Semiclassical dynamics in Wigner phase space II: Nonadiabatic hybrid Wigner dynamics

We present an approximate semiclassical (SC) framework for mixed quantized dynamics in Wigner phase space in a two-part series. In the first article, we introduced the Adiabatic Hybrid Wigner Dynamics (AHWD) method that allows for a few important "system" degrees of freedom to be quantized using high-level double Herman-Kluk SC theory while describing the rest (the "bath") using classical-limit linearized SC theory. In this second article, we extend our hybrid Wigner dynamics to nonadiabatic processes. The resulting Nonadiabatic Hybrid Wigner Dynamics (NHWD) has two variants that differ in the choice of degrees of freedom to be quantized. Specifically, we introduce NHWD(E) where only the electronic state variables are quantized and the NHWD(V) where both electronic state variables and a handful of strongly coupled nuclear modes are quantized. We show that while NHWD(E) proves accurate for a wide range of scattering models and spin-boson models, systems where a few nuclear modes are strongly coupled to electronic states require NHWD(V) to accurately capture the long-time dynamics. Taken together, we show that AHWD and NHWD represent a new framework for SC simulations of high-dimensional systems with significant quantum effects.

Spiers Memorial Lecture: New directions in molecular scattering

The field of molecular scattering is reviewed as it pertains to gas-gas as well as gas-surface chemical reaction dynamics. We emphasize the importance of collaboration of experiment and theory, from which new directions of research are being pursued on increasingly complex problems. We review both experimental and theoretical advances that provide the modern toolbox available to molecular-scattering studies. We distinguish between two classes of work. The first involves simple systems and uses experiment to validate theory so that from the validated theory, one may learn far more than could ever be measured in the laboratory. The second class involves problems of great complexity that would be difficult or impossible to understand without a partnership of experiment and theory. Key topics covered in this review include crossed-beams reactive scattering and scattering at extremely low energies, where quantum effects dominate. They also include scattering from surfaces, reactive scattering and kinetics at surfaces, and scattering work done at liquid surfaces. The review closes with thoughts on future promising directions of research.

i-PI 3.0: A flexible and efficient framework for advanced atomistic simulations

Atomic-scale simulations have progressed tremendously over the past decade, largely thanks to the availability of machine-learning interatomic potentials. These potentials combine the accuracy of electronic structure calculations with the ability to reach extensive length and time scales. The i-PI package facilitates integrating the latest developments in this field with advanced modeling techniques thanks to a modular software architecture based on inter-process communication through a socket interface. The choice of Python for implementation facilitates rapid prototyping but can add computational overhead. In this new release, we carefully benchmarked and optimized i-PI for several common simulation scenarios, making such overhead negligible when i-PI is used to model systems up to tens of thousands of atoms using widely adopted machine learning interatomic potentials, such as Behler-Parinello, DeePMD, and MACE neural networks. We also present the implementation of several new features, including an efficient algorithm to model bosonic and fermionic exchange, a framework for uncertainty quantification to be used in conjunction with machine-learning potentials, a communication infrastructure that allows for deeper integration with electronic-driven simulations, and an approach to simulate coupled photon-nuclear dynamics in optical or plasmonic cavities.

Vibrationally Mode-Specific Molecular Energy Transfer to Surface Electrons in Metastable Formaldehyde Scattering from Cesium-Covered Au(111)

Nonadiabatic interaction of adsorbate nuclear motion with the continuum of electronic states is known to affect the dynamics of chemical reactions at metal surfaces. A large body of work has probed the fundamental mechanisms of such interactions for atomic and diatomic molecules at surfaces. In polyatomic molecules, the possibility of mode-specific damping of vibrational motion due to the effects of electronic friction raises the question of whether such interactions could profoundly affect the outcome of chemistry at surfaces by selectively removing energy from a particular intramolecular adsorbate mode. However, to date, there have not been any fundamental experiments demonstrating nonadiabatic electron-vibration coupling in a polyatomic molecule at a surface. In this work, we scatter excited metastable formaldehyde and formaldehyde-d2 from a low work function surface and detect ejected exoelectrons that accompany molecular relaxation. The exoelectron ejection efficiency exhibits a strong dependence on the vibrational mode that is excited: out-of-plane bending excitation (ν4) leads to significantly more exoelectrons than does CO stretching excitation (ν2). The results provide clear evidence for mode-specific energy transfer from vibration to surface electrons.

