Electron-hole pair effects in methane dissociative chemisorption on Ni(111)

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.

Stochastic Schrödinger Equation Approach to Real-Time Dynamics of Anderson-Holstein Impurities: An Open Quantum System Perspective

We develop a stochastic Schrödinger equation (SSE) framework to simulate the real-time dynamics of Anderson-Holstein (AH) impurities coupled to a continuous Fermionic bath. The bath degrees of freedom are incorporated through fluctuating terms determined by exact system-bath correlations, which is derived in an ab initio manner. We show that such an SSE treatment provides a middle ground between numerically expansive microscopic simulations and macroscopic master equations. Computationally, the SSE model enables efficient numerical methods for propagating stochastic trajectories. We demonstrate that this approach not only naturally provides microscopically detailed information unavailable from reduced models but also captures effects beyond master equations, thus serving as a promising tool to study open quantum dynamics emerging in physics and chemistry.

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.

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.

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.

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.

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.

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).

Electrons and Phonons Cooperate in the Laser-Induced Desorption of CO from Pd(111)

Femtosecond laser induced desorption of CO from a CO-covered Pd(111) surface is investigated with ab initio molecular dynamics with electronic friction that incorporates effects due to the excited electronic and phononic systems, as well as out-of-phase coadsorbate interactions. Our simulations show evidence of an important electron-phonon synergy in promoting CO desorption that has largely been neglected in other similar systems. At the saturated coverage of 0.75 ML, effects due to CO-CO interadsorbate energy exchange are also important. Our dynamics simulations, in concert with site-specific desorption energy calculations, allow us to understand the large coverage dependence of the desorption yields observed in experiments.

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.

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.

Hot-electron effects during reactive scattering of H2 from Ag(111): the interplay between mode-specific electronic friction and the potential energy landscape

The breakdown of the Born-Oppenheimer approximation gives rise to nonadiabatic effects in gas-surface reactions at metal surfaces. However, for a given reaction, it remains unclear which factors quantitatively determine whether these effects measurably contribute to surface reactivity in catalysis and photo/electrochemistry. Here, we systematically investigate hot electron effects during H2 scattering from Ag(111) using electronic friction theory. We combine first-principles calculations of tensorial friction by time-dependent perturbation theory based on density functional theory and an analytical neural network representation, to overcome the limitations of existing approximations and explicitly simulate mode-specific nonadiabatic energy loss during molecular dynamics. Despite sizable hot-electron-induced energy loss, no measurable nonadiabatic effects can be found for H2 scattering on Ag(111). This is in stark contrast to previous reports for vibrationally excited H2 scattering on Cu(111). By detailed analysis of the two systems, we attribute this discrepancy to a subtle interplay between the magnitude of electronic friction along intramolecular vibration and the shape of the potential energy landscape that controls the molecular velocity at impact. On the basis of this characterization, we offer guidance for the search of highly nonadiabatic surface reactions.

Perspective: How to understand electronic friction

Electronic friction is a correction to the Born-Oppenheimer approximation, whereby nuclei in motion experience a drag in the presence of a manifold of electronic states. The notion of electronic friction has a long history and has been (re-)discovered in the context of a wide variety of different chemical and physical systems including, but not limited to, surface scattering events, surface reactions or chemisorption, electrochemistry, and conduction through molecular-(or nano-) junctions. Over the years, quite a few different forms of electronic friction have been offered in the literature. In this perspective, we briefly review these developments of electronic friction, highlighting the fact that we can now isolate a single, unifying form for (Markovian) electronic friction. We also focus on the role of electron-electron interactions for understanding frictional effects and offer our thoughts on the strengths and weaknesses of using electronic friction to model dynamics in general.

Electron-Mediated Phonon-Phonon Coupling Drives the Vibrational Relaxation of CO on Cu(100)

We bring forth a consistent theory for the electron-mediated vibrational intermode coupling that clarifies the microscopic mechanism behind the vibrational relaxation of adsorbates on metal surfaces. Our analysis points out the inability of state-of-the-art nonadiabatic theories to quantitatively reproduce the experimental linewidth of the CO internal stretch mode on Cu(100) and it emphasizes the crucial role of the electron-mediated phonon-phonon coupling in this regard. The results demonstrate a strong electron-mediated coupling between the internal stretch and low-energy CO modes, but also a significant role of surface motion. Our nonadiabatic theory is also able to explain the temperature dependence of the internal stretch phonon linewidth, thus far considered a sign of the direct anharmonic coupling.

