Monte Carlo wave packet study of negative ion mediated vibrationally inelastic scattering of NO from the metal surface

First-Principles Nonadiabatic Dynamics of Molecules at Metal Surfaces with Vibrationally Coupled Electron Transfer

Accurate description of nonadiabatic dynamics of molecules at metal surfaces involving electron transfer has been a long-standing challenge for theory. Here, we tackle this problem by first constructing high-dimensional neural network diabatic potentials including state crossings determined by constrained density functional theory, then applying mixed quantum-classical surface hopping simulations to evolve coupled electron-nuclear motion. Our approach accurately describes the nonadiabatic effects in CO scattering from Au(111) without empirical parameters and yields results agreeing well with experiments under various conditions for this benchmark system. We find that both adiabatic and nonadiabatic energy loss channels have important contributions to the vibrational relaxation of highly vibrationally excited CO(v_{i}=17), whereas relaxation of low vibrationally excited states of CO(v_{i}=2) is weak and dominated by nonadiabatic energy loss. The presented approach paves the way for accurate first-principles simulations of electron transfer mediated nonadiabatic dynamics at metal surfaces.

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.

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.

Stereodynamics of adiabatic and non-adiabatic energy transfer in a molecule surface encounter

Molecular energy transfer and reactions at solid surfaces depend on the molecular orientation relative to the surface. While such steric effects have been largely understood in electronically adiabatic processes, the orientation-dependent energy transfer in NO scattering from Au(111) was complicated by electron-mediated nonadiabatic effects, thus lacking a clear interpretation and posing a great challenge for theories. Herein, we investigate the stereodynamics of adiabatic and nonadiabatic energy transfer via molecular dynamics simulations of NO(v = 3) scattering from Au(111) using realistic initial orientation distributions based on accurate neural network fitted adiabatic potential energy surface and electronic friction tensor. Our results reproduce the observed stronger vibrational relaxation for N-first orientation and enhanced rotational rainbow for O-first orientation, and demonstrate how adiabatic anisotropic interactions steer molecules into the more attractive N-first orientation to experience more significant energy transfer. Remaining disagreements with experiment suggest the direction for further developments of nonadiabatic theories for gas-surface scattering.

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.

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.

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.

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).

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.

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.

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.

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.

When is electronic friction reliable for dynamics at a molecule–metal interface?

Conditions under which electronic friction dynamics are applicable in the nonadiabatic limit are determined by examination of three model systems.

Vibrational Relaxation of Highly Vibrationally Excited CO Scattered from Au(111): Evidence for CO- Formation

Electronically nonadiabatic dynamics can be important in collisions of molecules at surfaces; for example, when vibrational degrees of freedom of molecules are coupled to electron-hole-pair (EHP) excitation of a metal. Such dynamics have been inferred from a host of observations involving multiquantum relaxation of NO molecules scattered from metal surfaces. Electron transfer forming transient NO^- is thought to be essential to the nonadiabatic coupling. The question remains: is this behavior usual? Here, we present final vibrational state distributions resulting from the scattering of CO(v_i = 17) from Au(111), which exhibits significantly less vibrational relaxation than NO(v_i = 16). We explain this observation in terms of the lower electron affinity of CO compared to NO, a result that is consistent with the formation of a transient CO^- ion being important to CO vibrational relaxation.

Relaxation dynamics in quantum dissipative systems: the microscopic effect of intramolecular vibrational energy redistribution

We investigate the effect of inter-mode coupling on the vibrational relaxation dynamics of molecules in weak dissipative environments. The simulations are performed within the reduced density matrix formalism in the Markovian regime, assuming a Lindblad form for the system-bath interaction. The prototypical two-dimensional model system representing two CO molecules approaching a Cu(100) surface is adapted from an ab initio potential, while the diatom-diatom vibrational coupling strength is systematically varied. In the weak system-bath coupling limit and at low temperatures, only first order non-adiabatic uni-modal coupling terms contribute to surface-mediated vibrational relaxation. Since dissipative dynamics is non-unitary, the choice of representation will affect the evolution of the reduced density matrix. Two alternative representations for computing the relaxation rates and the associated operators are thus compared: the fully coupled spectral basis, and a factorizable ansatz. The former is well-established and serves as a benchmark for the solution of Liouville-von Neumann equation. In the latter, a contracted grid basis of potential-optimized discrete variable representation is tailored to incorporate most of the inter-mode coupling, while the Lindblad operators are represented as tensor products of one-dimensional operators, for consistency. This procedure results in a marked reduction of the grid size and in a much more advantageous scaling of the computational cost with respect to the increase of the dimensionality of the system. The factorizable method is found to provide an accurate description of the dissipative quantum dynamics of the model system, specifically of the time evolution of the state populations and of the probability density distribution of the molecular wave packet. The influence of intra-molecular vibrational energy redistribution appears to be properly taken into account by the new model on the whole range of coupling strengths. It demontrates that most of the mode mixing during relaxation is due to the potential part of the Hamiltonian and not to the coupling among relaxation operators.

