Multidimensional effects on dissociation of N2 on Ru(0001)

Charge-Transfer-Controlled Quantum Dynamics of HCl Dissociation on the Ag/Au(111) Bimetallic Alloy Surface

Understanding polar molecule dynamics on bimetallic surfaces, especially electropositivity and electronegativity, remains a challenge. Here, we report the reactivity of HCl on a strained Ag monolayer on Au(111) using six-dimensional quantum dynamics with a new machine-learning-based potential energy surface. Surprisingly, HCl reactivity is significantly suppressed by the Ag-Au interaction despite a lower HCl+Ag/Au(111) barrier than pure Ag(111). This arises from charge transfer between Ag and Au, where electronegative Au makes the top Ag layer on Ag/Au(111) electropositive, unlike that on pure Ag(111). Electropositive Ag in HCl+Ag/Au(111) attracts Cl, yielding an unfavorable H-Cl configuration and reduced reactivity. These findings deepen our understanding of polar molecule interactions on bimetallic surfaces, highlighting the role of charge transfer in dissociative chemisorption and the implications for catalyst design in heterogeneous catalysis.

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.

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.

Neural Network Sampling of the Free Energy Landscape for Nitrogen Dissociation on Ruthenium

In heterogeneous catalysis, free energy profiles of reactions govern the mechanisms, rates, and equilibria. Energetics are conventionally computed using the harmonic approximation (HA), which requires determination of critical states a priori. Here, we use neural networks to efficiently sample and directly calculate the free energy surface (FES) of a prototypical heterogeneous catalysis reaction-the dissociation of molecular nitrogen on ruthenium-at density-functional-theory-level accuracy. We find that the vibrational entropy of surface atoms, often neglected in HA for transition metal catalysts, contributes significantly to the reaction barrier. The minimum free energy path for dissociation reveals an "on-top" adsorbed molecular state prior to the transition state. While a previously reported flat-lying molecular metastable state can be identified in the potential energy surface, it is absent in the FES at relevant reaction temperatures. These findings demonstrate the importance of identifying critical points self-consistently on the FES for reactions that involve considerable entropic effects.

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.

Prominent out-of-plane diffraction in helium scattering from a methyl-terminated Si(111) surface

Due to their electrochemical and oxidative stability, organic-terminated semiconductor surfaces are well suited to applications in, for example, photoelectrodes and electrochemical cells, which explains the lively interest in their detailed characterization. Helium atom scattering (HAS) is a useful tool to carry out such characterization. Here, we have simulated HAS in He/CH3-Si(111) based on density functional theory (DFT) potential energy surfaces (PESs) and multi-configuration time-dependent Hartree (MCTDH) dynamics. Our analysis of HAS shows that most diffraction taking place in this system corresponds to high-order out-of-plane peaks. This is a general trend that does not depend on the specific features of the simulations, such as the inclusion or not of the van der Waals long-range effects. This is the first and only He-surface system for which such huge out-of-plane diffraction has been described. This striking theoretical finding should encourage new experimental developments to confirm this previously unreported effect.

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.

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

The excitation of electron-hole pairs in reactive scattering of molecules at metal surfaces often affects the physical and dynamical observables of interest, including the reaction probability. Here, we study the influence of electron-hole pair excitation on the dissociative chemisorption of N2 on Ru(0001) using the local density friction approximation method. The effect of surface atom motion has also been taken into account by a high-dimensional neural network potential. Our nonadiabatic molecular dynamics simulations with electronic friction show that the reaction of N2 is more strongly affected by the energy transfer to surface phonons than by the energy loss to electron-hole pairs. The discrepancy between the computed reaction probabilities and experimental results is within the experimental error both with and without friction; however, the incorporation of electron-hole pairs yields somewhat better agreement with experiments, especially at high collision energies. We also calculate the vibrational efficacy for the N2 + Ru(0001) reaction and demonstrate that the N2 reaction is more enhanced by exciting the molecular vibrations than by adding an equivalent amount of energy into translation.

Dynamics of N2 sticking on W(100): the decisive role of van der Waals interactions

The reactive dynamics of N₂ on W(100) has been investigated by means of quasi-classical trajectory calculations using an interpolated six-dimensional potential energy surface (PES) based on density functional theory energies obtained employing the vdW-DF2 functional.

Accurate Neural Network Description of Surface Phonons in Reactive Gas-Surface Dynamics: N2 + Ru(0001)

Ab initio molecular dynamics (AIMD) simulations enable the accurate description of reactive molecule-surface scattering especially if energy transfer involving surface phonons is important. However, presently, the computational expense of AIMD rules out its application to systems where reaction probabilities are smaller than about 1%. Here we show that this problem can be overcome by a high-dimensional neural network fit of the molecule-surface interaction potential, which also incorporates the dependence on phonons by taking into account all degrees of freedom of the surface explicitly. As shown for N₂ + Ru(0001), which is a prototypical case for highly activated dissociative chemisorption, the method allows an accurate description of the coupling of molecular and surface atom motion and accurately accounts for vibrational properties of the employed slab model of Ru(0001). The neural network potential allows reaction probabilities as low as 10^-5 to be computed, showing good agreement with experimental results.

