. The manifestation of our predictions apparently appeared in solid state EPR experimental measurements on [Cu(en)₃]SO₄ more than 40 years ago, without the authors realizing that it was a quantum outcome.

How coverage influences thermodynamic and kinetic isotope effects for H2/D2 dissociative adsorption on transition metals

Hydrogen isotope effects are influenced by adsorbate coverage: at high coverages, isotope effects are lower than at low coverages. This helps to rationalize observed isotope effects, allowing more precise elucidation of reaction mechanisms.

Heavy atom tunnelling on XeF6 pseudorotation

XeF₆ has multiple C_3v equivalent minima due to the Jahn–Teller effect. Through computational means we prove that the rearrangement between isomers occurs through fluorine quantum mechanical tunnelling.

Advances and challenges for experiment and theory for multi-electron multi-proton transfer at electrified solid–liquid interfaces

Understanding microscopic mechanism of multi-electron multi-proton transfer reactions at complexed systems is important for advancing electrochemistry-oriented science in the 21st century.

Quantum Diffusion of Deuterium in Sodium

The online nuclear reaction analysis technique has been applied to study the temperature dependence of deuterium diffusion coefficients for deuterium in sodium at temperatures ranging between 110 and 240 K, and at cryogenic temperatures, below 160 K, tunneling of deuterium atoms in the metal lattice has been observed. Above 160 K, diffusion occurs by the classical mechanism of overbarrier atomic jumps. Results of quantum diffusion of deuterium in a metal have been obtained for the first time; they used to be known only for the lightest hydrogen isotope, protium, in niobium and tantalum. The analysis has shown that the necessary condition for carrying out the quantum mechanism of deuterium migration is low Debye temperature of a metal, below 200 K. Experimental data on diffusion of hydrogen isotope in an alkali metal have also been obtained for the first time in this paper.

Nonadiabatic Dynamics of Hydrogen Diffusion on Cu(001): Classical Mapping Model with Multistate Projection Window in Real Space

Diffusion of atomic hydrogen on metallic surfaces is a longstanding research topic of both fundamental and practical interests. However, full understanding of the microscopic mechanisms and development of effective strategy for surface dynamics control at the molecular level remain elusive. In this paper, we propose a new nonadiabatic multistate model for surface diffusion based on a real space decomposition scheme by generalizing the classical mapping theory of Meyer and Miller. The model suggests a general multistate perspective on real-time surface dynamics by mapping it into spatially disjointed windowing functions, which feature the explicit nonadiabatic controllability. Within this framework, the first nonadiabatic molecular dynamics simulation is performed for atomic hydrogen diffusion on the Cu(001) surface, and the nonequilibrium effect of lattice distortion is studied.

Emerging hydrovoltaic technology

Water contains tremendous energy in a variety of forms, but very little of this energy has yet been harnessed. Nanostructured materials can generate electricity on interaction with water, a phenomenon that we term the hydrovoltaic effect, which potentially extends the technical capability of water energy harvesting and enables the creation of self-powered devices. In this Review, starting by describing fundamental properties of water and of water-solid interfaces, we discuss key aspects pertaining to water-carbon interactions and basic mechanisms of harvesting water energy with nanostructured materials. Experimental advances in generating electricity from water flows, waves, natural evaporation and moisture are then reviewed to show the correlations in their basic mechanisms and the potential for their integration towards harvesting energy from the water cycle. We further discuss potential device applications of hydrovoltaic technologies, analyse main challenges in improving the energy conversion efficiency and scaling up the output power, and suggest prospects for developments of the emerging technology.

Proton Migration in Hybrid Lead Iodide Perovskites: From Classical Hopping to Deep Quantum Tunneling

The organic-inorganic halide perovskites (OIHPs) have shown enormous potential for solar cells, while problems like the current-voltage hysteresis and the long-term instability have seriously hindered their applications. Ion migrations are believed to be relevant. But the atomistic details still remain unclear. Here we study the migrations of ions in CH₃NH₃PbI₃ (MAPbI₃) at varying temperatures ( T's), using combined experimental and first-principle theoretical methods. Classical hopping of the iodide ions is the main migration mechanism at moderate T's. Below ∼270 K, the kinetic constant for ionic migration still shows an Arrenhius dependency, but the much lower activation energy is attributed to the migration of H⁺. A gradual classical-to-quantum transition takes place between ∼140 and ∼80 K. Below ∼80 K, the kinetic constant becomes T-independent, suggesting that deep quantum tunneling of H⁺ takes over. This study gives direct experimental evidence for the migrations of H⁺s in MAPbI₃ and confirms their quantum nature.

Effects of the cooperative interaction on the diffusion of hydrogen on MgO(100)

Understanding hydrogen diffusion is important for applications such as hydrogen storage and spillover materials. On semiconductors, where paired electron acceptors and donors stabilize each other, the hydrogen diffusion depends on the number of adsorbed fragments. Using density functional theory, we investigate the effects of preadsorbed hydrogens on activation energy and reaction path for hydrogen diffusion on MgO(100): the presence of an unpaired hydrogen causes a diffusion, on O-sites, above the surface with a lower activation energy compared to the case of paired hydrogens where the diffusion distorts the surface. This effect is missing for diffusion on Mg-sites.

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.