The effects of electron-hole pair coupling on the infrared laser-controlled vibrational excitation of NO on Au(111)

In this work, we present theoretical simulations of laser-driven vibrational control of NO adsorbed on a gold surface. Our goal is to tailor laser pulses to selectively excite specific modes and vibrational eigenstates, as well as to favor photodesorption of the adsorbed molecule. To this end, various control schemes and algorithms are applied. For adsorbates at metallic surfaces, the creation of electron-hole pairs in the substrate is known to play a dominant role in the transfer of energy from the system to the surroundings. These nonadiabatic couplings are included perturbatively in our reduced density matrix simulations using a generalization of the state-resolved position-dependent anharmonic rate model we recently introduced. An extension of the reduced density matrix is also proposed to provide a sound model for photodesorption in dissipative systems.

Monte carlo wave packet theory of dissociative double ionization

Nuclear dynamics in strong-field double ionization processes is predicted using a stochastic Monte Carlo wave packet technique. Using input from electronic structure calculations and strong-field electron dynamics the description allows for field-dressed dynamics within a given molecule as well as transitions between several different charge states. The description is computationally efficient and applicable to a wide range of systems. As a proof of principle, theoretical nuclear kinetic energy release spectra for H2 (D2) in strong near-infrared laser pulses of 40 fs duration are compared to experiments and very good agreement is obtained.

Vibrational relaxation of NO on Au(111) via electron-hole pair generation

Recent experiments have demonstrated the breakdown of the Born-Oppenheimer approximation when NO undergoes inelastic scattering from a Au(111) surface. In this paper, we provide a simple theoretical model for understanding this phenomenon. Our model predicts multiquanta vibrational relaxation through the creation of high-energy electron-hole pair excitations in the metal. Using experimentally determined parameters, our model gives qualitatively accurate predictions for the final vibrational state populations of the scattered molecule and predicts efficient conversion of vibrational energy into electronic energy.

Vibrationally promoted electron emission from low work-function metal surfaces

We observe electron emission when vibrationally excited NO molecules with vibrational state v, in the range of 9 < or = v < or =18, are scattered from a Cs-dosed Au surface. The quantum efficiency increases strongly with v, increasing up to 10(-2) electrons per NO (v) collision, a value several orders of magnitude larger than that observed in experiments with similar molecules in the ground vibrational state. The electron emission signal, as a function of v, has a threshold where the vibrational excitation energy slightly exceeds the surface work function. This threshold behavior strongly suggests that we are observing the direct conversion of NO vibrational energy into electron kinetic energy. Several potential mechanisms for the observed electron emission are explored, including (1) vibrational autodetachment, (2) an Auger-type two-electron process, and (3) vibrationally promoted dissociation. The results of this work provide direct evidence for nonadiabatic energy-transfer events associated with large amplitude vibrational motion at metal surfaces.

Role of Vibrationally Excited NO in Promoting Electron Emission When Colliding with a Metal Surface: A Nonadiabatic Dynamic Model

A nonadiabatic quantum dynamic model has been developed to study the process of electron emission from a low-work-function metal surface. The process is initiated by scattering a highly vibrationally excited NO molecule from a surface composed of a Cs layer covering a Ru crystal. The model addresses the increasing quantum yield of the electron emission as a function of the molecular vibrational excitation and incident kinetic energy. The reaction mechanism is identified as a long-range harpooning electron transfer to a molecular ion which is then accelerated toward the surface. Upon impact, the molecular ion emits its excess electron.