Six-dimensional quantum dynamics of an Eley-Rideal reaction between gaseous and adsorbed hydrogen atoms on Cu(111)

In the form of direct abstraction of a surface adsorbate by a gaseous projectile, the Eley-Rideal (ER) reaction at the gas-surface interface manifests interesting dynamics. Unfortunately, high-dimensional quantum dynamical (QD) studies for ER reactions remain very challenging, which demands a large configuration space and the coordinate transformation of wavefunctions. Here, we report the first six-dimensional (6D) fully coupled quantum scattering method for studying the ER reaction between gas phase H(D) atoms and adsorbed D(H) atoms on a rigid Cu(111) surface. Reaction probabilities and product rovibrational state distributions obtained by this 6D model are found to be quite different from those obtained by reduced-dimensional QD models, demonstrating the high-dimensional nature of the ER reaction. Using two distinct potential energy surfaces (PESs), we further discuss the influence of the PES on the calculated product vibrational and rotational state distributions, in comparison with experimental results. The lateral corrugation and the exothermicity of the PES are found to play a critical role in controlling the energy disposal in the ER reaction.

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.

Direct or Precursor-Mediated? Mechanisms for Methane Dissociation on Pt(110)-(2 × 1) at Both Low and High Incidence Energies

The activation of alkanes on metal catalysts may involve a precursor-mediated mechanism, in which impinging molecules are first trapped on the catalyst surface to form an adsorbed precursor and may undergo extensive excursion on the surface in search of an active site. A characteristic feature of such a mechanism is an increasing initial sticking probability (S0) with decreasing incidence energy at low incidence energies. Indeed, such "negative activation" was observed on the reconstructed Pt(110)-(2 × 1) surface with a missing row structure. In this paper, we describe an extensive theoretical investigation of methane dissociation on Pt(110)-(2 × 1) using a machine-learned high-dimensional potential energy surface (PES) based on a first-principles training data set. Quasi-classical trajectories (QCTs) are calculated on the PES to simulate the dissociation of both CH4 and CHD3 at various incidence energies. The agreement with the measured initial sticking probabilities is shown to be substantially improved for high incidence energies when compared to previous theoretical studies, indicating a better characterization of the dissociation barrier. Additional QCT calculations have been carried out for the trapping and diffusion of CHD3 under experimental conditions at low incidence energies. The trapping probability is shown to increase with decreasing incidence energy, consistent with the experimentally observed "negative activation" below 10 kJ/mol. The reactivity of the trapped methane is attributed to the combined effect of its nonthermal diffusion across the surface Pt rows and the lowered barrier reached by surface thermal fluctuation. These simulations shed valuable light on the microscopic dynamics of the initial and often rate-limiting step in heterogeneous catalytic processes involving alkanes.

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.

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.

Landing Proteins on Graphene Trampoline Preserves Their Gas-Phase Folding on the Surface

Molecule-surface collisions are known to initiate dynamics that lead to products inaccessible by thermal chemistry. These collision dynamics, however, have mostly been examined on bulk surfaces, leaving vast opportunities unexplored for molecular collisions on nanostructures, especially on those that exhibit mechanical properties radically different from those of their bulk counterparts. Probing energy-dependent dynamics on nanostructures, particularly for large molecules, has been challenging due to their fast time scales and high structural complexity. Here, by examining the dynamics of a protein impinging on a freestanding, single-atom-thick membrane, we discover molecule-on-trampoline dynamics that disperse the collision impact away from the incident protein within a few picoseconds. As a result, our experiments and ab initio calculations show that cytochrome c retains its gas-phase folded structure when it collides onto freestanding single-layer graphene at low energies (∼20 meV/atom). The molecule-on-trampoline dynamics, expected to be operative on many freestanding atomic membranes, enable reliable means to transfer gas-phase macromolecular structures onto freestanding surfaces for their single-molecule imaging, complementing many bioanalytical techniques.

