First-Principles Nonadiabatic Dynamics of Molecules at Metal Surfaces with Vibrationally Coupled Electron Transfer

Accurate description of nonadiabatic dynamics of molecules at metal surfaces involving electron transfer has been a long-standing challenge for theory. Here, we tackle this problem by first constructing high-dimensional neural network diabatic potentials including state crossings determined by constrained density functional theory, then applying mixed quantum-classical surface hopping simulations to evolve coupled electron-nuclear motion. Our approach accurately describes the nonadiabatic effects in CO scattering from Au(111) without empirical parameters and yields results agreeing well with experiments under various conditions for this benchmark system. We find that both adiabatic and nonadiabatic energy loss channels have important contributions to the vibrational relaxation of highly vibrationally excited CO(v_{i}=17), whereas relaxation of low vibrationally excited states of CO(v_{i}=2) is weak and dominated by nonadiabatic energy loss. The presented approach paves the way for accurate first-principles simulations of electron transfer mediated nonadiabatic dynamics at metal surfaces.

On the quantum dynamical treatment of surface vibrational modes for reactive scattering of H2 from Cu(111) at 925 K

We construct the effective Hartree potential for H2 on Cu(111) as introduced in our earlier work [Dutta et al., J. Chem. Phys. 154, 104103 (2021), and Dutta et al., J. Chem. Phys. 157, 194112 (2022)] starting from the same gas-metal interaction potential obtained for 0 K. Unlike in that work, we now explicitly account for surface expansion at 925 K and investigate different models to describe the surface vibrational modes: (i) a cluster model yielding harmonic normal modes at 0 K and (ii) slab models resulting in phonons at 0 and 925 K according to the quasi-harmonic approximation-all consistently calculated at the density functional theory level with the same exchange-correlation potential. While performing dynamical calculations for the H2(v = 0, j = 0)-Cu(111) system employing Hartree potential constructed with 925 K phonons and surface temperature, (i) the calculated chemisorption probabilities are the highest compared to the other approaches over the energy domain and (ii) the threshold for the reaction probability is the lowest, in close agreement with the experiment. Although the survival probabilities (v' = 0) depict the expected trend (lower in magnitude), the excitation probabilities (v' = 1) display a higher magnitude since the 925 K phonons and surface temperature are more effective for the excitation process compared to the phonons/normal modes obtained from the other approaches investigated to describe the surface.

Six-dimensional quantum dynamics study for the dissociative chemisorption of H2 on pure and alloyed AgAu surfaces

The 6D time-dependent wave packet calculations were performed to explore H2 dissociation on Ag, Au, and two AgAu alloy surfaces, using four newly fitted potential energy surfaces based on the neural network fitting to density functional theory energy points. The ligand effect resulting from the Ag-Au interaction causes a reduction in the barrier height for H2+Ag/Au(111) compared to H2+Ag(111). However, the scenario is reversed for H2+Au/Ag(111) and H2+Au(111). The 6D dissociation probabilities of H2 on Ag/Au(111) surfaces are significantly higher than those on the pure Ag(111) surface, but the corresponding results for H2 on Au/Ag(111) surfaces are substantially lower than those on the pure Au(111) surface. The reactivity of H2 on Au(111) is larger than that on Ag(111), despite Ag(111) having a slightly lower static barrier height. This can be attributed to the exceptionally small dissociation probabilities at the hcp and fcc regions, which are at least 100 times smaller compared to those at the bridge or top site for H2+Ag(111). Due to the late barrier being more pronounced, the vibrational excitation of H2 on Ag(111) is more effective in promoting the reaction than on Au(111). Moreover, a high degree of alignment dependence is detected for the four reactions, where the H2 dissociation has the highest probability at the helicopter alignment, as opposed to the cartwheel alignment.

Machine Learning Interatomic Potentials for Reactive Hydrogen Dynamics at Metal Surfaces Based on Iterative Refinement of Reaction Probabilities

The reactive chemistry of molecular hydrogen at surfaces, notably dissociative sticking and hydrogen evolution, plays a crucial role in energy storage and fuel cells. Theoretical studies can help to decipher underlying mechanisms and reaction design, but studying dynamics at surfaces is computationally challenging due to the complex electronic structure at interfaces and the high sensitivity of dynamics to reaction barriers. In addition, ab initio molecular dynamics, based on density functional theory, is too computationally demanding to accurately predict reactive sticking or desorption probabilities, as it requires averaging over tens of thousands of initial conditions. High-dimensional machine learning-based interatomic potentials are starting to be more commonly used in gas-surface dynamics, yet robust approaches to generate reliable training data and assess how model uncertainty affects the prediction of dynamic observables are not well established. Here, we employ ensemble learning to adaptively generate training data while assessing model performance with full uncertainty quantification (UQ) for reaction probabilities of hydrogen scattering on different copper facets. We use this approach to investigate the performance of two message-passing neural networks, SchNet and PaiNN. Ensemble-based UQ and iterative refinement allow us to expose the shortcomings of the invariant pairwise-distance-based feature representation in the SchNet model for gas-surface dynamics.

