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

Vibrational energy transfer in collisions of molecules with metal surfaces

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

Microcanonical treatment of HCl dissociative chemisorption on Au(111): Reactive dampening through inefficient translational energy coupling and an active surface

Microcanonical unimolecular rate theory is applied to Shirhatti and Wodtke's recent supersonic molecular beam experiments examining the activated dissociative chemisorption of HCl on Au(111). A precursor mediated microcanonical trapping (PMMT) model (where the surface vibrates and HCl rotations, vibration, and translation directed along the surface normal are treated as active degrees of freedom) gave dissociative sticking coefficient predictions that are several orders of magnitude higher than experimental values but in good accord with prior quantum and molecular dynamics simulations. Density functional theory (DFT) electronic structure calculations using the Perdew-Burke-Ernzerhof (PBE) functional served to fix the vibrational frequencies of the reactive transition state and the threshold energy for dissociation, E0 = 72.9 kJ/mol. To explore the possibilities of varying threshold energy, coupling to phonons, and dynamics, a three-parameter [E0, s, ɛn] dynamically biased (d-) PMMT model was fit to the experiments. A dynamical bias was introduced using an efficiency, ɛn, of normal translational energy to contribute to the active exchangeable energy capable of promoting reactivity. To achieve the low sticking probabilities observed in experiment, severe normal translational energy dampening (ɛn → 0.26) was imposed, leading to a large vibrational efficacy of ηv = εv/εn = 3.85. The optimal threshold energy for dissociation was E0 = 30.88 kJ/mol, some 40 kJ/mol below the PBE-DFT prediction, and the optimal number of Au surface oscillators was s = 1. The d-PMMT modeling indicates that HCl/Au(111) reactivity can be consistent with electronically adiabatic passage across a relatively low and late transition state that dynamically disfavors normal translational energy.

Mechanism of Ultraviolet-Induced CO Desorption from CO Ice: Role of Vibrational Relaxation Highlighted

Although UV photon-induced CO ice desorption is clearly observed in many cold regions of the Universe as well as in the laboratory, the fundamental question of the mechanisms involved at the molecular scale remains debated. In particular, the exact nature of the involved energy transfers in the indirect desorption pathway highlighted in previous experiments is not explained. Using ab initio molecular dynamics simulations, we explore a new indirect desorption mechanism in which a highly vibrationally excited CO (v=40) within an aggregate of 50 CO molecules triggers the desorption of molecules at the surface. The desorption originates first from a mutual attraction between the excited molecule and the surrounding molecule(s), followed by a cascade of energy transfers, ultimately resulting in the desorption of vibrationally cold CO (∼95% in v=0). The theoretical vibrational distribution, along with the kinetic energy one, which peaks around 25 meV for CO with low rotational levels (v=0, J<7), is in excellent agreement with the results obtained from VUV laser induced desorption (157 nm) of CO (v=0, 1) probed using REMPI.

Assessing Mixed Quantum-Classical Molecular Dynamics Methods for Nonadiabatic Dynamics of Molecules on Metal Surfaces

Mixed quantum-classical (MQC) methods for simulating the dynamics of molecules at metal surfaces have the potential to accurately and efficiently provide mechanistic insight into reactive processes. Here, we introduce simple two-dimensional models for the scattering of diatomic molecules at metal surfaces based on recently published electronic structure data. We apply several MQC methods to investigate their ability to capture how nonadiabatic effects influence molecule-metal energy transfer during the scattering process. Specifically, we compare molecular dynamics with electronic friction, Ehrenfest dynamics, independent electron surface hopping, and the broadened classical master equation approach. In the case of independent electron surface hopping, we implement a simple decoherence correction approach and assess its impact on vibrationally inelastic scattering. Our results show that simple, low-dimensional models can be used to qualitatively capture experimentally observed vibrational energy transfer and provide insight into the relative performance of different MQC schemes. We observe that all approaches predict similar kinetic energy dependence but return different vibrational energy distributions. Finally, by varying the molecule-metal coupling, we can assess the coupling regime in which some MQC methods become unsuitable.

Classical Quantum Friction at Water-Carbon Interfaces

Friction at water-carbon interfaces remains a major puzzle with theories and simulations unable to explain experimental trends in nanoscale waterflow. A recent theoretical framework─quantum friction (QF)─proposes to resolve these experimental observations by considering nonadiabatic coupling between dielectric fluctuations in water and graphitic surfaces. Here, using a classical model that enables fine-tuning of the solid's dielectric spectrum, we provide evidence from simulations in general support of QF. In particular, as features in the solid's dielectric spectrum begin to overlap with water's librational and Debye modes, we find an increase in friction in line with that proposed by QF. At the microscopic level, we find that this contribution to friction manifests more distinctly in the dynamics of the solid's charge density than that of water. Our findings suggest that experimental signatures of QF may be more pronounced in the solid's response rather than liquid water's.