The topology of the reaction stereo-dynamics in chemi-ionizations

Details on the stereo-dynamic topology of chemi-ionizations highlight the role of the centrifugal barrier of colliding reactants: it acts as a selector of the orbital quantum number effective for reaction in a state-to-state treatment. Here, an accurate internally consistent formulation of the Optical interaction potentials, obtained by the combined analysis of scattering and spectroscopic experimental findings, casts light on structure, energy and angular momentum couplings of the precursor (pre-reactive) state controlling the stereo-dynamics of prototypical chemi-ionization reactions. The closest approach (turning point) of reagents, is found to control the relative weight of two different reaction mechanisms: (i) A direct mechanism stimulated by exchange chemical forces mainly acting at short separation distances and high collision energy; (ii) An indirect mechanism, caused by the combination of weak chemical and physical forces dominant at larger distances, mainly probed at low collision energy, that can be triggered by a virtual photon exchange between reagents.

An examination of phonon-inelastic molecule-metal scattering using reduced density matrix and stochastic wave packet methods

We explore the application of reduced density matrix-based approaches to molecules interacting with the lattice vibrations of metals, an interaction responsible for the temperature dependence of many of the fundamental steps of catalysis. We avoid the use of simple models for the bath and instead use density functional theory to compute all molecule-phonon interactions and the properties of the lattice phonons, for methane scattering from Ir(111). We find that while the large metal mass leads to long bath correlation times, these are not significantly longer than the time over which the reduced density matrix changes due to interactions with the bath. We show that the neglect of memory is reasonable and the use of the Redfield equation is justified. We also show how the commonly used rotating wave approximation is far too severe for this scattering problem. A less restrictive approximation that is nearly exact for our system gives an equation of motion in the Lindblad form. As a result, the Monte Carlo wave packet methods can be used to describe gas-phonon scattering, guaranteeing positivity, and with all couplings derived from first-principles.

Plasma-Catalysis of Nonoxidative Methane Coupling: A Dynamic Investigation of Plasma and Surface Microkinetics over Ni(111)

A heterogeneous catalytic microkinetic model is developed and implemented in a zero-dimensional (0D) plasma model for the dynamic study of methane nonoxidative coupling over Ni(111) at residence times and power densities consistent with experimental reactors. The microkinetic model is thermodynamically consistent and is parameterized based on the heats of chemisorption of surface species on Ni(111). The surface network explicitly accounts for the interactions of plasma species, namely, molecules, radicals, and vibrationally excited states, with the catalyst active sites via adsorption and Eley-Rideal reactions. The Fridman-Macheret model is used to describe the enhancement of the rate of the dissociative adsorption of vibrationally excited CH₄, H₂, and C₂H₆. In combination with a previously developed detailed kinetic scheme for nonthermal methane plasma, 0D simulation results bring insights into the complex dynamic interactions between the plasma phase and the catalyst during methane nonoxidative coupling. Differential turnover frequencies achieved by plasma-catalysis are higher than those of equivalent plasma-only and catalysis-only simulations combined; however, this performance can only be sustained momentarily. Hydrogen produced from dehydrogenation of ethane via electron collisions within the plasma is found to quickly saturate the surface and even promote the conversion of surface CH₃* back to methane.

Adiabatic models for the quantum dynamics of surface scattering with lattice effects

In this contribution, we review models for the lattice effects in quantum dynamics calculations on surface scattering, which is important to modeling heterogeneous catalysis for achieving an interpretation of experimental measurements. Unlike dynamics models for reactions in the gas phase, those for heterogeneous reactions have to include the effects of the surface. For manageable computational costs in calculations, the effects of static surface (SS) are firstly modeled as this is simply and easily implemented. Then, the SS model has to be improved to include the effects of the flexible surface, that is the lattice effects. To do this, various surface models have been designed where the coordinates of the surface atoms are introduced in the Hamiltonian operator, especially those of the top surface atom. Based on this model Hamiltonian operator, extensive multi-dimension quantum dynamics calculations can be performed to recover the lattice effects. Here, we first review an overview of the techniques in constructing the Hamiltonian operator, which is a sum of the kinetic energy operator (KEO) and potential energy surface (PES). Since the PES containing the coordinates of the surface atoms in a cell is still expensive, the SS model is often accepted. We consider a mathematical model, called the coupled harmonic oscillator (CHO) model, to introduce the concepts of adiabatic and diabatic representations for separating the molecule and surface. Under the adiabatic model, we further introduce the expansion model where the potential function is Taylor expanded around the optimized geometry of the surface. By an expansion model truncated at the first and second order, various coupling surface models between the molecule and surface are derived. Moreover, by further and deeply understanding the adiabatic representation, an effective Hamiltonian operator is obtained by optimizing the total wave function in factorized form. By this factorized form of wave function and effective Hamiltonian operator, the geometry phase of the surface wave function is theoretically found. This theoretical prediction may be measured by carefully designing experiments. Finally, discussions on the adiabatic representation, the PES construction, and possibility of the classical-dynamics solutions are given. Based on these discussions, a simple outlook on the dynamics of photocatalytics is finally given.

