Chemically Accurate Simulation of a Polyatomic Molecule-Metal Surface Reaction

Accurate Reaction Probabilities for Translational Energies on Both Sides of the Barrier of Dissociative Chemisorption on Metal Surfaces

Molecular dynamics simulations are essential for a better understanding of dissociative chemisorption on metal surfaces, which is often the rate-controlling step in heterogeneous and plasma catalysis. The workhorse quasi-classical trajectory approach ubiquitous in molecular dynamics is able to accurately predict reactivity only for high translational and low vibrational energies. In contrast, catalytically relevant conditions generally involve low translational and elevated vibrational energies. Existing quantum dynamics approaches are intractable or approximate as a result of the large number of degrees of freedom present in molecule-metal surface reactions. Here, we extend a ring polymer molecular dynamics approach to fully include, for the first time, the degrees of freedom of a moving metal surface. With this approach, experimental sticking probabilities for the dissociative chemisorption of methane on Pt(111) are reproduced for a large range of translational and vibrational energies by including nuclear quantum effects and employing full-dimensional simulations.

Constructing Mixed Density Functionals for Describing Dissociative Chemisorption on Metal Surfaces: Basic Principles

The production of a majority of chemicals involves heterogeneous catalysis at some stage, and the rates of many heterogeneously catalyzed processes are governed by transition states for dissociative chemisorption on metals. Accurate values of barrier heights for dissociative chemisorption on metals are therefore important to benchmarking electronic structure theory in general and density functionals in particular. Such accurate barriers can be obtained using the semiempirical specific reaction parameter (SRP) approach to density functional theory. However, this approach has thus far been rather ad hoc in its choice of the generic expression of the SRP functional to be used, and there is a need for better heuristic approaches to determining the mixing parameters contained in such expressions. Here we address these two issues. We investigate the ability of several mixed, parametrized density functional expressions combining exchange at the generalized gradient approximation (GGA) level with either GGA or nonlocal correlation to reproduce barrier heights for dissociative chemisorption on metal surfaces. For this, seven expressions of such mixed density functionals are tested on a database consisting of results for 16 systems taken from a recently published slightly larger database called SBH17. Three expressions are derived that exhibit high tunability and use correlation functionals that are either of the PBE GGA form or of one of two limiting nonlocal forms also describing the attractive van der Waals interaction in an approximate way. We also find that, for mixed density functionals incorporating GGA correlation, the optimum fraction of repulsive RPBE GGA exchange obtained with a specific GGA density functional is correlated with the charge-transfer parameter, which is equal to the difference in the work function of the metal surface and the electron affinity of the molecule. However, the correlation is generally not large and not large enough to obtain accurate guesses of the mixing parameter for the systems considered, suggesting that it does not give rise to a very effective search strategy.

Simulating Highly Activated Sticking of H2 on Al(110): Quantum versus Quasi-Classical Dynamics

We evaluate the importance of quantum effects on the sticking of H₂ on Al(110) for conditions that are close to those of molecular beam experiments that have been done on this system. Calculations with the quasi-classical trajectory (QCT) method and with quantum dynamics (QD) are performed using a model in which only motion in the six molecular degrees of freedom is allowed. The potential energy surface used has a minimum barrier height close to the value recently obtained with the quantum Monte Carlo method. Monte Carlo averaging over the initial rovibrational states allowed the QD calculations to be done with an order of magnitude smaller computational expense. The sticking probability curve computed with QD is shifted to lower energies relative to the QCT curve by 0.21 to 0.05 kcal/mol, with the highest shift obtained for the lowest incidence energy. Quantum effects are therefore expected to play a small role in calculations that would evaluate the accuracy of electronic structure methods for determining the minimum barrier height to dissociative chemisorption for H₂ + Al(110) on the basis of the standard procedure for comparing results of theory with molecular beam experiments.