Vibrational energy transfer in collisions of molecules with metal surfaces

The Born-Oppenheimer approximation (BOA), which serves as the basis for our understanding of chemical bonding, reactivity and dynamics, is routinely violated for vibrationally inelastic scattering of molecules at metal surfaces. The title-field therefore represents a fascinating challenge to our conventional wisdom calling for new concepts that involve explicit electron dynamics occurring in concert with nuclear motion. Here, we review progress made in this field over the last decade, which has witnessed dramatic advances in experimental methods, thereby providing a much more extensive set of diverse observations than has ever before been available. We first review the experimental methods used in this field and then provide a systematic tour of the vast array of observations that are currently available. We show how these observations - taken together and without reference to computational simulations - lead us to a simple and intuitive picture of BOA failure in molecular dynamics at metal surfaces, one where electron transfer between the molecule and the metal plays a preeminent role. We also review recent progress made in the theory of electron transfer mediated BOA failure in molecule-surface interactions, describing the most important methods and their ability to reproduce experimental observation. Finally, we outline future directions for research and important unanswered questions.

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.

A Linearized Semiclassical Dynamics Study of the Multiquantum Vibrational Relaxation of NO Scattering from a Au(111) Surface

The vibrational relaxation of NO molecules scattering from a Au(111) surface has served as the focus of efforts to understand nonadiabatic energy transfer at metal-molecule interfaces. Experimental measurements and previous theoretical efforts suggest that multiquantal NO vibrational energy relaxation occurs via electron-hole pair excitations in the metal. Here, using a linearized semiclassical approach, we accurately predict the vibrational relaxation of NO from the νi = 3 state for different incident translational energies. We also accurately capture the central role of transient electron transfer from the metal to the molecule in mediating the vibrational relaxation process but fall short of quantitatively predicting the full extent of multiquantum relaxation for high incident vibrational excitations (νi = 16).

Theoretical study of nonadiabatic hydrogen atom scattering dynamics on metal surfaces using the hierarchical equations of motion method

Hydrogen atom scattering on metal surfaces is investigated based on a simplified Newns-Anderson model. Both the nuclear and electronic degrees of freedom are treated quantum mechanically. By partitioning all the surface electronic states as the bath, the hierarchical equations of motion method for the fermionic bath is employed to simulate the scattering dynamics. It is found that, with a reasonable set of parameters, the main features of the recent experimental studies of hydrogen atom scattering on metal surfaces can be reproduced. Vibrational states on the chemisorption state whose energies are close to the incident energy are found to play an important role, and the scattering process is dominated by a single-pass electronic transition forth and back between the diabatic physisorption and chemisorption states. Further study on the effects of the atom-surface coupling strength reveals that, upon increasing the atom-surface coupling strength, the scattering mechanism changes from typical nonadiabatic transitions to dynamics in the electronic friction regime.

How Hot Electron Generation at the Solid-Liquid Interface Is Different from the Solid-Gas Interface

Excitation of hot electrons by energy dissipation under exothermic chemical reactions on metal catalyst surfaces occurs at both solid-gas and solid-liquid interfaces. Despite extensive studies, a comparative operando study directly comparing electronic excitation by electronically nonadiabatic interactions at solid-gas and solid-liquid interfaces has not been reported. Herein, on the basis of our in situ techniques for monitoring energy dissipation as a chemicurrent using a Pt/n-Si nanodiode sensor, we observed the generation of hot electrons in both gas and liquid phases during H₂O₂ decomposition. As a result of comparing the current signal and oxygen evolution rate in the two phases, surprisingly, the efficiency of reaction-induced excitation of hot electrons increased by ∼100 times at the solid-liquid interface compared to the solid-gas interface. The boost of hot electron excitation in the liquid phase is due to the presence of an ionic layer lowering the potential barrier at the junction for transferring hot electrons.