Adsorption dynamics of molecular nitrogen at an Fe(111) surface

We present an extensive theoretical study of N₂ adsorption mechanisms on an Fe(111) surface.

Dissociative and non-dissociative adsorption of O2 on Cu(111) and CuML/Ru(0001) surfaces: adiabaticity takes over

Adiabatic molecular spin-quenching during the approach of O₂ to Cu(111) and Cu_ML/Ru(0001) surfaces.

Energy Dissipation during Diffusion at Metal Surfaces: Disentangling the Role of Phonons versus Electron-Hole Pairs

Helium spin echo experiments combined with ab initio based Langevin molecular dynamics simulations are used to quantify the adsorbate-substrate coupling during the thermal diffusion of Na atoms on Cu(111). An analysis of trajectories within the local density friction approximation allows the contribution from electron-hole pair excitations to be separated from the total energy dissipation. Despite the minimal electronic friction coefficient of Na and the relatively small mass mismatch to Cu promoting efficient phononic dissipation, about (20±5)% of the total energy loss is attributable to electronic friction. The results suggest a significant role of electronic nonadiabaticity in the rapid thermalization generally relied upon in adiabatic diffusion theories.

Experimental and theoretical study of rotationally inelastic diffraction of H2(D2) from methyl-terminated Si(111)

Fundamental details concerning the interaction between H2 and CH3-Si(111) have been elucidated by the combination of diffractive scattering experiments and electronic structure and scattering calculations. Rotationally inelastic diffraction (RID) of H2 and D2 from this model hydrocarbon-decorated semiconductor interface has been confirmed for the first time via both time-of-flight and diffraction measurements, with modest j = 0 → 2 RID intensities for H2 compared to the strong RID features observed for D2 over a large range of kinematic scattering conditions along two high-symmetry azimuthal directions. The Debye-Waller model was applied to the thermal attenuation of diffraction peaks, allowing for precise determination of the RID probabilities by accounting for incoherent motion of the CH3-Si(111) surface atoms. The probabilities of rotationally inelastic diffraction of H2 and D2 have been quantitatively evaluated as a function of beam energy and scattering angle, and have been compared with complementary electronic structure and scattering calculations to provide insight into the interaction potential between H2 (D2) and hence the surface charge density distribution. Specifically, a six-dimensional potential energy surface (PES), describing the electronic structure of the H2(D2)/CH3-Si(111) system, has been computed based on interpolation of density functional theory energies. Quantum and classical dynamics simulations have allowed for an assessment of the accuracy of the PES, and subsequently for identification of the features of the PES that serve as classical turning points. A close scrutiny of the PES reveals the highly anisotropic character of the interaction potential at these turning points. This combination of experiment and theory provides new and important details about the interaction of H2 with a hybrid organic-semiconductor interface, which can be used to further investigate energy flow in technologically relevant systems.

Two distinctive energy migration pathways of monolayer molecules on metal nanoparticle surfaces

Energy migrations at metal nanomaterial surfaces are fundamentally important to heterogeneous reactions. Here we report two distinctive energy migration pathways of monolayer adsorbate molecules on differently sized metal nanoparticle surfaces investigated with ultrafast vibrational spectroscopy. On a 5 nm platinum particle, within a few picoseconds the vibrational energy of a carbon monoxide adsorbate rapidly dissipates into the particle through electron/hole pair excitations, generating heat that quickly migrates on surface. In contrast, the lack of vibration-electron coupling on approximately 1 nm particles results in vibrational energy migration among adsorbates that occurs on a twenty times slower timescale. Further investigations reveal that the rapid carbon monoxide energy relaxation is also affected by the adsorption sites and the nature of the metal but to a lesser extent. These findings reflect the dependence of electron/vibration coupling on the metallic nature, size and surface site of nanoparticles and its significance in mediating energy relaxations and migrations on nanoparticle surfaces.

Energy migrations at metal nanomaterial surfaces are fundamentally important to heterogeneous reactions. Here, the authors employ ultrafast vibrational spectroscopy to show two distinctive energy migration pathways of monolayer adsorbate molecules on differently sized metal nanoparticle surfaces.

Electron-Hole Pair Effects in Polyatomic Dissociative Chemisorption: Water on Ni(111)

The influence of electron-hole pairs in dissociative chemisorption of a polyatomic molecule (water) on metal surfaces is assessed for the first time using a friction approach. The atomic local density dependent friction coefficients computed based on a free electron gas embedding model are employed in classical molecular dynamics simulations of the water dissociation dynamics on rigid Ni(111) using a recently developed nine dimensional interaction potential energy surface for the system. The results indicate that nonadiabatic effects are relatively small and they do not qualitatively alter the mode specificity in the dissociation.