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.

Direct conversion of N2 and O2: status, challenge and perspective

As key components of air, nitrogen (N₂) and oxygen (O₂) are the vital constituents of lives. Synthesis of NO₂, and C-N-O organics direct from N₂ and O₂, rather than from an intermediate NH₃ (known as the Haber-Bosch process), is tantalizing. However, the extremely strong N≡N triple bond (945 kJ mol^-1) and the nonpolar stable electron configuration of dinitrogen lead to its conversion being extensively energy demanding. The further selective synthesis of high-value C-N-O organics directly from N₂, O₂ and C-containing molecules is attractive yet greatly challenging from both scientific and engineering perspectives. Enormous efforts have been dedicated to the direct conversion of N₂ and O₂ via traditional and novel techniques, including thermochemical, plasma, electrochemical, ultrasonic and photochemical conversion. In this review, we aim to provide a thorough comprehension of the status and challenge of the direct conversion of N₂, O₂ and C-containing molecules (particularly N₂ and O₂). Moreover, we will propose some future perspectives to stimulate more inspiration from the scientific community to tackle the scientific and engineering challenges.

Machine-Learned Free Energy Surfaces for Capillary Condensation and Evaporation in Mesopores

Using molecular simulations, we study the processes of capillary condensation and capillary evaporation in model mesopores. To determine the phase transition pathway, as well as the corresponding free energy profile, we carry out enhanced sampling molecular simulations using entropy as a reaction coordinate to map the onset of order during the condensation process and of disorder during the evaporation process. The structural analysis shows the role played by intermediate states, characterized by the onset of capillary liquid bridges and bubbles. We also analyze the dependence of the free energy barrier on the pore width. Furthermore, we propose a method to build a machine learning model for the prediction of the free energy surfaces underlying capillary phase transition processes in mesopores.

Mode Selective Chemistry for the Dissociation of Methane on Efficient Ni/Pt-Bimetallic Alloy Catalysts

The mode selectivity of methane dissociation is studied on three different Ni/Pt-bimetallic alloy surfaces using a fully quantum approach based on reaction path Hamiltonian. Dissociative sticking probability depends on the...

Mechanochemistry of phosphate esters confined between sliding iron surfaces

The molecular structure of lubricant additives controls not only their adsorption and dissociation behaviour at the nanoscale, but also their ability to reduce friction and wear at the macroscale. Here, we show using nonequilibrium molecular dynamics simulations with a reactive force field that tri(s-butyl)phosphate dissociates much faster than tri(n-butyl)phosphate when heated and compressed between sliding iron surfaces. For both molecules, dissociative chemisorption proceeds through cleavage of carbon-oxygen bonds. The dissociation rate increases exponentially with temperature and stress. When the rate-temperature-stress data are fitted with the Bell model, both molecules have similar activation energies and activation volumes and the higher reactivity of tri(s-butyl)phosphate is due to a larger pre-exponential factor. These observations are consistent with experiments using the antiwear additive zinc dialkyldithiophosphate. This study represents a crucial step towards the virtual screening of lubricant additives with different substituents to optimise tribological performance.