An examination of phonon-inelastic molecule-metal scattering using reduced density matrix and stochastic wave packet methods

We explore the application of reduced density matrix-based approaches to molecules interacting with the lattice vibrations of metals, an interaction responsible for the temperature dependence of many of the fundamental steps of catalysis. We avoid the use of simple models for the bath and instead use density functional theory to compute all molecule-phonon interactions and the properties of the lattice phonons, for methane scattering from Ir(111). We find that while the large metal mass leads to long bath correlation times, these are not significantly longer than the time over which the reduced density matrix changes due to interactions with the bath. We show that the neglect of memory is reasonable and the use of the Redfield equation is justified. We also show how the commonly used rotating wave approximation is far too severe for this scattering problem. A less restrictive approximation that is nearly exact for our system gives an equation of motion in the Lindblad form. As a result, the Monte Carlo wave packet methods can be used to describe gas-phonon scattering, guaranteeing positivity, and with all couplings derived from first-principles.

Quantum dynamics reveal different ligand effects by vibrational excitation in the dissociative chemisorption of HCl on the Au/Ag(111) surface

The reactivity and selectivity of bimetallic surfaces are of fundamental importance in industrial applications. Here, we report the first six-dimensional (6D) quantum dynamics study for the role of surface strain and ligand effects on the reactivity of HCl on a strained pseudomorphic monolayer of Au deposited onto a Ag(111) substrate, with the aid of accurate machine learning-based potential energy surfaces. The substitute of Au into Ag changes the location of the transition state; however, the static barrier height remains roughly the same as pure Au(111). The 6D quantum dynamics calculations reveal that the surface strain due to lattice expansion slightly enhances the reactivity. The ligand effect due to electronic structure interactions between Au and Ag substantially suppresses the reactivity of HCl in the ground vibrational state but promotes the reactivity via vibrational excitation at high kinetic energies. This finding can be attributed to more close interaction with Ag atoms at the transition state close to the fcc site, as well as the tight transition-state region, making the vibrational excitation highly efficient in enhancing the reactivity. Our study quantitatively unravels the dynamical origin of reactivity control by two metals, which will ultimately provide valuable insight into the selectivity of the catalyst.

SBH17: Benchmark Database of Barrier Heights for Dissociative Chemisorption on Transition Metal Surfaces

Accurate barriers for rate controlling elementary reactions on metal surfaces are key to understanding, controlling, and predicting the rate of heterogeneously catalyzed processes. While barrier heights for gas phase reactions have been extensively benchmarked, dissociative chemisorption barriers for the reactions of molecules on metal surfaces have received much less attention. The first database called SBH10 and containing 10 entries was recently constructed based on the specific reaction parameter approach to density functional theory (SRP-DFT) and experimental results. We have now constructed a new and improved database (SBH17) containing 17 entries based on SRP-DFT and experiments. For this new SBH17 benchmark study, we have tested three algorithms (high, medium, and light) for calculating barrier heights for dissociative chemisorption on metals, which we have named for the amount of computational effort involved in their use. We test the performance of 14 density functionals at the GGA, GGA+vdW-DF, and meta-GGA rungs. Our results show that, in contrast with the previous SBH10 study where the BEEF-vdW-DF2 functional seemed to be most accurate, the workhorse functional PBE and the MS2 density functional are the most accurate of the GGA and meta-GGA functionals tested. Of the GGA+vdW functionals tested, the SRP32-vdW-DF1 functional is the most accurate. Additionally, we found that the medium algorithm is accurate enough for assessing the performance of the density functionals tested, while it avoids geometry optimizations of minimum barrier geometries for each density functional tested. The medium algorithm does require metal lattice constants and interlayer distances that are optimized separately for each functional. While these are avoided in the light algorithm, this algorithm is found not to give a reliable description of functional performance. The combination of relative ease of use and demonstrated reliability of the medium algorithm will likely pave the way for incorporation of the SBH17 database in larger databases used for testing new density functionals and electronic structure methods.

Adiabatic models for the quantum dynamics of surface scattering with lattice effects