Toward a Database of Chemically Accurate Barrier Heights for Reactions of Molecules with Metal Surfaces

Being able to calculate reaction barrier heights to within chemical accuracy (errors < 1 kcal/mol) is crucial to the accurate modeling of chemical reactions. Although accurate databases exist that can help theorists with benchmarking new electronic structure theories on gas-phase chemical reactions, no such databases exist for reactions of molecules with metal surfaces. Nonetheless, most chemicals are made in heterogeneously catalyzed processes, of which many take place over metal particles. Presently, barrier heights for molecule-metal surface reactions have been determined with chemical accuracy for only two systems, that is, H2 + Cu(111) and H2 + Cu(100). This has been done with semiempirically determined density functionals, which were fitted through comparisons of dynamics results with molecular beam sticking probabilities. The prospects of extending the database with chemically accurate data for other molecule-metal reactions, either with the use of semiempirical density functional theory or with first-principles theory, are discussed.

Electronic friction dominates hydrogen hot-atom relaxation on Pd(100)

We study the dynamics of transient hot H atoms on Pd(100) that originated from dissociative adsorption of H2. The methodology developed here, denoted AIMDEF, consists of ab initio molecular dynamics simulations that include a friction force to account for the energy transfer to the electronic system. We find that the excitation of electron-hole pairs is the main channel for energy dissipation, which happens at a rate that is five times faster than energy transfer into Pd lattice motion. Our results show that electronic excitations may constitute the dominant dissipation channel in the relaxation of hot atoms on surfaces.

Electronic energy dissipation during scattering of vibrationally excited molecules at metal surfaces: ab initio simulations for HCl/Al(111)

In this Letter, ab initio molecular dynamics simulations based on time-dependent density functional theory for the electrons and Ehrenfest dynamics for the nuclei are reported that detail the interaction of a vibrating HCl molecule with an Al(111) substrate. The mechanism responsible for the strong electron-hole-pair (EHP)-vibrational coupling in case of highly vibrationally excited molecules is traced back to a large eigenenergy shift of the spz*-like antibonding HCl lowest unoccupied molecular orbital with the bond length. As a consequence of this mechanism, the electronic excitation spectra turn out to be highly asymmetric. The simulations suggest an explanation of how to reconcile a strong EHP-vibrational coupling in case of highly vibrationally excited molecules with the small, but clearly evident, electronic contribution to the v=0 → v=1 vibrational excitation observed experimentally during the scattering of HCl molecules at a hot Au surface by Ran et al. [Phys. Rev. Lett. 98 237601 (2007)].

Towards chemically accurate simulation of molecule-surface reactions

This perspective addresses four challenges facing theorists whose aim is to make quantitatively accurate predictions for reactions of molecules on metal surfaces, and suggests ways of meeting these challenges, focusing on dissociative chemisorption reactions of H(2), N(2), and CH(4). Addressing these challenges is ultimately of practical importance to a more accurate description of overall heterogeneously catalysed reactions, which play a role in the production of more than 90% of man-made chemicals. One challenge is to describe the interaction of a molecule with a metal surface with chemical accuracy, i.e., with errors in reaction barrier heights less than 1 kcal mol(-1). In this framework, the potential of a new implementation of specific reaction parameter density functional theory (SRP-DFT) will be discussed, with emphasis on applications to reaction of H(2) with metal surfaces. Two additional challenges are to come up with improved descriptions of the effects of phonons and electron-hole pairs on reaction of molecules like N(2) on metal surfaces. Phonons can be tackled using sudden approximations in quantum dynamics, and through Ab Initio Molecular Dynamics (AIMD) calculations using classical dynamics. To additionally achieve an accurate description of the effect of electron-hole pair excitation on dissociative chemisorption within a classical dynamics framework, it may be possible to combine AIMD with electronic friction. The fourth challenge we will consider is how to achieve an accurate quantum mechanical description of the dissociative chemisorption of a polyatomic molecule, like methane, on a metal surface. A method of potential interest is the Multi-Configuration Time-Dependent Hartree (MCTDH) method.

Competition between electron and phonon excitations in the scattering of nitrogen atoms and molecules off tungsten and silver metal surfaces

We investigate the role played by electron-hole pair and phonon excitations in the interaction of reactive gas molecules and atoms with metal surfaces. We present a theoretical framework that allows us to evaluate within a full-dimensional dynamics the combined contribution of both excitation mechanisms while the gas particle-surface interaction is described by an ab initio potential energy surface. The model is applied to study energy dissipation in the scattering of N(2) on W(110) and N on Ag(111). Our results show that phonon excitation is the dominant energy loss channel, whereas electron-hole pair excitations represent a minor contribution. We substantiate that, even when the energy dissipated is quantitatively significant, important aspects of the scattering dynamics are well captured by the adiabatic approximation.