The trapping of methane on Ir(111): A first-principles quantum study

We implement a fully quantum mechanical study of methane trapping on Ir(111), where the phonons, the molecule-surface interaction, and the molecule-phonon coupling are all computed from first-principles. We find that both the surface corrugation and the phonon coupling vary strongly with molecular orientation and that there is a "chemical" aspect to this due to the catalytic nature of the metal. For example, molecules with reactive orientations can approach close to surface sites with low barriers to dissociation. Moreover, lattice motion can lower the barrier to dissociation, leading to unusual behavior for the phonon coupling. We find good agreement with experiment and two recent classical studies if we average our potential energy surface over several orientations of the molecule. We also find reasonable agreement with a recent study of methane diffraction, although we show that diffraction does not play a major role in trapping on the smooth Ir(111) surface and that trapping obeys normal energy scaling, consistent with experiment. We show that the trapping probability can be sensitive to the temperature at both high and low incidence energies. Relaxation and desorption of trapped particles are examined.

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.

Insights into adsorption, diffusion, and reactions of atomic nitrogen on a highly oriented pyrolytic graphite surface

To gain insight into the nitrogen-related gas-surface reaction dynamics on carbon-based thermal protection systems of hypersonic vehicles, we have investigated the adsorption, diffusion, and reactions of atomic nitrogen, N(⁴S), on the (0001) face of graphite using periodic density functional theory with a dispersion corrected functional. The atomic nitrogen is found to bind with pristine graphite at a bridge site, with a barrier of 0.88 eV for diffusing to an adjacent bridge site. Its adsorption energy at defect sites is significantly higher, while that between graphene layers is lower. The formation of N₂ via Langmuir-Hinshelwood (LH) and Eley-Rideal (ER) mechanisms was also investigated. In the LH pathway, the recombinative desorption of N₂ proceeds via a transition state with a relatively low barrier (0.53 eV). In addition, there is a metastable surface species, which is capable of trapping the nascent N₂ at low surface temperatures as a result of the large energy disposal into the N-N vibration. The desorbed N₂ is highly excited in both of its translational and vibrational degrees of freedom. The ER reaction is direct and fast, and it also leads to translationally and internally excited N₂. Finally, the formation of CN from a defect site is calculated to be endoergic by 2.75 eV. These results are used to rationalize the results of recent molecular beam experiments.

Fast Molecular Compression by a Hyperthermal Collision Gives Bond-Selective Mechanochemistry

Using electrospray ion beam deposition, we collide the complex molecule Reichardt's dye (C_{41}H_{30}NO^{+}) at low, hyperthermal translational energy (2-50 eV) with a Cu(100) surface and image the outcome at single-molecule level by scanning tunneling microscopy. We observe bond-selective reaction induced by the translational kinetic energy. The collision impulse compresses the molecule and bends specific bonds, prompting them to react selectively. This dynamics drives the system to seek thermally inaccessible reactive pathways, since the compression timescale (subpicosecond) is much shorter than the thermalization timescale (nanosecond), thereby yielding reaction products that are unobtainable thermally.

Towards bridging the structure gap in heterogeneous catalysis: the impact of defects in dissociative chemisorption of methane on Ir surfaces

The negatively activated region in CH₄ dissociation is attributed to a precursor-mediated mechanism involving surface defects.

Quantum-State Controlled Reaction Channels in Chemi-ionization Processes: Radiative (Optical-Physical) and Exchange (Oxidative-Chemical) Mechanisms