In this contribution, we review models for the lattice effects in quantum dynamics calculations on surface scattering, which is important to modeling heterogeneous catalysis for achieving an interpretation of experimental measurements. Unlike dynamics models for reactions in the gas phase, those for heterogeneous reactions have to include the effects of the surface. For manageable computational costs in calculations, the effects of static surface (SS) are firstly modeled as this is simply and easily implemented. Then, the SS model has to be improved to include the effects of the flexible surface, that is the lattice effects. To do this, various surface models have been designed where the coordinates of the surface atoms are introduced in the Hamiltonian operator, especially those of the top surface atom. Based on this model Hamiltonian operator, extensive multi-dimension quantum dynamics calculations can be performed to recover the lattice effects. Here, we first review an overview of the techniques in constructing the Hamiltonian operator, which is a sum of the kinetic energy operator (KEO) and potential energy surface (PES). Since the PES containing the coordinates of the surface atoms in a cell is still expensive, the SS model is often accepted. We consider a mathematical model, called the coupled harmonic oscillator (CHO) model, to introduce the concepts of adiabatic and diabatic representations for separating the molecule and surface. Under the adiabatic model, we further introduce the expansion model where the potential function is Taylor expanded around the optimized geometry of the surface. By an expansion model truncated at the first and second order, various coupling surface models between the molecule and surface are derived. Moreover, by further and deeply understanding the adiabatic representation, an effective Hamiltonian operator is obtained by optimizing the total wave function in factorized form. By this factorized form of wave function and effective Hamiltonian operator, the geometry phase of the surface wave function is theoretically found. This theoretical prediction may be measured by carefully designing experiments. Finally, discussions on the adiabatic representation, the PES construction, and possibility of the classical-dynamics solutions are given. Based on these discussions, a simple outlook on the dynamics of photocatalytics is finally given.

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.

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.

Mode Selective Chemistry for the Dissociation of Methane on Efficient Ni/Pt-Bimetallic Alloy Catalysts

The mode selectivity of methane dissociation is studied on three different Ni/Pt-bimetallic alloy surfaces using a fully quantum approach based on reaction path Hamiltonian. Dissociative sticking probability depends on the...

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.

The trapping of methane on Ir(111): A first-principles quantum study

We implement a fully quantum mechanical study of methane trapping on Ir(111), where the phonons, the molecule-surface interaction, and the molecule-phonon coupling are all computed from first-principles. We find that both the surface corrugation and the phonon coupling vary strongly with molecular orientation and that there is a "chemical" aspect to this due to the catalytic nature of the metal. For example, molecules with reactive orientations can approach close to surface sites with low barriers to dissociation. Moreover, lattice motion can lower the barrier to dissociation, leading to unusual behavior for the phonon coupling. We find good agreement with experiment and two recent classical studies if we average our potential energy surface over several orientations of the molecule. We also find reasonable agreement with a recent study of methane diffraction, although we show that diffraction does not play a major role in trapping on the smooth Ir(111) surface and that trapping obeys normal energy scaling, consistent with experiment. We show that the trapping probability can be sensitive to the temperature at both high and low incidence energies. Relaxation and desorption of trapped particles are examined.

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.

Towards bridging the structure gap in heterogeneous catalysis: the impact of defects in dissociative chemisorption of methane on Ir surfaces

The negatively activated region in CH₄ dissociation is attributed to a precursor-mediated mechanism involving surface defects.

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.

Designing new SRP density functionals including non-local vdW-DF2 correlation for H2 + Cu(111) and their transferability to H2 + Ag(111), Au(111) and Pt(111)

Specific reaction parameter density functionals (SRP-DFs) that can describe dissociative chemisorption molecular beam experiments of hydrogen (H₂) on cold transition metal surfaces with chemical accuracy have so far been shown to be only transferable among different facets of the same metal, but not among different metals. We design new SRP-DFs that include non-local vdW-DF2 correlation for the H₂ + Cu(111) system, and evaluate their transferability to the highly activated H₂ + Ag(111) and H₂ + Au(111) systems and the non-activated H₂ + Pt(111) system. We design our functionals for the H₂ + Cu(111) system since it is the best studied system both theoretically and experimentally. Here we demonstrate that a SRP-DF fitted to reproduce molecular beam sticking experiments for H₂ + Cu(111) with chemical accuracy can also describe such experiments for H₂ + Pt(111) with chemical accuracy, and vice versa. Chemically accurate functionals have been obtained that perform very well with respect to reported van der Waals well geometries, and which improve the description of the metal over current generalized gradient approximation (GGA) based SRP-DFs. From a systematic comparison of our new SRP-DFs that include non-local correlation to previously developed SRP-DFs, for both activated and non-activated systems, we identify non-local correlation as a key ingredient in the construction of transferable SRP-DFs for H₂ interacting with transition metals. Our results are in excellent agreement with experiment when accurately measured observables are available. It is however clear from our analysis that, except for the H₂ + Cu(111) system, there is a need for more, more varied, and more accurately described experiments in order to further improve the design of SRP-DFs. Additionally, we confirm that, when including non-local correlation, the sticking of H₂ on Cu(111) is still well described quasi-classically.