The role of precursor states in adsorption, surface reactions and catalysis

Among the many concepts which have been developed in surface science to explain the nature of adsorption, the role of weakly-held intermediate states, so-called precursor states, is one of the most important. The kinetics of precursor-mediated adsorption is described, together with examples showing how significant such effects can be, not just in adsorption itself, but also in surface reactions on crystals and on model-supported catalysts.

Role of electron-hole pair excitations in the dissociative adsorption of diatomic molecules on metal surfaces

We quantitatively evaluate the contribution of electron-hole pair excitations to the reactive dynamics of H2 on Cu(110) and N2 on W(110), including the six dimensionality of the process in the entire calculation. The interaction energy between molecule and surface is represented by an ab initio six-dimensional potential energy surface. Electron friction coefficients are calculated with density functional theory in a local density approximation. Contrary to previous claims, only minor differences between the adiabatic and nonadiabatic results for dissociative adsorption are found. Our calculations demonstrate the validity of the adiabatic approximation to analyze adsorption dynamics in these two representative systems.

Ab initio molecular dynamics of hydrogen dissociation on metal surfaces using neural networks and novelty sampling

We outline a hybrid multiscale approach for the construction of ab initio potential energy surfaces (PESs) useful for performing six-dimensional (6D) classical or quantum mechanical molecular dynamics (MD) simulations of diatomic molecules reacting at single crystal surfaces. The algorithm implements concepts from the corrugation reduction procedure, which reduces energetic variation in the PES, and uses neural networks for interpolation of smoothed ab initio data. A novelty sampling scheme is implemented and used to identify configurations that are most likely to be predicted inaccurately by the neural network. This hybrid multiscale approach, which couples PES construction at the electronic structure level to MD simulations at the atomistic scale, reduces the number of density functional theory (DFT) calculations needed to specify an accurate PES. Due to the iterative nature of the novelty sampling algorithm, it is possible to obtain a quantitative measure of the convergence of the PES with respect to the number of ab initio calculations used to train the neural network. We demonstrate the algorithm by first applying it to two analytic potentials, which model the H2/Pt(111) and H2/Cu(111) systems. These potentials are of the corrugated London-Eyring-Polanyi-Sato form, which are based on DFT calculations, but are not globally accurate. After demonstrating the convergence of the PES using these simple potentials, we use DFT calculations directly and obtain converged semiclassical trajectories for the H2/Pt(111) system at the PW91/generalized gradient approximation level. We obtain a converged PES for a 6D hydrogen-surface dissociation reaction using novelty sampling coupled directly to DFT. These results, in excellent agreement with experiments and previous theoretical work, are compared to previous simulations in order to explore the sensitivity of the PES (and therefore MD) to the choice of exchange and correlation functional. Despite having a lower energetic corrugation in our PES, we obtain a broader reaction probability curve than previous simulations, which is attributed to increased geometric corrugation in the PES and the effect of nonparallel dissociation pathways.

Reactive and nonreactive scattering of N2 from Ru(0001): a six-dimensional adiabatic study

We have studied the dissociative chemisorption and scattering of N(2) on and from Ru(0001), using a six-dimensional quasiclassical trajectory method. The potential energy surface, which depends on all the molecular degrees of freedom, has been built applying a modified Shepard interpolation method to a data set of results from density functional theory, employing the RPBE generalized gradient approximation. The frozen surface and Born-Oppenheimer [Ann. Phys. (Leipzig) 84, 457 (1927)] approximations were used, neglecting phonons and electron-hole pair excitations. Dissociative chemisorption probabilities are found to be very small even for translational energies much higher than the minimum reaction barrier, in good agreement with experiment. A comparison to previous low dimensional calculations shows the importance of taking into account the multidimensional effects of N(2) rotation and translation parallel to the surface. The new calculations strongly suggest a much smaller role of nonadiabatic effects than previously assumed on the basis of a comparison between low dimensional results and experiments [J. Chem. Phys. 115, 9028 (2001)]. Also in agreement with experiment, our theoretical results show a strong dependence of reaction on the initial vibrational state. Computed angular scattering distributions and parallel translation energy distributions are in good agreement with experiments on scattering, but the theory overestimates vibrational and rotational excitations in scattering.

Spectrum of electronic excitations due to the adsorption of atoms on metal surfaces

The time-dependent, mean-field Newns-Anderson model for a spin-polarized adsorbate approaching a metallic surface is solved in the wide-band limit. Equations for the time evolution of the electronic structure of the adsorbate-metal system are derived and the spectrum of electronic excitations is found. The behavior of the model is demonstrated for a set of physically reasonable parameters.