Hot Electron Phenomena at Solid-Liquid Interfaces

Understanding the role of energy dissipation and charge transfer under exothermic chemical reactions on metal catalyst surfaces is important for elucidating the fundamental phenomena at solid-gas and solid-liquid interfaces. Recently, many surface chemistry studies have been conducted on the solid-liquid interface, so correlating electronic excitation in the liquid-phase with the reaction mechanism plays a crucial role in heterogeneous catalysis. In this review, we introduce the detection principle of electron transfer at the solid-liquid interface by developing cutting-edge technologies with metal-semiconductor Schottky nanodiodes. The kinetics of hot electron excitation are well correlated with the reaction rates, demonstrating that the operando method for understanding nonadiabatic interactions is helpful in studying the reaction mechanism of surface molecular processes. In addition to the detection of hot electrons excited by a catalytic reaction, we highlight recent results on how the transfer of the hot electrons influences surface chemical and photoelectrochemical reactions.

Detailed Balance and Independent Electron Surface-Hopping Method: The Importance of Decoherence and Correct Calculation of Diabatic Populations

We benchmark and improve the independent electron surface-hopping (IESH) method developed by J. C. Tully's group for nonadiabatic simulations near metal surfaces. We have incorporated decoherence within the IESH method as well as implemented a scheme for the accurate calculation of diabatic populations. We benchmark the original IESH method with the above inclusions for a model system to calculate rate constants and long-time populations. The original IESH method fails to capture the detailed balance for some of the parameters, which is corrected with the inclusion of decoherence and accurate calculation of diabatic populations. Total rate constants are well captured both within the original IESH method as well as within our modified IESH.

Quantitative molecular simulations

All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.

Dissipative tunneling rates through the incorporation of first-principles electronic friction in instanton rate theory. II. Benchmarks and applications

In Paper I [Litman et al., J. Chem. Phys. (in press) (2022)], we presented the ring-polymer instanton with explicit friction (RPI-EF) method and showed how it can be connected to the ab initio electronic friction formalism. This framework allows for the calculation of tunneling reaction rates that incorporate the quantum nature of the nuclei and certain types of non-adiabatic effects (NAEs) present in metals. In this paper, we analyze the performance of RPI-EF on model potentials and apply it to realistic systems. For a 1D double-well model, we benchmark the method against numerically exact results obtained from multi-layer multi-configuration time-dependent Hartree calculations. We demonstrate that RPI-EF is accurate for medium and high friction strengths and less accurate for extremely low friction values. We also show quantitatively how the inclusion of NAEs lowers the crossover temperature into the deep tunneling regime, reduces the tunneling rates, and, in certain regimes, steers the quantum dynamics by modifying the tunneling pathways. As a showcase of the efficiency of this method, we present a study of hydrogen and deuterium hopping between neighboring interstitial sites in selected bulk metals. The results show that multidimensional vibrational coupling and nuclear quantum effects have a larger impact than NAEs on the tunneling rates of diffusion in metals. Together with Paper I [Litman et al., J. Chem. Phys. (in press) (2022)], these results advance the calculations of dissipative tunneling rates from first principles.

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.

First-Principles Insights into Adiabatic and Nonadiabatic Vibrational Energy-Transfer Dynamics during Molecular Scattering from Metal Surfaces: The Importance of Surface Reactivity

Energy transfer is ubiquitous during molecular collisions and reactions at gas-surface interfaces. Of particular importance is vibrational energy transfer because of its relevance to bond forming and breaking. In this Perspective, we review recent first-principles studies on vibrational energy-transfer dynamics during molecular scattering from metal surfaces at the state-to-state level. Taking several representative systems as examples, we highlight the intrinsic correlation between vibrational energy transfer in nonreactive scattering and surface reactivity and how it operates in both electronically adiabatic and nonadiabatic pathways. Adiabatically, the presence of a dissociation barrier softens a bond in the impinging molecule and increases its couplings with other molecular modes and surface phonons. In the meantime, the stronger interaction between the molecule and the surface also changes the electronic structure at the barrier, resulting in an increase of nonadiabatic effects. We further discuss future prospects toward a more quantitative understanding of this important surface dynamical process.