ConspectusMost chemical processes are triggered by electron or charge transfer phenomena (CT). An important class of processes involving CT are chemi-ionization reactions. Such processes are very common in nature, involving neutral species in ground or excited electronic states with sufficient energy (X*) to yield ionic products, and are considered as the primary initial step in flames. They are characterized by pronounced electronic rearrangements that take place within the collisional complex (X···M)* formed by approaching reagents, as shown by the following scheme, where M is an atomic or molecular target: X* + M → (X···M)* → [(X+···M) ↔ (X···M+)]e- → via ⁡ e - ⁡ CT (X···M)+ + e- → final ions.Despite their important role in fundamental and applied research, combustion, plasmas, and astrochemistry, a unifying description of these basic processes is still lacking. This Account describes a new general theoretical methodology that demonstrates, for the first time, that chemi-ionization reactions are prototypes of gas phase oxidation processes occurring via two different microscopic mechanisms whose relative importance varies with collision energy, Ec, and separation distance, R. These mechanisms are illustrated for simple collisions involving Ne*(3P2,0) and noble gases (Ng). In thermal and hyperthermal collisions probing interactions at intermediate and short R, the transition state [(Ne···Ng)+]e- is a molecular species described as a molecular ion core with an orbiting Rydberg electron in which the neon reagent behaves as a halogen atom (i.e., F) with high electron affinity promoting chemical oxidation. Conversely, subthermal collisions favor a different reaction mechanism: Ng chemi-ionization proceeds through another transition state [Ne*······Ng], a weakly bound diatomic-lengthened complex where Ne* reagent, behaving as a Na atom, loses its metastability and stimulates an electron ejection from M by a concerted emission-absorption of a "virtual" photon. This is a physical radiative mechanism promoting an effective photoionization. In the thermal regime of Ec, there is a competition between these two mechanisms. The proposed method overcomes previous approaches for the following reasons: (1) it is consistent with all assumptions invoked in previous theoretical descriptions dating back to 1970; (2) it provides a simple and general description able to reproduce the main experimental results from our and other laboratories during last 40 years; (3) it demonstrates that the two "exchange" and "radiative" mechanisms are simultaneously present with relative weights that change with Ec (this viewpoint highlights the fact that the "canonical" chemical oxidation process, dominant at high Ec, changes its nature in the subthermal regime to a direct photoionization process; therefore, it clarifies differences between the cold chemistry of terrestrial and interstellar environments and the energetic one of combustion and flames); (4) the proposed method explicitly accounts for the influence of the degree of valence orbital alignment on the selective role of each reaction channel as a function of Ec and also permits a description of the collision complex, a rotating adduct, in terms of different Hund's cases of angular momentum couplings that are specific for each reaction channel; (5) finally, the method can be extended to reaction mechanisms of redox, acid-base, and other important condensed phase reactions.

High-Fidelity Potential Energy Surfaces for Gas-Phase and Gas-Surface Scattering Processes from Machine Learning

In this Perspective, we review recent advances in constructing high-fidelity potential energy surfaces (PESs) from discrete ab initio points, using machine learning tools. Such PESs, albeit with substantial initial investments, provide significantly higher efficiency than direct dynamics methods and/or high accuracy at a level that is not affordable by on-the-fly approaches. These PESs not only are a necessity for quantum dynamical studies because of delocalization of wave packets but also enable the study of low-probability and long-time events in (quasi-)classical treatments. Our focus here is on inelastic and reactive scattering processes, which are more challenging than bound systems because of the involvement of continua. Relevant applications and developments for dynamical processes in both the gas phase and at gas-surface interfaces are discussed.

Setting benchmarks for modelling gas-surface interactions using coherent control of rotational orientation states

The coherent evolution of a molecular quantum state during a molecule-surface collision is a detailed descriptor of the interaction potential which was so far inaccessible to measurements. Here we use a magnetically controlled molecular beam technique to study the collision of rotationally oriented ground state hydrogen molecules with a lithium fluoride surface. The coherent control nature of the technique allows us to measure the changes in the complex amplitudes of the rotational projection quantum states, and express them using a scattering matrix formalism. The quantum state-to-state transition probabilities we extract reveal a strong dependency of the molecule-surface interaction on the rotational orientation of the molecules, and a remarkably high probability of the collision flipping the rotational orientation. The scattering matrix we obtain from the experimental data delivers an ultra-sensitive benchmark for theory to reproduce, guiding the development of accurate theoretical models for the interaction of H₂ with a solid surface.

A fundamental and predictive understanding of molecule-surface interactions is challenging to obtain. Here the authors report an experimental technique allowing direct measurement of the scattering matrix, which reports on the coherent evolution of quantum states of a molecule scattering from a surface.

