On the Role of Electronic Friction for Dissociative Adsorption and Scattering of Hydrogen Molecules at a Ru(0001) Surface

Performance of Made Simple Meta-GGA Functionals with rVV10 Nonlocal Correlation for H2 + Cu(111), D2 + Ag(111), H2 + Au(111), and D2 + Pt(111)

Accurately modeling heterogeneous catalysis requires accurate descriptions of rate-controlling elementary reactions of molecules on metal surfaces, but standard density functionals (DFs) are not accurate enough for this. The problem can be solved with the specific reaction parameter approach to density functional theory (SRP-DFT), but the transferability of SRP DFs among chemically related systems is limited. We combine the MS-PBEl, MS-B86bl, and MS-RPBEl semilocal made simple (MS) meta-generalized gradient approximation (GGA) (mGGA) DFs with rVV10 nonlocal correlation, and we evaluate their performance for the hydrogen (H2) + Cu(111), deuterium (D2) + Ag(111), H2 + Au(111), and D2 + Pt(111) gas-surface systems. The three MS mGGA DFs that have been combined with rVV10 nonlocal correlation were not fitted to reproduce particular experiments, nor has the b parameter present in rVV10 been reoptimized. Of the three DFs obtained the MS-PBEl-rVV10 DF yields an excellent description of van der Waals well geometries. The three original MS mGGA DFs gave a highly accurate description of the metals, which was comparable in quality to that obtained with the PBEsol DF. Here, we find that combining the three original MS mGGA DFs with rVV10 nonlocal correlation comes at the cost of a slightly less accurate description of the metal. However, the description of the metal obtained in this way is still better than the descriptions obtained with SRP DFs specifically optimized for individual systems. Using the Born-Oppenheimer static surface (BOSS) model, simulations of molecular beam dissociative chemisorption experiments yield chemical accuracy for the D2 + Ag(111) and D2 + Pt(111) systems. A comparison between calculated and measured E 1/2(ν, J) parameters describing associative desorption suggests chemical accuracy for the associative desorption of H2 from Au(111) as well. Our results suggest that ascending Jacob's ladder to the mGGA rung yields increasingly more accurate results for gas-surface reactions of H2 (D2) interacting with late transition metals.

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.

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.

Transferability of the Specific Reaction Parameter Density Functional for H2 + Pt(111) to H2 + Pt(211)

The accurate description of heterogeneously catalyzed reactions may require chemically accurate evaluation of barriers for reactions of molecules at the edges of metal nanoparticles. It was recently shown that a semiempirical density functional describing the interaction of a molecule dissociating on a flat metal surface (CHD₃ + Pt(111)) is transferable to the same molecule reacting on a stepped surface of the same metal (Pt(211)). However, validation of the method for additional systems is desirable. To address the question whether the specific reaction parameter (SRP) functional that describes H₂ + Pt(111) with chemical accuracy is also capable of accurately describing H₂ + Pt(211), we have performed molecular beam simulations with the quasi-classical trajectory (QCT) method, using the SRP functional developed for H₂ + Pt(111). Our calculations used the Born-Oppenheimer static surface model. The accuracy of the QCT method was assessed by comparison with quantum dynamics results for reaction of the ro-vibrational ground state of H₂. The theoretical results for sticking of H₂ and D₂ on Pt(211) are in quite good agreement with the experiment, but uncertainties remain because of a lack of accuracy of the QCT simulations at low incidence energies and possible inaccuracies in the reported experimental incidence energies at high energies. We also investigated the nonadiabatic effect of electron-hole pair excitation on the reactivity using the molecular dynamics with the electron friction (MDEF) method, employing the local density friction approximation (LDFA). Only small effects of electron-hole pair excitation on sticking are found.

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

The HCl + Au(111) system has recently become a benchmark for highly activated dissociative chemisorption, which presumably is strongly affected by electron-hole pair excitation. Previous dynamics calculations, which were based on density functional theory at the generalized gradient approximation level (GGA-DFT) for the molecule-surface interaction, have all overestimated measured reaction probabilities by at least an order of magnitude. Here, we perform ab initio molecular dynamics (AIMD) and AIMD with electronic friction (AIMDEF) calculations employing a density functional that includes the attractive van der Waals interaction. Our calculations model the simultaneous and possibly synergistic effects of surface temperature, surface atom motion, electron-hole pair excitation, the molecular beam conditions of the experiments, and the van der Waals interaction on the reactivity. We find that reaction probabilities computed with AIMDEF and the SRP32-vdW functional still overestimate the measured reaction probabilities, by a factor 18 for the highest incidence energy at which measurements were performed (≈2.5 eV). Even granting that the experiment could have underestimated the sticking probability by about a factor three, this still translates into a considerable overestimation of the reactivity by the current theory. Likewise, scaled transition probabilities for vibrational excitation from ν = 1, j = 1 to ν = 2 are overestimated by the AIMDEF theory, by factors 3-8 depending on the initial conditions modeled. Energy losses to the surface and translational energy losses are, however, in good agreement with experimental values.