Prominence of Terahertz Acoustic Surface Plasmon Excitation in Gas-Surface Interaction with Metals

The current understanding of the dynamics of gas-surface interactions is that all of the energy lost in the collision is transferred to vibrations of the target. Electronic excitations were shown to play a marginal role except for cases in which the impinging particles have energies of several electronvolts. Here we show that this picture does not hold for metal surfaces supporting acoustic surface plasmons. Such loss, dressed with a vibronic structure, is shown to make up a prominent energy transfer route down to the terahertz region for Ne atoms scattering off Cu(111) and is expected to dominate for most metals. This mechanism determines, e.g., the drag force acting on telecommunication satellites, which are typically gold-plated to reduce overheating by sunshine. The electronic excitations can be unambiguously discerned from the vibrational ones under mild hyperthermal impact conditions.

Inelastic Scattering of H Atoms from Surfaces

We have developed an instrument that uses photolysis of hydrogen halides to produce nearly monoenergetic hydrogen atom beams and Rydberg atom tagging to obtain accurate angle-resolved time-of-flight distributions of atoms scattered from surfaces. The surfaces are prepared under strict ultrahigh vacuum conditions. Data from these experiments can provide excellent benchmarks for theory, from which it is possible to obtain an atomic scale understanding of the underlying dynamical processes governing H atom adsorption. In this way, the mechanism of adsorption on metals is revealed, showing a penetration-resurfacing mechanism that relies on electronic excitation of the metal by the H atom to succeed. Contrasting this, when H atoms collide at graphene surfaces, the dynamics of bond formation involving at least four carbon atoms govern adsorption. Future perspectives of H atom scattering from surfaces are also outlined.

Mechanical Vibrational Relaxation of NO Scattering from Metal and Insulator Surfaces: When and Why They Are Different

NO scattering from metallic and insulating surfaces represents contrasting benchmark systems for understanding energy transfer at gas-surface interface. Strikingly different behaviors of highly vibrationally excited NO scattered from Au(111) and LiF(001) were observed and attributed to disparate electronic structures between metals and insulators. Here, we reveal an alternative mechanical origin of this discrepancy by comparative molecular dynamics simulations with globally accurate adiabatic neural network potentials of both systems. We find that highly vibrating NO can reach for the high-dissociation barrier on Au(111), by which vibrational energy can largely transfer to translation or rotation and further dissipate into substrate phonons. This mechanical energy transfer channel is forbidden in the purely repulsive NO/LiF(001) system or for low-vibrating NO on Au(111), where molecular vibration is barely coupled to other degrees of freedom. Our results emphasize that the initial state and potential energy landscape concurrently influence the mechanical energy transfer dynamics of gas-surface scattering.

Computational approaches to dissociative chemisorption on metals: towards chemical accuracy

