Analysis of Energy Dissipation Channels in a Benchmark System of Activated Dissociation: N2 on Ru(0001)

A theory of phonon-induced friction on molecular adsorbates

In this manuscript, we provide a general theory for how surface phonons couple to molecular adsorbates. Our theory maps the extended dynamics of a surface's atomic vibrational motions to a generalized Langevin equation, and by doing so captures these dynamics in a single quantity: the non-Markovian friction. The different frequency components of this friction are the phonon modes of the surface slab weighted by their coupling to the adsorbate degrees of freedom. Using this formalism, we demonstrate that physisorbed species couple primarily to acoustic phonons while chemisorbed species couple to dispersionless local vibrations. We subsequently derive equations for phonon-adjusted reaction rates using transition state theory and demonstrate that these corrections improve agreement with experimental results for CO desorption rates from Pt(111).

Modeling Surface Vibrations and Their Role in Molecular Adsorption: A Generalized Langevin Approach

The atomic vibrations of a solid surface can play a significant role in the reactions of surface-bound molecules, as well as their adsorption and desorption. Relevant phonon modes can involve the collective motion of atoms over a wide array of length scales. In this paper, we demonstrate how the generalized Langevin equation can be utilized to describe these collective motions weighted by their coupling to individual sites. Our approach builds upon the generalized Langevin oscillator (GLO) model originally developed by Tully. We extend the GLO by deriving parameters from atomistic simulation data. We apply this approach to study the memory kernel of a model platinum surface and demonstrate that the memory kernel has a bimodal form due to coupling to both low-energy acoustic modes and high-energy modes near the Debye frequency. The same bimodal form was observed across a wide variety of solids of different elemental compositions, surface structures, and solvation states. By studying how these dominant modes depend on the simulation size, we argue that the acoustic modes are frozen in the limit of macroscopic lattices. By simulating periodically replicated slabs of various sizes, we quantify the influence of phonon confinement effects in the memory kernel and their concomitant effect on simulated sticking coefficients.

STM Visualization of N2 Dissociative Chemisorption on Ru(0001) at High Impinging Kinetic Energies

This paper examines the reactive surface dynamics of energy- and angle-selected N₂ dissociation on a clean Ru(0001) surface. Presented herein are the first STM images of highly energetic N₂ dissociation on terrace sites utilizing a novel UHV instrument that combines a supersonic molecular beam with an in situ STM that is in-line with the molecular beam. Atomically resolved visualization of individual N₂ dissociation events elucidates the fundamental reactive dynamics of the N₂/Ru(0001) system by providing a detailed understanding of the on-surface dissociation dynamics: the distance and angle between nitrogen atoms from the same dissociated N₂ molecule, site specificity and coordination of binding on terrace sites, and the local evolution of surrounding nanoscopic areas. These properties are precisely measured over a range of impinging N₂ kinetic energies and angles, revealing previously unattainable information about the energy dissipation channels that govern the reactivity of the system. The experimental results presented in this paper provide insight into the fundamental N₂ dissociation mechanism that, in conjunction with ongoing theoretical modeling, will help determine the role of dynamical processes such as energy transfer to surface phonons and nonadiabatic excitation of electron-hole pairs (ehps). These results will not only help uncover the underlying chemistry and physics that give rise to the unique behavior of this activated dissociative chemisorption system but also represent an exciting approach to studying reaction dynamics by pairing the angstrom-level spatiotemporal resolution of an in situ STM with nonequilibrium fluxes of reactive gases generated in a supersonic molecular beam to access highly activated chemical dynamics and observe the results of individual reaction events.

Photoinduced Desorption Dynamics of CO from Pd(111): A Neural Network Approach

Modeling the ultrafast photoinduced dynamics and reactivity of adsorbates on metals requires including the effect of the laser-excited electrons and, in many cases, also the effect of the highly excited surface lattice. Although the recent ab initio molecular dynamics with electronic friction and thermostats, (T_e,T_l)-AIMDEF [AlducinM.;Phys. Rev. Lett.2019, 123, 246802]31922860, enables such complex modeling, its computational cost may limit its applicability. Here, we use the new embedded atom neural network (EANN) method [ZhangY.;J. Phys. Chem. Lett.2019, 10, 496231397157] to develop an accurate and extremely complex potential energy surface (PES) that allows us a detailed and reliable description of the photoinduced desorption of CO from the Pd(111) surface with a coverage of 0.75 monolayer. Molecular dynamics simulations performed on this EANN-PES reproduce the (T_e,T_l)-AIMDEF results with a remarkable level of accuracy. This demonstrates the outstanding performance of the obtained EANN-PES that is able to reproduce available density functional theory (DFT) data for an extensive range of surface temperatures (90–1000 K); a large number of degrees of freedom, those corresponding to six CO adsorbates and 24 moving surface atoms; and the varying CO coverage caused by the abundant desorption events.

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.

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

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

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.