Test of the Transferability of the Specific Reaction Parameter Functional for H2 + Cu(111) to D2 + Ag(111)

The accurate description of the dissociative chemisorption of a molecule on a metal surface requires a chemically accurate description of the molecule-surface interaction. Previously, it was shown that the specific reaction parameter approach to density functional theory (SRP-DFT) enables accurate descriptions of the reaction of dihydrogen with metal surfaces in, for instance, H₂ + Pt(111), H₂ + Cu(111), and H₂ + Cu(100). SRP-DFT likewise allowed a chemically accurate description of dissociation of methane on Ni(111) and Pt(111), and the SRP functional for CH₄ + Ni(111) was transferable to CH₄ + Pt(111), where Ni and Pt belong to the same group. Here, we investigate whether the SRP density functional derived for H₂ + Cu(111) also gives chemically accurate results for H₂ + Ag(111), where Ag belongs to the same group as Cu. To do this, we have performed quasi-classical trajectory calculations using the six-dimensional potential energy surface of H₂ + Ag(111) within the Born-Oppenheimer static surface approximation. The computed reaction probabilities are compared with both state-resolved associative desorption and molecular beam sticking experiments. Our results do not yet show transferability, as the computed sticking probabilities and initial-state selected reaction probabilities are shifted relative to experiment to higher energies by about 2-3 kcal/mol. The lack of transferability may be due to the different character of the SRP functionals for H₂ + Cu and CH₄ + group 10 metals, the latter containing a van der Waals correlation functional and the former not.

Strong Anisotropic Interaction Controls Unusual Sticking and Scattering of CO at Ru(0001)

Complete sticking at low incidence energies and broad angular scattering distributions at higher energies are often observed in molecular beam experiments on gas-surface systems which feature a deep chemisorption well and lack early reaction barriers. Although CO binds strongly on Ru(0001), scattering is characterized by rather narrow angular distributions and sticking is incomplete even at low incidence energies. We perform molecular dynamics simulations, accounting for phononic (and electronic) energy loss channels, on a potential energy surface based on first-principles electronic structure calculations that reproduce the molecular beam experiments. We demonstrate that the mentioned unusual behavior is a consequence of a very strong rotational anisotropy in the molecule-surface interaction potential. Beyond the interpretation of scattering phenomena, we also discuss implications of our results for the recently proposed role of a precursor state for the desorption and scattering of CO from ruthenium.

Vibrational Excitation of H2 Scattering from Cu(111): Effects of Surface Temperature and of Allowing Energy Exchange with the Surface

In scattering of H₂ from Cu(111), vibrational excitation has so far defied an accurate theoretical description. To expose the causes of the large discrepancies with experiment, we investigate how the feature due to vibrational excitation (the "gain peak") in the simulated time-of-flight spectrum of (v = 1, j = 3) H₂ scattering from Cu(111) depends on the surface temperature (T_s) and the possibility of energy exchange with surface phonons and electron-hole pairs (ehp's). Quasi-classical dynamics calculations are performed on the basis of accurate semiempirical density functionals for the interaction with H₂ + Cu(111). The methods used include the quasi-classical trajectory method within the Born-Oppenheimer static surface model, the generalized Langevin oscillator (GLO) method incorporating energy transfer to surface phonons, the GLO + friction (GLO+F) method also incorporating energy exchange with ehp's, and ab initio molecular dynamics with electronic friction (AIMDEF). Of the quasi-classical methods tested, comparison with AIMDEF suggests that the GLO+F method is accurate enough to describe vibrational excitation as measured in the experiments. The GLO+F calculations also suggest that the promoting effect of raising T_s on the measured vibrational excitation is due to an electronically nonadiabatic mechanism. However, by itself, enabling energy exchange with the surface by modeling surface phonons and ehp's leads to reduced vibrational excitation, further decreasing the agreement with experiment. The simulated gain peak is quite sensitive to energy shifts in calculated vibrational excitation probabilities and to shifts in a specific experimental parameter (the chopper opening time). While the GLO+F calculations allow important qualitative conclusions, comparison to quantum dynamics results suggests that, with the quasi-classical way of describing nuclear motion and the present box quantization method for assigning the final vibrational state, the gain peak is not yet described with quantitative accuracy. Ways in which this problem might be resolved in the future are discussed.