We review the state-of-the-art in the theory of dissociative chemisorption (DC) of small gas phase molecules on metal surfaces, which is important to modeling heterogeneous catalysis for practical reasons, and for achieving an understanding of the wealth of experimental information that exists for this topic, for fundamental reasons. We first give a quick overview of the experimental state of the field. Turning to the theory, we address the challenge that barrier heights (E_b, which are not observables) for DC on metals cannot yet be calculated with chemical accuracy, although embedded correlated wave function theory and diffusion Monte-Carlo are moving in this direction. For benchmarking, at present chemically accurate E_b can only be derived from dynamics calculations based on a semi-empirically derived density functional (DF), by computing a sticking curve and demonstrating that it is shifted from the curve measured in a supersonic beam experiment by no more than 1 kcal mol^-1. The approach capable of delivering this accuracy is called the specific reaction parameter (SRP) approach to density functional theory (DFT). SRP-DFT relies on DFT and on dynamics calculations, which are most efficiently performed if a potential energy surface (PES) is available. We therefore present a brief review of the DFs that now exist, also considering their performance on databases for E_b for gas phase reactions and DC on metals, and for adsorption to metals. We also consider expressions for SRP-DFs and briefly discuss other electronic structure methods that have addressed the interaction of molecules with metal surfaces. An overview is presented of dynamical models, which make a distinction as to whether or not, and which dissipative channels are modeled, the dissipative channels being surface phonons and electronically non-adiabatic channels such as electron-hole pair excitation. We also discuss the dynamical methods that have been used, such as the quasi-classical trajectory method and quantum dynamical methods like the time-dependent wave packet method and the reaction path Hamiltonian method. Limits on the accuracy of these methods are discussed for DC of diatomic and polyatomic molecules on metal surfaces, paying particular attention to reduced dimensionality approximations that still have to be invoked in wave packet calculations on polyatomic molecules like CH₄. We also address the accuracy of fitting methods, such as recent machine learning methods (like neural network methods) and the corrugation reducing procedure. In discussing the calculation of observables we emphasize the importance of modeling the properties of the supersonic beams in simulating the sticking probability curves measured in the associated experiments. We show that chemically accurate barrier heights have now been extracted for DC in 11 molecule-metal surface systems, some of which form the most accurate core of the only existing database of E_b for DC reactions on metal surfaces (SBH10). The SRP-DFs (or candidate SRP-DFs) that have been derived show transferability in many cases, i.e., they have been shown also to yield chemically accurate E_b for chemically related systems. This can in principle be exploited in simulating rates of catalyzed reactions on nano-particles containing facets and edges, as SRP-DFs may be transferable among systems in which a molecule dissociates on low index and stepped surfaces of the same metal. In many instances SRP-DFs have allowed important conclusions regarding the mechanisms underlying observed experimental trends. An important recent observation is that SRP-DFT based on semi-local exchange DFs has so far only been successful for systems for which the difference of the metal work function and the molecule's electron affinity exceeds 7 eV. A main challenge to SRP-DFT is to extend its applicability to the other systems, which involve a range of important DC reactions of e.g. O₂, H₂O, NH₃, CO₂, and CH₃OH. Recent calculations employing a PES based on a screened hybrid exchange functional suggest that the road to success may be based on using exchange functionals of this category.

Electronic Control of Hot Electron Transport Using Modified Schottky Barriers in Metal-Semiconductor Nanodiodes

Hot electron flux, generated by both incident light energy and the heat of the catalytic reaction, is a major element for energy conversion at the surface. Controlling hot electron flux in a reversible manner is extremely important for achieving high energy conversion efficiency. Here we demonstrate that hot electron flux can be controlled by tuning the Schottky barrier height. This phenomenon was monitored by using a Schottky nanodiode composed of a metal-semiconductor. The formation of a Schottky barrier at a nanometer scale inevitably accompanies an intrinsic image potential between the metal-semiconductor junction, which lowers the effective Schottky barrier height. When a reverse bias is applied to the nanodiode, an additional image potential participates in a secondary barrier lowering, leading to the increased hot electron flow. Besides, a decrease of tunneling width results in facile electron transport through the barrier. The increased hot electron flux by the chemical reaction (chemicurrent) and by the photon absorption (photocurrent) indicates hot electrons are captured more effectively by modifying the Schottky barrier. This study can shed light on a quantitative understanding and application of charge behavior at metal-semiconductor interfaces, in solar energy conversion, or in a catalytic reaction.

Determining the Effect of Hot Electron Dissipation on Molecular Scattering Experiments at Metal Surfaces

Nonadiabatic effects that arise from the concerted motion of electrons and atoms at comparable energy and time scales are omnipresent in thermal and light-driven chemistry at metal surfaces. Excited (hot) electrons can measurably affect molecule-metal reactions by contributing to state-dependent reaction probabilities. Vibrational state-to-state scattering of NO on Au(111) has been one of the most studied examples in this regard, providing a testing ground for developing various nonadiabatic theories. This system is often cited as the prime example for the failure of electronic friction theory, a very efficient model accounting for dissipative forces on metal-adsorbed molecules due to the creation of hot electrons in the metal. However, the exact failings compared to experiment and their origin from theory are not established for any system because dynamic properties are affected by many compounding simulation errors of which the quality of nonadiabatic treatment is just one. We use a high-dimensional machine learning representation of electronic structure theory to minimize errors that arise from quantum chemistry. This allows us to perform a comprehensive quantitative analysis of the performance of nonadiabatic molecular dynamics in describing vibrational state-to-state scattering of NO on Au(111) and compare directly to adiabatic results. We find that electronic friction theory accurately predicts elastic and single-quantum energy loss but underestimates multiquantum energy loss and overestimates molecular trapping at high vibrational excitation. Our analysis reveals that multiquantum energy loss can potentially be remedied within friction theory whereas the overestimation of trapping constitutes a genuine breakdown of electronic friction theory. Addressing this overestimation for dynamic processes in catalysis and surface chemistry will likely require more sophisticated theories.