Quantitative molecular simulations

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

Quantum Dynamics with Electronic Friction

A theory of electronic friction is developed using the exact factorization of the electronic-nuclear wave function. No assumption is made regarding the electronic bath, which can be made of independent or interacting electrons, and the nuclei are treated quantally. The ensuing equation of motion for the nuclear wave function is a nonlinear Schrödinger equation including a friction term. The resulting friction kernel agrees with a previously derived mixed quantum-classical result by Dou et al., [Phys. Rev. Lett. 119, 046001 (2017)]PRLTAO0031-900710.1103/PhysRevLett.119.046001, except for a pseudomagnetic contribution in the latter that is here removed. More specifically, it is shown that the electron dynamics generally washes out the gauge fields appearing in the adiabatic dynamics. However, these are fully re-established in the typical situation where the electrons respond rapidly on the slow time scale of the nuclear dynamics (Markov limit). Hence, we predict Berry's phase effects to be observable also in the presence of electronic friction. Application to a model vibrational relaxation problem proves that the proposed approach represents a viable way to account for electronic friction in a fully quantum setting for the nuclear dynamics.

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.

Highly Efficient Activation of HCl Dissociation on Au(111) via Rotational Preexcitation

The probability for dissociation of molecules on metal surfaces, which often controls the rate of industrially important catalytic processes, can depend strongly on how energy is partitioned in the incident molecule. There are many example systems where the addition of vibrational energy promotes reaction more effectively than the addition of translational energy, but for rotational pre-excitation similar examples have not yet been discovered. Here, we make an experimentally testable theoretical prediction that adding energy to the rotation of HCl can promote its dissociation on Au(111) 20 times more effectively than increasing its translational energy. In the underlying mechanism, the molecule's initial rotational motion allows it to pass through a critical region of the reaction path, where this path shows a strong and nonmonotonic dependence on the molecular orientation.

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.

High-Dimensional Atomistic Neural Network Potential to Study the Alignment-Resolved O2 Scattering from Highly Oriented Pyrolytic Graphite

A high dimensional and accurate atomistic neural network potential energy surface (ANN-PES) that describes the interaction between one O₂ molecule and a highly oriented pyrolytic graphite (HOPG) surface has been constructed using the open-source package (aenet). The validation of the PES is performed by paying attention to static characteristics as well as by testing its performance in reproducing previous ab initio molecular dynamics simulation results. Subsequently, the ANN-PES is used to perform quasi-classical molecular dynamics calculations of the alignment-dependent scattering of O₂ from HOPG. The results are obtained for 200 meV O₂ molecules with different initial alignments impinging with a polar incidence angle with respect to the surface normal of 22.5° on a thermalized (110 and 300 K) graphite surface. The choice of these initial conditions in our simulations is made to perform comparisons to recent experimental results on this system. Our results show that the scattering of O₂ from the HOPG surface is a rather direct process, that the angular distributions are alignment dependent, and that the final translational energy of end-on molecules is around 20% lower than that of side-on molecules. Upon collision with the surface, the molecules that are initially aligned perpendicular to the surface become highly rotationally excited, whereas a very small change in the rotational state of the scattered molecules is observed for the initial parallel alignments. The latter confirms the energy transfer dependence on the stereodynamics for the present system. The results of our simulations are in overall agreement with the experimental observations regarding the shape of the angular distributions and the alignment dependence of the in-plane reflected molecules.

Density Functional Theory for Molecule-Metal Surface Reactions: When Does the Generalized Gradient Approximation Get It Right, and What to Do If It Does Not

While density functional theory (DFT) is perhaps the most used electronic structure theory in chemistry, many of its practical aspects remain poorly understood. For instance, DFT at the generalized gradient approximation (GGA) tends to fail miserably at describing gas-phase reaction barriers, while it performs surprisingly well for many molecule-metal surface reactions. GGA-DFT also fails for many systems in the latter category, and up to now it has not been clear when one may expect it to work. We show that GGA-DFT tends to work if the difference between the work function of the metal and the molecule's electron affinity is greater than ∼7 eV and to fail if this difference is smaller, with sticking of O₂ on Al(111) being a spectacular example. Using dynamics calculations we show that, for this system, the DFT problem may be solved as done for gas-phase reactions, i.e., by resorting to hybrid functionals, but using screening at long-range to obtain a correct description of the metal. Our results suggest the GGA error in the O₂ + Al(111) barrier height to be functional driven. Our results also suggest the possibility to compute potential energy surfaces for the difficult-to-treat systems with computationally cheap nonself-consistent calculations in which a hybrid functional is applied to a GGA density.

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).

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.

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.