Energy dissipation to tungsten surfaces upon hot-atom and Eley–Rideal recombination of H2

Adiabatic and nonadiabatic quasi-classical molecular dynamics simulations are performed to investigate the role of electron–hole pair excitations in hot-atom and Eley–Rideal H₂ recombination mechanisms on H-covered W(100). The influence of the surface structure is analyzed by comparing with previous results for W(110).

The dissociation and recombination rates of CH4 through the Ni(111) surface: The effect of lattice motion

Methane dissociation is a prototypical system for the study of surface reaction dynamics. The dissociation and recombination rates of CH₄ through the Ni(111) surface are calculated by using the quantum instanton method with an analytical potential energy surface. The Ni(111) lattice is treated rigidly, classically, and quantum mechanically so as to reveal the effect of lattice motion. The results demonstrate that it is the lateral displacements rather than the upward and downward movements of the surface nickel atoms that affect the rates a lot. Compared with the rigid lattice, the classical relaxation of the lattice can increase the rates by lowering the free energy barriers. For instance, at 300 K, the dissociation and recombination rates with the classical lattice exceed the ones with the rigid lattice by 6 and 10 orders of magnitude, respectively. Compared with the classical lattice, the quantum delocalization rather than the zero-point energy of the Ni atoms further enhances the rates by widening the reaction path. For instance, the dissociation rate with the quantum lattice is about 10 times larger than that with the classical lattice at 300 K. On the rigid lattice, due to the zero-point energy difference between CH₄ and CD₄, the kinetic isotope effects are larger than 1 for the dissociation process, while they are smaller than 1 for the recombination process. The increasing kinetic isotope effect with decreasing temperature demonstrates that the quantum tunneling effect is remarkable for the dissociation process.

High-Dimensional Atomistic Neural Network Potentials for Molecule-Surface Interactions: HCl Scattering from Au(111)

Ab initio molecular dynamics (AIMD) simulations of molecule-surface scattering allow first-principles characterization of the dynamics. However, the large number of density functional theory calculations along the trajectories is very costly, limiting simulations of long-time events and giving rise to poor statistics. To avoid this computational bottleneck, we report here the development of a high-dimensional molecule-surface interaction potential energy surface (PES) with movable surface atoms, using a machine learning approach. With 60 degrees of freedom, this PES allows energy transfer between the energetic impinging molecule and thermal surface atoms. Classical trajectory calculations for the scattering of DCl from Au(111) on this PES are found to agree well with AIMD simulations, with ∼10⁵-fold acceleration. Scattering of HCl from Au(111) is further investigated and compared with available experimental results.

Dissociative chemisorption of methane on Ni(111) using a chemically accurate fifteen dimensional potential energy surface

A new chemically accurate potential energy surface for the dissociative chemisorption of methane on the rigid Ni(111) surface.

Effects of Lattice Motion on Dissociative Chemisorption: Toward a Rigorous Comparison of Theory with Molecular Beam Experiments

The dissociative chemisorption of small molecules such as methane and water on metal surfaces is a key step in many important catalyzed reactions. However, it has only very recently become possible to directly compare theory with molecular beam studies of these reactions. For most experimental conditions, such a comparison requires accurate methods for introducing the effects of lattice motion into quantum reactive scattering calculations. We examine these methods and their recent application to methane and water dissociative chemisorption. New results are presented for CO₂ chemisorption and methane dissociation at step edges. The type of molecule-lattice coupling that leads to a strong variation in the dissociative sticking of methane with temperature is shown to occur for many polyatomic-metal systems. Improvements to these models are discussed. The ability to accurately compare theory with molecular beam experiments should lead to improved density functionals and consequently more accurate thermal rate constants for these important reactions.