Controlling hot electron flux and catalytic selectivity with nanoscale metal-oxide interfaces

Interaction between metal and oxides is an important molecular-level factor that influences the selectivity of a desirable reaction. Therefore, designing a heterogeneous catalyst where metal-oxide interfaces are well-formed is important for understanding selectivity and surface electronic excitation at the interface. Here, we utilized a nanoscale catalytic Schottky diode from Pt nanowire arrays on TiO2 that forms a nanoscale Pt-TiO2 interface to determine the influence of the metal-oxide interface on catalytic selectivity, thereby affecting hot electron excitation; this demonstrated the real-time detection of hot electron flow generated under an exothermic methanol oxidation reaction. The selectivity to methyl formate and hot electron generation was obtained on nanoscale Pt nanowires/TiO2, which exhibited ~2 times higher partial oxidation selectivity and ~3 times higher chemicurrent yield compared to a diode based on Pt film. By utilizing various Pt/TiO2 nanostructures, we found that the ratio of interface to metal sites significantly affects the selectivity, thereby enhancing chemicurrent yield in methanol oxidation. Density function theory (DFT) calculations show that formation of the Pt-TiO2 interface showed that selectivity to methyl formate formation was much larger in Pt nanowire arrays than in Pt films because of the different reaction mechanism.

Scattering of NO(ν = 3) from Au(111): a stochastic dissipative quantum dynamical perspective

In this work, we present a theoretical study of the scattering dynamics of NO(ν = 3) from an ideal unreconstructed Au(111) surface. The simulations are performed in reduced dimensions at the three high-symmetry sites employing our recent modification to the stochastic wave packet approach for diatomic-metal scattering [J. Chem. Phys., 2019, 150, 184105]. Energy exchange between molecular vibrational degrees of freedom and the electron-hole pairs (EHP) of the metal is accounted for by quantized stochastic jump operators, with associated rates obtained from a microscopic model based on Fermi's golden rule. The simulations are found to reproduce the experimentally observed trend of enhanced vibrational relaxation probabilities with increasing initial translational energy. Molecular dynamics simulations with electronic friction (MDEF) in the independent atom approximation were performed to compare classical and quantum dynamical descriptions of that system. Significant differences between these two descriptions were found indicating that intermode coupling must be described accurately by using a good potential energy surface, and pointing out at the potentially important influence of a quantized description of energy relaxation in describing the scattering of NO from Au(111).

Direct matter disassembly via electron beam control: electron-beam-mediated catalytic etching of graphene by nanoparticles

We report electron-beam activated motion of a catalytic nanoparticle along a graphene step edge and associated etching of the edge. The catalytic hydrogenation process was observed to be activated by a combination of elevated temperature and electron beam irradiation. Reduction of beam fluence on the particle was sufficient to stop the process, leading to the ability to switch on and off the etching. Such an approach enables the targeting of individual nanoparticles to induce motion and beam-controlled etching of matter through activated electrocatalytic processes. The applications of electron-beam control as a paradigm for molecular-scale robotics are discussed.

Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications

This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.

First principles rates for surface chemistry employing exact transition state theory: application to recombinative desorption of hydrogen from Cu(111)

We present first principles calculations of the reactive flux for thermal recombinative desorption of hydrogen from Cu(111).

Unified and transferable description of dynamics of H2 dissociative adsorption on multiple copper surfaces via machine learning

Schematic of the developed neural network potential energy surface enabling a unified and transferable description of dynamics of H₂ dissociative adsorption on multiple copper surfaces.

When Classical Trajectories Get to Quantum Accuracy: The Scattering of H2 on Pd(111)

When elementary reactive processes occur at such low energies that only a few states of reactants and/or products are available, quantum effects strongly manifest and the standard description of the dynamics within the classical framework fails. We show here, for H₂ scattering on Pd(111), that by pseudoquantizing in the spirit of Bohr the relevant final actions of the system, along with adequately treating the diffraction-mediated trapping of the incoming wave, classical simulations achieve an unprecedented agreement with state-of-the-art quantum dynamics calculations.