Mode Specific Electronic Friction in Dissociative Chemisorption on Metal Surfaces: H_{2} on Ag(111)

Electronic friction and the ensuing nonadiabatic energy loss play an important role in chemical reaction dynamics at metal surfaces. Using molecular dynamics with electronic friction evaluated on the fly from density functional theory, we find strong mode dependence and a dominance of nonadiabatic energy loss along the bond stretch coordinate for scattering and dissociative chemisorption of H_{2} on the Ag(111) surface. Exemplary trajectories with varying initial conditions indicate that this mode specificity translates into modulated energy loss during a dissociative chemisorption event. Despite minor nonadiabatic energy loss of about 5%, the directionality of friction forces induces dynamical steering that affects individual reaction outcomes, specifically for low-incidence energies and vibrationally excited molecules. Mode-specific friction induces enhanced loss of rovibrational rather than translational energy and will be most visible in its effect on final energy distributions in molecular scattering experiments.

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

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

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.

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.

Quantum and classical dynamics of reactive scattering of H2 from metal surfaces

State-of-the-art theoretical models allow nowadays an accurate description of H₂/metal surface systems and phenomena relative to heterogeneous catalysis. Here we review the most relevant ones investigated during the last 10 years.

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-Based Vibrational Lifetimes of Molecular Adsorbates: Beyond the Independent-Atom Approximation

We assess the accuracy of vibrational damping rates of diatomic adsorbates on metal surfaces as calculated within the local-density friction approximation (LDFA). An atoms-in-molecules (AIM) type charge partitioning scheme accounts for intramolecular contributions and overcomes the systematic underestimation of the nonadiabatic losses obtained within the prevalent independent-atom approximation. The quantitative agreement obtained with theoretical and experimental benchmark data suggests the LDFA-AIM scheme as an efficient and reliable approach to account for electronic dissipation in ab initio molecular dynamics simulations of surface chemical reactions.

The effect of phonon modes and electron–hole pair couplings on molecule–surface scattering processes

The effect of phonon modes and electron–hole pair (elhp) couplings at different surface temperature on D 2(v = 0, 1; j = 0)– Cu (111) collision has been explored by assuming weakly correlated interactions between molecular Degrees of Freedoms (DOFs) with surface modes and elhp excitations through a Hartree product type wavefunction, where the initial state distributions for the phonon modes and the elhp couplings are incorporated by using Bose–Einstein and Fermi–Dirac probability factors, respectively. We carry out four (4D⊗2D)- and six (6D)- dimensional quantum dynamics on such an effective Hamiltonian, and depict the calculated sticking/transition probabilities and energy transfer from molecule to the surface. The phonon modes slightly affect the sticking probability by broadening the profile, but the transition probability are substantially changed with respect to the rigid surface. On the contrary, the inclusion of elhp coupling along with phonon modes does not change the results much compared to the only phonon case.

The direct and precursor mediated dissociation rates of H2 on a Ni(111) surface

The dissociation and recombination rates of physisorbed H2, and the direct and steady state dissociation (i.e., the precursor mediated dissociation) rates of gas phase H2 on Ni(111), as well as the corresponding kinetic isotope effects, are calculated using the quantum instanton method, together with path integral Monte Carlo and adaptive umbrella sampling techniques. All these rates except the recombination one first decrease and then increase with the increasing temperature, and their minimum values appear at about 250, 300 and 250 K, respectively. These non-monotonic behaviors reveal that the quantum effect of H2 should be very remarkable at low temperatures. The steady state rates are smaller than the direct rates at low temperatures, however, they become larger than the direct ones at high temperatures, these two kinds of rates become equal at about 400 and 300 K on the rigid and quantum lattices, respectively. The quantum motion of the lattice can enhance the direct and steady state rates, and it increases the steady state rate much more than the direct one, for instance, the direct and steady state rates on the quantum lattice are 1.30 and 2.08 times larger than that on the rigid one at 300 K. The calculated kinetic isotope effects are much larger than 1, which reveals that H2 always has a larger rate than that of D2, and the direct process predicts much larger kinetic isotope effects than the steady state process at low temperatures. In addition, the kinetic isotope effects are not affected by the lattice motion.

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.