Nonadiabatic Molecular Dynamics at Metal Surfaces

Dynamics at molecule-metal interfaces are a subject of intense current interest and come in many different flavors of experiments: gas-phase scattering, chemisorption, electrochemistry, nanojunction transport, and heterogeneous catalysis, to name a few. These dynamics involve nuclear degrees of freedom entangled with many electronic degrees of freedom (in the metal), and as such there is always the possibility for nonadiabatic phenomena to appear: the nuclei do not necessarily need to move slower than the electrons to break the Born-Oppenheimer (BO) approximation. In this Feature Article, we review a set of dynamical methods developed recently to deal with such nonadiabatic phenomena at a metal surface, methods that serve as alternatives to Tully's independent electron surface hopping (IESH) model. In the weak molecule-metal coupling regime, a classical master equation (CME) can be derived and a simple surface hopping approach is proposed to propagate nuclear and electronic dynamics stochastically. In the strong molecule-metal interaction regime, a Fokker-Planck equation can be derived for the nuclear dynamics, with electronic DoFs incorporated into the overall friction and random force. Lastly, a broadened classical master equation (BCME) can interpolate between the weak and strong molecule-metal interactions. Here, we briefly review these methods and the relevant benchmarking data, showing in particular how the methods can be used to calculate nonequilibrium transport properties. We highlight several open questions and pose several avenues for future study.

Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective

The onset of facile intramolecular vibrational energy flow can be related to features in the connected network of anharmonic resonances in the classical phase space.

Plasma-enhanced catalysis for the upgrading of methane: a review of modelling and simulation methods

Modelling methods and simulation works on the upgrading of methane via plasma and plasma-enhanced catalysis reviewed.

Ring Polymer Molecular Dynamics in Gas-Surface Reactions: Inclusion of Quantum Effects Made Simple

Accurately modeling gas-surface collision dynamics presents a great challenge for theory, especially in the low-energy (or temperature) regime where quantum effects are important. Here, a path integral-based nonequilibrium ring polymer molecular dynamics (NE-RPMD) approach is adapted to calculate dissociative initial sticking probabilities (S₀) of H₂ on Cu(111) and D₂O on Ni(111), revealing the distinct quantum nature in the two benchmark surface reactions. NE-RPMD successfully captures quantum tunneling in H₂ dissociation at very low energies, where the quasi-classical trajectory (QCT) method suddenly fails. Additionally, QCT substantially overestimates S₀ of D₂O because of severe zero point energy (ZPE) leakage, even at collision energies greater than the ZPE-corrected barrier. Instead, NE-RPMD predicts S₀ values of D₂O in much improved agreement with reference results obtained by the quantum wavepacket method with reasonable corrections of the thermal contribution. Our results suggest NE-RPMD as a promising approach to model quantum effects in gas-surface reactions.

Dynamical Study of the Dissociative Chemisorption of CHD3 on Pd(111)

The specific reaction parameter (SRP) approach to density functional theory has been shown to model reactions of polyatomic molecules with metal surfaces important for heterogeneous catalysis in the industry with chemical accuracy. However, transferability of the SRP functional among systems in which methane interacts with group 10 metals remains unclear for methane + Pd(111). Therefore, in this work, predictions have been made for the reaction of CHD₃ on Pd(111) using Born-Oppenheimer molecular dynamics while also performing a rough comparison with experimental data for CH₄ + Pd(111) obtained for lower incidence energies. Hopefully, future experiments can test the transferability of the SRP functional among group 10 metals also for Pd(111). We found that the reactivity of CHD₃ on Pd(111) is intermediate between and similar to either Pt(111) or Ni(111), depending on the incidence energy and the initial vibrational state distribution. This is surprising because the barrier height and experiments performed at lower incidence energies than investigated here suggest that the reactivity of Pd(111) should be similar to that of Pt(111) only. The relative decrease in the reactivity of Pd(111) at high incidence energies is attributed to site specificity of the reaction and to dynamical effects such as the bobsled effect and energy transfer from methane to the surface.

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.