Vibrational Relaxation Lifetime of a Physisorbed Molecule at a Metal Surface

Previous measurements of vibrational relaxation lifetimes for molecules adsorbed at metal surfaces yielded values of 1-3 ps; however, only chemisorbed molecules have been studied. We report the first measurements of the vibrational relaxation lifetime of a molecule physisorbed to a metal surface. For CO(v=1) adsorbed on Au(111) at 35 K the vibrational lifetime of the excited stretching mode is 49±3  ps. The long lifetime seen here is likely to be a general feature of physisorption, which involves weaker electronic coupling between the adsorbate and the solid due to bonding at larger distances.

Strong Vibrational Relaxation of NO Scattered from Au(111): Importance of the Adiabatic Potential Energy Surface

Experimental observations of multiquantum relaxation of highly vibrationally excited NO scattering from Au(111) are a benchmark for the breakdown of the Born-Oppenheimer approximation in molecule-surface systems. This remarkable vibrational inelasticity was long thought to be almost exclusively mediated by electron transfer; however, no theories have quantitatively reproduced various experimental data. This was suggested to be due to errors in the adiabatic potential energy surface (PES) used in those studies. Here, we investigate electronically adiabatic molecular dynamics of this system with a globally accurate high-dimensional PES that is newly developed with neural networks from first principles. The NO vibrational energy loss is much larger than that on the earlier adiabatic PES. Additionally, the translational inelasticity and translational energy dependence of vibrational inelasticity are also more accurately reproduced. There is reason to be optimistic that electronically nonadiabatic theories using this adiabatic PES as a starting point might accurately reproduce experimental results on this important system.

Fundamental mechanisms for molecular energy conversion and chemical reactions at surfaces

The dream of theoretical surface chemistry is to predict the outcome of reactions in order to find the ideal catalyst for a certain application. Having a working ab initio theory in hand would not only enable these predictions but also provide insights into the mechanisms of surface reactions. The development of theoretical models can be assisted by experimental studies providing benchmark data. Though for some reactions a quantitative agreement between experimental observations and theoretical calculations has been achieved, theoretical surface chemistry is in general still far away from gaining predictive power. Here we review recent experimental developments towards the understanding of surface reactions. It is demonstrated how quantum-state resolved scattering experiments on reactive and nonreactive systems can be used to test front-running theoretical approaches. Two challenges for describing dynamics at surfaces are addressed: nonadiabaticity in diatomic molecule surface scattering and the increasing system size when observing and describing the dynamics of polyatomic molecules at surfaces. Finally recent experimental studies on reactive systems are presented. It is shown how elementary steps in a complex surface reaction can be revealed experimentally.

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.

Orbital-Dependent Electronic Friction Significantly Affects the Description of Reactive Scattering of N2 from Ru(0001)

Electron-hole pair (ehp) excitation is thought to substantially affect the dynamics of molecules on metal surfaces, but it is not clear whether this can be better addressed by orbital-dependent friction (ODF) or the local density friction approximation (LDFA). We investigate the effect of ehp excitation on the dissociative chemisorption of N2 on and its inelastic scattering from Ru(0001), which is the benchmark system of highly activated dissociation, with these two different models. ODF is in better agreement with the best experimental estimates for the reaction probabilities than LDFA, yields results for vibrational excitation in better agreement with experiment, but slightly overestimates the translational energy loss during scattering. N2 on Ru(0001) is thus the first system for which the ODF and LDFA approaches are shown to yield substantially different results for easily accessible experimental observables, including reaction probabilities.