Next-Generation Nonlocal van der Waals Density Functional

The fundamental ideas for a nonlocal density functional theory-capable of reliably capturing van der Waals interactions-were already conceived in the 1990s. In 2004, a seminal paper introduced the first practical nonlocal exchange-correlation functional called vdW-DF, which has become widely successful and laid the foundation for much further research. However, since then, the functional form of vdW-DF has remained unchanged. Several successful modifications paired the original functional with different (local) exchange functionals to improve performance, and the successor vdW-DF2 also updated one internal parameter. Bringing together different insights from almost 2 decades of development and testing, we present the next-generation nonlocal correlation functional called vdW-DF3, in which we change the functional form while staying true to the original design philosophy. Although many popular functionals show good performance around the binding separation of van der Waals complexes, they often result in significant errors at larger separations. With vdW-DF3, we address this problem by taking advantage of a recently uncovered and largely unconstrained degree of freedom within the vdW-DF framework that can be constrained through empirical input, making our functional semiempirical. For two different parameterizations, we benchmark vdW-DF3 against a large set of well-studied test cases and compare our results with the most popular functionals, finding good performance in general for a wide array of systems and a significant improvement in accuracy at larger separations. Finally, we discuss the achievable performance within the current vdW-DF framework, the flexibility in functional design offered by vdW-DF3, as well as possible future directions for nonlocal van der Waals density functional theory.

Reagent-Triggered Isomerization of Fluxional Cluster Catalyst via Dynamic Coupling

Metallic cluster catalysts have many thermodynamically accessible isomers with diverse active sites and low reaction barriers, and lately a strong hypothesis emerged that the many catalyst states collectively drive the catalysis. However, it remained a hypothesis that catalyst isomerization is actually kinetically feasible under the current reaction conditions. Using high-temperature dynamics simulations and sampling, a range of orientations, and vibrational energy distributions, we probe how thermal effects and molecular events affect cluster catalyst dynamics. We show that even such a delicate affair as the dissociation or scattering of a methane molecule on the heavy and thus slow Pt₁₃ cluster triggers substantial isomerization of the catalyst, far beyond thermal at 700 K. A kinetic coupling between the methane activity and cluster catalyst dynamics is observed. In return, the thermal dynamics of the cluster affects the methane reaction and scattering probabilities. Hence, molecular events at the surfaces of fluxional cluster catalysts should facilitate the population of an ensemble of catalyst states under the current reaction conditions, with implications for available active sites, reaction mechanisms, and apparent rates.

Evidence of Skewness and Sub-Gaussian Character in Temperature-Dependent Distributions of One Million Electronic Excitation Energies in PbS Quantum Dots

Obtaining statistical distributions by sampling a large number of conformations is vital for an accurate description of temperature-dependent properties of chemical systems. However, constructing distributions with 10⁵-10⁶ samples is computationally challenging because of the prohibitively high computational cost of performing first-principles quantum mechanical calculations. In this work, we present a new technique called the effective stochastic potential configuration interaction singles (ESP-CIS) method to obtain excitation energies. The ESP-CIS method uses random matrix theory for the construction of an effective stochastic representation of the Fock operator and combines it with the CIS method. Excited-state energies of PbS quantum dots (0.75-1.75 nm) at temperatures of 10-400 K were calculated using the ESP-CIS method. Results from a total of 27 million excitation energy calculations revealed the distributions to be sub-Gaussian in nature with negative skewness, which progressively became red-shifted with increasing temperature. This study demonstrates the efficacy of the ESP-CIS method as a general-purpose method for efficient excited-state calculations.

When classical trajectories get to quantum accuracy: II. The scattering of rotationally excited H2 on Pd(111)

The classical trajectory method in a quantum spirit assigns statistical weights to classical paths on the basis of two semiclassical corrections: Gaussian binning and the adiabaticity correction.