Efficient Vibrational Energy Redistribution between Stretching Modes: State-to-State Quantum Scattering of H_{2}O from Cu(111)

State-to-state scattering dynamics of H_{2}O from Cu(111) has been studied by a fully coupled quantum mechanical model which explicitly accounts for the most important molecular degrees of freedom, based on a first-principles determined potential energy surface. When H_{2}O in its antisymmetric O-H stretching vibration (ν_{3}) collides with the surface, we find that the intramolecular vibrational energy redistribution (IVR) is predominant from ν_{3} to the symmetric stretching mode (ν_{1}), while rather inefficient to the bending mode (ν_{2}). This mode-specific IVR results from the strong couplings between stretching modes, which equally dispose the initial energy in ν_{3} into local stretching modes differing by a phase factor. Given the number of stretching modes in H_{2}O and CH_{4}, this mechanism naturally explains why the product ν_{1}/ν_{3} ratio calculated here is ∼3 times over that recently measured for CH_{4} scattering on Ni(111), suggesting that the nonstatistical IVR is more general than expected in polyatomic molecules.

Theoretical Study of Barrierless Chemical Reactions Involving Nearly Elastic Rebound: The Case of S(1D) + X2, X = H, D

For some values of the total angular momentum consistent with reaction, the title processes involve nonreactive trajectories proceeding through a single rebound mechanism during which the internal motion of the reagent diatom is nearly unperturbed. When such paths are in a significant amount, the classical reaction probability is found to be markedly lower than the quantum mechanical one. This finding was recently attributed to an unusual quantum effect called diffraction-mediated trapping, and a semiclassical correction was proposed in order to take into account this effect in the classical trajectory method. In the present work, we apply the resulting approach to the calculation of opacity functions as well as total and state-resolved integral cross sections (ICSs) and compare the values obtained with exact quantum ones, most of which are new. As the title reactions proceed through a deep insertion well, mean potential statistical calculations are also presented. Seven values of the collision energy, ranging from 30 to 1127 K, are considered. Two remarkable facts stand out: (i) The corrected classical treatment strongly improves the accuracy of the opacity function as compared to the usual classical treatment. When the entrance transition state is tight, however, those trajectories crossing it with a bending vibrational energy below the zero point energy must be discarded. (ii) The quantum opacity function, particularly its cutoff, is finely reproduced by the statistical approach. Consequently, the total ICS is also very well described by the two previous approximate methods. These, however, do not predict state-resolved ICSs with the same accuracy, proving thereby that (i) one or several genuine quantum effects involved in the dynamics are missed by the corrected classical treatment and (ii) the dynamics are not fully statistical.

Dynamics in reactions on metal surfaces: A theoretical perspective

Recent advances in theoretical characterization of reaction dynamics on metal surfaces are reviewed. It is shown that the widely available density functional theory of metals and their interactions with molecules have enabled first principles theoretical models for treating surface reaction dynamics. The new theoretical tools include methods to construct high-dimensional adiabatic potential energy surfaces, to characterize nonadiabatic processes within the electronic friction models, and to describe dynamics both quantum mechanically and classically. Three prototypical surface reactions, namely, dissociative chemisorption, Eley-Rideal reactions, and recombinative desorption, are surveyed with a focus on some representative examples. While principles governing gas phase reaction dynamics may still be applicable, the presence of the surface introduces a higher level of complexity due to strong interaction between the molecular species and metal substrate. Furthermore, most of these reactive processes are impacted by energy exchange with surface phonons and/or electron-hole pair excitations. These theoretical studies help to interpret and rationalize experimental observations and, in some cases, guide experimental explorations. Knowledge acquired in these fundamental studies is expected to impact many practical problems in a wide range of interfacial processes.

Accurate Probabilities for Highly Activated Reaction of Polyatomic Molecules on Surfaces Using a High-Dimensional Neural Network Potential: CHD3 + Cu(111)

An accurate description of reactive scattering of molecules on metal surfaces often requires the modeling of energy transfer between the molecule and the surface phonons. Although ab initio molecular dynamics (AIMD) can describe this energy transfer, AIMD is at present untractable for reactions with reaction probabilities smaller than 1%. Here, we show that it is possible to use a neural network potential to describe a polyatomic molecule reacting on a mobile metal surface with considerably reduced computational effort compared to AIMD. The highly activated reaction of CHD₃ on Cu(111) is used as a test case for this method. It is observed that the reaction probability is influenced considerably by dynamical effects such as the bobsled effect and surface recoil. A special dynamical effect for CHD₃ + Cu(111) is that a higher vibrational efficacy is obtained for two quanta in the CH stretch mode than for a single quantum.