Ring Polymer Molecular Dynamics Approach to Quantum Dissociative Chemisorption Rates

A ring polymer molecular dynamics (RPMD) method is proposed for the calculation of the dissociative chemisorption rate coefficient on surfaces. The RPMD rate theory is capable of handling quantum effects such as the zero-point energy and tunneling in dissociative chemisorption, while it relies on classical trajectories for the simulation. Applications to H2 dissociative chemisorption are demonstrated. For the highly activated process on Ag(111), strong deviations from Arrhenius behavior are found at low temperatures and attributed to tunneling. On Pt(111), where the dissociation has a barrierless pathway, the RPMD rate coefficient is found to agree with the experimentally derived thermal sticking coefficient within a factor of 2 over a large temperature range. Significant quantum effects are also found.

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.

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.

An accurate many-body expansion potential energy surface for AlH2 (22A') and quantum dynamics in Al(3P) + H2 (v0 = 0-3, j0 = 0, 2, 4, 6) collisions

An accurate potential energy surface is constructed for the excited state of AlH₂ by fitting extensive ab initio points calculated at the multi-reference configuration interaction level based on aug-cc-pV(Q+d)Z and aug-cc-pV(5+d)Z basis sets. All the calculated energies are corrected via the many-body expansion method and extrapolated to the complete basis set limit. The various topographic features of the new potential energy surface are investigated to demonstrate the correct behavior of Al(³P) + H₂(X¹Σ_g⁺) and AlH(a³Π) + H(²S) dissociation limits. By employing the time-dependent wave packet approach, the integral scattering cross-sections obtained from the Coriolis coupling calculation and the centrifugal sudden approximation, respectively, are compared in detail and show that the former has a higher effect on the reaction. Moreover, the thermal rate constants for Al(³P) + H₂ (v₀ = 0-3, j₀ = 0, 2, 4, 6) in the temperature range of 0-5000 K are calculated, thereby providing insights into the influence of ro-vibrational quantum numbers on the thermal rate constants.

Accurate Description of the Quantum Dynamical Surface Temperature Effects on the Dissociative Chemisorption of H2 from Cu(111)

Accurately describing surface temperature effects for the dissociative scattering of H2 on a metal surface on a quantum dynamical level is currently one of the open challenges for theoretical surface scientists. We present the first quantum dynamical (QD) simulations of hydrogen dissociating on a Cu(111) surface which accurately describe all relevant surface temperature effects, using the static corrugation model (SCM). The reaction probabilities we obtain show very good agreement with those found using quasi-classical dynamics (QCD), both for individual surface slabs and for an averaged, thus Monte-Carlo sampled, set of thermally distorted surface configurations. Rovibrationally elastic scattering probabilities show a much clearer difference between the QCD and QD results, which appears to be traceable back towards thermally distorted surface configurations with very low dissociation probabilities and underlines the importance of investigating more observables than just dissociation. By reducing the number of distorted surface atoms included in the dynamical model, we also show that only including one, or even three, surface atoms is generally not enough to accurately describe the effects of surface temperature on dissociation and elastic scattering. These results are a major step forward in accurately describing hydrogen scattering from a thermally excited Cu(111) surface, and open up a pathway to better describe reaction and scattering from other relevant crystal facets, such as stepped surfaces, at moderately elevated surface temperatures where quantum effects are expected to play a more important role in the dissociation of H2 on Cu.

NQCDynamics.jl: A Julia package for nonadiabatic quantum classical molecular dynamics in the condensed phase

Accurate and efficient methods to simulate nonadiabatic and quantum nuclear effects in high-dimensional and dissipative systems are crucial for the prediction of chemical dynamics in the condensed phase. To facilitate effective development, code sharing, and uptake of newly developed dynamics methods, it is important that software implementations can be easily accessed and built upon. Using the Julia programming language, we have developed the NQCDynamics.jl package, which provides a framework for established and emerging methods for performing semiclassical and mixed quantum-classical dynamics in the condensed phase. The code provides several interfaces to existing atomistic simulation frameworks, electronic structure codes, and machine learning representations. In addition to the existing methods, the package provides infrastructure for developing and deploying new dynamics methods, which we hope will benefit reproducibility and code sharing in the field of condensed phase quantum dynamics. Herein, we present our code design choices and the specific Julia programming features from which they benefit. We further demonstrate the capabilities of the package on two examples of chemical dynamics in the condensed phase: the population dynamics of the spin-boson model as described by a wide variety of semiclassical and mixed quantum-classical nonadiabatic methods and the reactive scattering of H₂ on Ag(111) using the molecular dynamics with electronic friction method. Together, they exemplify the broad scope of the package to study effective model Hamiltonians and realistic atomistic systems.