When Classical Trajectories Get to Quantum Accuracy: The Scattering of H2 on Pd(111)

When elementary reactive processes occur at such low energies that only a few states of reactants and/or products are available, quantum effects strongly manifest and the standard description of the dynamics within the classical framework fails. We show here, for H₂ scattering on Pd(111), that by pseudoquantizing in the spirit of Bohr the relevant final actions of the system, along with adequately treating the diffraction-mediated trapping of the incoming wave, classical simulations achieve an unprecedented agreement with state-of-the-art quantum dynamics calculations.

Ring Polymer Molecular Dynamics in Gas-Surface Reactions: Inclusion of Quantum Effects Made Simple

Accurately modeling gas-surface collision dynamics presents a great challenge for theory, especially in the low-energy (or temperature) regime where quantum effects are important. Here, a path integral-based nonequilibrium ring polymer molecular dynamics (NE-RPMD) approach is adapted to calculate dissociative initial sticking probabilities (S₀) of H₂ on Cu(111) and D₂O on Ni(111), revealing the distinct quantum nature in the two benchmark surface reactions. NE-RPMD successfully captures quantum tunneling in H₂ dissociation at very low energies, where the quasi-classical trajectory (QCT) method suddenly fails. Additionally, QCT substantially overestimates S₀ of D₂O because of severe zero point energy (ZPE) leakage, even at collision energies greater than the ZPE-corrected barrier. Instead, NE-RPMD predicts S₀ values of D₂O in much improved agreement with reference results obtained by the quantum wavepacket method with reasonable corrections of the thermal contribution. Our results suggest NE-RPMD as a promising approach to model quantum effects in gas-surface reactions.

Dynamical Study of the Dissociative Chemisorption of CHD3 on Pd(111)

The specific reaction parameter (SRP) approach to density functional theory has been shown to model reactions of polyatomic molecules with metal surfaces important for heterogeneous catalysis in the industry with chemical accuracy. However, transferability of the SRP functional among systems in which methane interacts with group 10 metals remains unclear for methane + Pd(111). Therefore, in this work, predictions have been made for the reaction of CHD₃ on Pd(111) using Born-Oppenheimer molecular dynamics while also performing a rough comparison with experimental data for CH₄ + Pd(111) obtained for lower incidence energies. Hopefully, future experiments can test the transferability of the SRP functional among group 10 metals also for Pd(111). We found that the reactivity of CHD₃ on Pd(111) is intermediate between and similar to either Pt(111) or Ni(111), depending on the incidence energy and the initial vibrational state distribution. This is surprising because the barrier height and experiments performed at lower incidence energies than investigated here suggest that the reactivity of Pd(111) should be similar to that of Pt(111) only. The relative decrease in the reactivity of Pd(111) at high incidence energies is attributed to site specificity of the reaction and to dynamical effects such as the bobsled effect and energy transfer from methane to the surface.

Specific Reaction Parameter Density Functional Based on the Meta-Generalized Gradient Approximation: Application to H2 + Cu(111) and H2 + Ag(111)

Specific reaction parameter density functionals (SRP-DFs), which can describe dissociative chemisorption reactions on metals to within chemical accuracy, have so far been based on exchange functionals within the generalized gradient approximation (GGA) and on GGA correlation functionals or van der Waals correlation functionals. These functionals are capable of describing the molecule-metal surface interaction accurately, but they suffer from the general GGA problem that this can be done only at the cost of a rather poor description of the metal. Here, we show that it is possible also to construct SRP-DFs for H2 dissociation on Cu(111) based on meta-GGA functionals, introducing three new functionals based on the "made-simple" (MS) concept. The exchange parts of the three functionals (MS-PBEl, MS-B86bl, and MS-RPBEl) are based on the expressions for the PBE, B86b, and RPBE exchange functionals. Quasi-classical trajectory (QCT) calculations performed with potential energy surfaces (PESs) obtained with the three MS functionals reproduce molecular beam experiments on H2, D2 + Cu(111) with chemical accuracy. Therefore, these three non-empirical functionals themselves are also capable of describing H2 dissociation on Cu(111) with chemical accuracy. Similarly, QCT calculations performed on the MS-PBEl and MS-B86bl PESs reproduced molecular beam and associative desorption experiments on D2, H2 + Ag(111) more accurately than was possible with the SRP48 density functional for H2 + Cu(111). Also, the three new MS functionals describe the Cu, Ag, Au, and Pt metals more accurately than the all-purpose Perdew-Burke-Ernzerhof (PBE) functional. The only disadvantage we noted of the new MS functionals is that, as found for the example of H2 + Cu(111), the reaction barrier height obtained by taking weighted averages of the MS-PBEl and MS-RPBEl functionals is tunable over a smaller range (9 kJ/mol) than possible with the standard GGA PBE and RPBE functionals (33 kJ/mol). As a result of this restricted tunability, it is not possible to construct an SRP-DF for H2 + Ag(111) on the basis of the three examined MS meta-GGA functionals.