Reactive and Nonreactive Scattering of HCl from Au(111): An Ab Initio Molecular Dynamics Study

The HCl + Au(111) system has recently become a benchmark for highly activated dissociative chemisorption, which presumably is strongly affected by electron-hole pair excitation. Previous dynamics calculations, which were based on density functional theory at the generalized gradient approximation level (GGA-DFT) for the molecule-surface interaction, have all overestimated measured reaction probabilities by at least an order of magnitude. Here, we perform ab initio molecular dynamics (AIMD) and AIMD with electronic friction (AIMDEF) calculations employing a density functional that includes the attractive van der Waals interaction. Our calculations model the simultaneous and possibly synergistic effects of surface temperature, surface atom motion, electron-hole pair excitation, the molecular beam conditions of the experiments, and the van der Waals interaction on the reactivity. We find that reaction probabilities computed with AIMDEF and the SRP32-vdW functional still overestimate the measured reaction probabilities, by a factor 18 for the highest incidence energy at which measurements were performed (≈2.5 eV). Even granting that the experiment could have underestimated the sticking probability by about a factor three, this still translates into a considerable overestimation of the reactivity by the current theory. Likewise, scaled transition probabilities for vibrational excitation from ν = 1, j = 1 to ν = 2 are overestimated by the AIMDEF theory, by factors 3-8 depending on the initial conditions modeled. Energy losses to the surface and translational energy losses are, however, in good agreement with experimental values.

A comparison of surface hopping approaches for capturing metal-molecule electron transfer: A broadened classical master equation versus independent electron surface hopping

Within a generalized Anderson-Holstein model, we investigate electron transfer rates using two different surface hopping algorithms: a broadened classical master equation (BCME) and independent electron surface hopping (IESH). We find that for large enough bandwidth and density of one electron states, and in the presence of external friction, the IESH results converge to the BCME results for impurity-bath model systems, recovering both relaxation rates and equilibrium populations. Without external friction, however, the BCME and IESH results can strongly disagree, and preliminary evidence suggests that IESH does not always recover the correct equilibrium state. Finally, we also demonstrate that adding an electronic thermostat to IESH does help drive the metallic substrate to the correct equilibrium state, but this improvement can sometimes come at the cost of worse short time dynamics. Overall, our results should be of use for all computational chemists looking to model either gas phase scattering or electrochemical dynamics at a metal interface.

Electron transfer mediates vibrational relaxation of CO in collisions with Ag(111)

We report vibrational relaxation probabilities for CO(v = 17) scattered from Ag(111) and compare our results to studies on other molecule–surface systems, which indicates a clear dependence of the relaxation probability on the work function of the surface and the electron binding energy of the molecule.

The Sommerfeld ground-wave limit for a molecule adsorbed at a surface

Using a mid-infrared emission spectrometer based on a superconducting nanowire single-photon detector, we observed the dynamics of vibrational energy pooling of carbon monoxide (CO) adsorbed at the surface of a sodium chloride (NaCl) crystal. After exciting a majority of the CO molecules to their first vibrationally excited state (v = 1), we observed infrared emission from states up to v = 27. Kinetic Monte Carlo simulations showed that vibrational energy collects in a few CO molecules at the expense of those up to eight lattice sites away by selective excitation of NaCl’s transverse phonons. The vibrating CO molecules behave like classical oscillating dipoles, losing their energy to NaCl lattice vibrations via the electromagnetic near-field. This is analogous to Sommerfeld’s description of radio transmission along Earth’s surface by ground waves.

Boosting hot electron flux and catalytic activity at metal-oxide interfaces of PtCo bimetallic nanoparticles

Despite numerous studies, the origin of the enhanced catalytic performance of bimetallic nanoparticles (NPs) remains elusive because of the ever-changing surface structures, compositions, and oxidation states of NPs under reaction conditions. An effective strategy for obtaining critical clues for the phenomenon is real-time quantitative detection of hot electrons induced by a chemical reaction on the catalysts. Here, we investigate hot electrons excited on PtCo bimetallic NPs during H₂ oxidation by measuring the chemicurrent on a catalytic nanodiode while changing the Pt composition of the NPs. We reveal that the presence of a CoO/Pt interface enables efficient transport of electrons and higher catalytic activity for PtCo NPs. These results are consistent with theoretical calculations suggesting that lower activation energy and higher exothermicity are required for the reaction at the CoO/Pt interface.

The real-time quantitative detection of hot electrons provides critical clues to understand the origin of the enhanced catalytic performance of bimetallic nanoparticles (NPs). Here, the authors investigate hot electrons generated on bimetallic PtCo NPs during H₂ oxidation by measuring the chemicurrent on a catalytic nanodiode.