Accurate many-body expansion potential energy surface for SiH2 (11 A′) using a switching function formalism

An accurate many-body expansion potential energy surface for the ground state of SiH2 is reported. To warrant the correct behavior at the Si (1D) + H2 (X1Σ+g) dissociation channels...

Theoretical studies on triplet-state driven dissociation of formaldehyde by quasi-classical molecular dynamics simulation on machine-learning potential energy surface

The H-atom dissociation of formaldehyde on the lowest triplet state (T1) is studied by quasi-classical molecular dynamic simulations on the high-dimensional machine-learning potential energy surface (PES) model. An atomic-energy based deep-learning neural network (NN) is used to represent the PES function, and the weighted atom-centered symmetry functions are employed as inputs of the NN model to satisfy the translational, rotational, and permutational symmetries, and to capture the geometry features of each atom and its individual chemical environment. Several standard technical tricks are used in the construction of NN-PES, which includes the application of clustering algorithm in the formation of the training dataset, the examination of the reliability of the NN-PES model by different fitted NN models, and the detection of the out-of-confidence region by the confidence interval of the training dataset. The accuracy of the full-dimensional NN-PES model is examined by two benchmark calculations with respect to ab initio data. Both the NN and electronic-structure calculations give a similar H-atom dissociation reaction pathway on the T1 state in the intrinsic reaction coordinate analysis. The small-scaled trial dynamics simulations based on NN-PES and ab initio PES give highly consistent results. After confirming the accuracy of the NN-PES, a large number of trajectories are calculated in the quasi-classical dynamics, which allows us to get a better understanding of the T1-driven H-atom dissociation dynamics efficiently. Particularly, the dynamics simulations from different initial conditions can be easily simulated with a rather low computational cost. The influence of the mode-specific vibrational excitations on the H-atom dissociation dynamics driven by the T1 state is explored. The results show that the vibrational excitations on symmetric C-H stretching, asymmetric C-H stretching, and C=O stretching motions always enhance the H-atom dissociation probability obviously.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Chemical Reactions

Machine learning (ML) techniques applied to chemical reactions have a long history. The present contribution discusses applications ranging from small molecule reaction dynamics to computational platforms for reaction planning. ML-based techniques can be particularly relevant for problems involving both computation and experiments. For one, Bayesian inference is a powerful approach to develop models consistent with knowledge from experiments. Second, ML-based methods can also be used to handle problems that are formally intractable using conventional approaches, such as exhaustive characterization of state-to-state information in reactive collisions. Finally, the explicit simulation of reactive networks as they occur in combustion has become possible using machine-learned neural network potentials. This review provides an overview of the questions that can and have been addressed using machine learning techniques, and an outlook discusses challenges in this diverse and stimulating field. It is concluded that ML applied to chemistry problems as practiced and conceived today has the potential to transform the way with which the field approaches problems involving chemical reactions, in both research and academic teaching.

Searching Configurations in Uncertainty Space: Active Learning of High-Dimensional Neural Network Reactive Potentials

Neural network (NN) potential energy surfaces (PESs) have been widely used in atomistic simulations with ab initio accuracy. While constructing NN PESs, their training data points are often sampled by molecular dynamics trajectories. This strategy can be however inefficient for reactive systems involving rare events. Here, we develop an uncertainty-driven active learning strategy to automatically and efficiently generate high-dimensional NN-based reactive potentials, taking a gas-surface reaction as an example. The difference between two independent NN models is used as a simple and differentiable uncertainty metric, allowing us to quickly search in the uncertainty space and place new samples at which the PES is less reliable. By interfacing this algorithm with the first-principles simulation package, we demonstrate that a globally accurate NN potential of the H₂ + Ag(111) system can be constructed with merely ∼150 data points. This PES can be further refined to describe H₂ dissociation on Ag(100) by adding ∼130 more configurations on this facet. The entire process is completely automatic and self-terminated once the relative error criterion is fulfilled. Impressively, data points sampled by this uncertainty-driven strategy are substantially fewer than by the traditional trajectory-based sampling. The final NN PES not only converges well the quantum dissociation probability of the molecule but also well-reproduces the phonon properties of the substrate and is capable of describing surface temperature effects. These results show the potential of this active learning approach in developing high-dimensional NN reactive potentials in gas and condensed phases.

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.