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.

Assessment of Two Problems of Specific Reaction Parameter Density Functional Theory: Sticking and Diffraction of H2 on Pt(111)

It is important that theory is able to accurately describe dissociative chemisorption reactions on metal surfaces, as such reactions are often rate-controlling in heterogeneously catalyzed processes. Chemically accurate theoretical descriptions have recently been obtained on the basis of the specific reaction parameter (SRP) approach to density functional (DF) theory (DFT), allowing reaction barriers to be obtained with chemical accuracy. However, being semiempirical, this approach suffers from two basic problems. The first is that sticking probabilities (to which SRP density functionals (DFs) are usually fitted) might show differences across experiments, of which the origins are not always clear. The second is that it has proven hard to use experiments on diffractive scattering of H₂ from metals for validation purposes, as dynamics calculations using a SRP-DF may yield a rather poor description of the measured data, especially if the potential used contains a van der Waals well. We address the first problem by performing dynamics calculations on three sets of molecular beam experiments on D₂ + Pt(111), using four sets of molecular beam parameters to obtain sticking probabilities, and the SRP-DF recently fitted to one set of experiments on D₂ + Pt(111). It is possible to reproduce all three sets of experiments with chemical accuracy with the aid of two sets of molecular beam parameters. The theoretical simulations with the four different sets of beam parameters allow one to determine for which range of incidence conditions the experiments should agree well and for which conditions they should show specific differences. This allows one to arrive at conclusions about the quality of the experiments and about problems that might affect the experiments. Our calculations on diffraction of H₂ scattering from Pt(111) show both quantitative and qualitative differences with previously measured diffraction probabilities, which were Debye-Waller (DW)-extrapolated to 0 K. We suggest that DW extrapolation, which is appropriate for direct scattering, might fail if the scattering is affected by the presence of a van der Waals well and that theory should attempt to model surface atom motion for reproducing diffraction experiments performed for surface temperatures of 500 K and higher.

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.

Diffraction of CH4 from a Metal Surface

Diffraction with matter waves has been reported since the beginning of quantum mechanics. In free space, diffraction effects have been observed even with objects as large as C₆₀ molecules. However, in scattering from a solid surface, pure elastic diffraction features have never been observed with molecules larger than D₂. Here we report the observation of pure molecular diffraction for CH₄ scattered off of an Ir(111) surface. These results prove that quantum coherence is preserved, despite the small separation between rotational levels and the interaction with surface phonons. Density functional theory calculations of the potential energy surface provide some clues to understand the larger corrugation sampled by CH₄ molecules in comparison to Ne atoms. Our results show that isotope separation of polyatomic molecules may be possible using gas-surface diffraction.

Bridging the Gap between Direct Dynamics and Globally Accurate Reactive Potential Energy Surfaces Using Neural Networks

Direct dynamics simulations become increasingly popular in studying reaction dynamics for complex systems where analytical potential energy surfaces (PESs) are unavailable. Yet, the number and/or the propagation time of trajectories are often limited by high computational costs, and numerous energies and forces generated on-the-fly become wasted after simulations. We demonstrate here an example of reusing only a very small portion of existing direct dynamics data to reconstruct a 90-dimensional globally accurate reactive PES describing the interaction of CO₂ with a movable Ni(100) surface based on a machine learning approach. In addition to reproducing previous results with much better statistics, we predict scattering probabilities of CO₂ at the state-to-state level, which is extremely demanding for direct dynamics. We propose this unified way to investigate gaseous and gas-surface reactions of medium size, initiating with hundreds of preliminary direct dynamics trajectories, followed by low-cost and high-quality simulations on full-dimensional analytical PESs.

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.