Effect of surface temperature on quantum dynamics of H2 on Cu(111) using a chemically accurate potential energy surface

The effect of surface atom vibrations on H₂ scattering from a Cu(111) surface at different temperatures is being investigated for hydrogen molecules in their rovibrational ground state (v = 0, j = 0). We assume weakly correlated interactions between molecular degrees of freedom and surface modes through a Hartree product type wavefunction. While constructing the six-dimensional effective Hamiltonian, we employ (a) a chemically accurate potential energy surface according to the static corrugation model [M. Wijzenbroek and M. F. Somers, J. Chem. Phys. 137, 054703 (2012)]; (b) normal mode frequencies and displacement vectors calculated with different surface atom interaction potentials within a cluster approximation; and (c) initial state distributions for the vibrational modes according to Bose-Einstein probability factors. We carry out 6D quantum dynamics with the so-constructed effective Hamiltonian and analyze sticking and state-to-state scattering probabilities. The surface atom vibrations affect the chemisorption dynamics. The results show physically meaningful trends for both reaction and scattering probabilities compared to experimental and other theoretical results.

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.

Neural Network Potential Energy Surfaces for Small Molecules and Reactions

We review progress in neural network (NN)-based methods for the construction of interatomic potentials from discrete samples (such as ab initio energies) for applications in classical and quantum dynamics including reaction dynamics and computational spectroscopy. The main focus is on methods for building molecular potential energy surfaces (PES) in internal coordinates that explicitly include all many-body contributions, even though some of the methods we review limit the degree of coupling, due either to a desire to limit computational cost or to limited data. Explicit and direct treatment of all many-body contributions is only practical for sufficiently small molecules, which are therefore our primary focus. This includes small molecules on surfaces. We consider direct, single NN PES fitting as well as more complex methods that impose structure (such as a multibody representation) on the PES function, either through the architecture of one NN or by using multiple NNs. We show how NNs are effective in building representations with low-dimensional functions including dimensionality reduction. We consider NN-based approaches to build PESs in the sums-of-product form important for quantum dynamics, ways to treat symmetry, and issues related to sampling data distributions and the relation between PES errors and errors in observables. We highlight combinations of NNs with other ideas such as permutationally invariant polynomials or sums of environment-dependent atomic contributions, which have recently emerged as powerful tools for building highly accurate PESs for relatively large molecular and reactive systems.

Unified and transferable description of dynamics of H2 dissociative adsorption on multiple copper surfaces via machine learning

Schematic of the developed neural network potential energy surface enabling a unified and transferable description of dynamics of H₂ dissociative adsorption on multiple copper surfaces.

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.

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.

Hot-electron effects during reactive scattering of H2 from Ag(111): the interplay between mode-specific electronic friction and the potential energy landscape

The breakdown of the Born-Oppenheimer approximation gives rise to nonadiabatic effects in gas-surface reactions at metal surfaces. However, for a given reaction, it remains unclear which factors quantitatively determine whether these effects measurably contribute to surface reactivity in catalysis and photo/electrochemistry. Here, we systematically investigate hot electron effects during H2 scattering from Ag(111) using electronic friction theory. We combine first-principles calculations of tensorial friction by time-dependent perturbation theory based on density functional theory and an analytical neural network representation, to overcome the limitations of existing approximations and explicitly simulate mode-specific nonadiabatic energy loss during molecular dynamics. Despite sizable hot-electron-induced energy loss, no measurable nonadiabatic effects can be found for H2 scattering on Ag(111). This is in stark contrast to previous reports for vibrationally excited H2 scattering on Cu(111). By detailed analysis of the two systems, we attribute this discrepancy to a subtle interplay between the magnitude of electronic friction along intramolecular vibration and the shape of the potential energy landscape that controls the molecular velocity at impact. On the basis of this characterization, we offer guidance for the search of highly nonadiabatic surface reactions.

Hot electron effects during reactive scattering of H2 from Ag(111): assessing the sensitivity to initial conditions, coupling magnitude, and electronic temperature

We use an analytical representation of electronic friction for H₂ on Ag(111) to assess the validity and robustness of the MDEF method based on TDPT.

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.

Water dissociating on rigid Ni(100): A quantum dynamics study on a full-dimensional potential energy surface

We constructed a nine-dimensional (9D) potential energy surface (PES) for the dissociative chemisorption of H₂O on a rigid Ni(100) surface using the neural network method based on roughly 110 000 energies obtained from extensive density functional theory (DFT) calculations. The resulting PES is accurate and smooth, based on the small fitting errors and the good agreement between the fitted PES and the direct DFT calculations. Time dependent wave packet calculations also showed that the PES is very well converged with respect to the fitting procedure. The dissociation probabilities of H₂O initially in the ground rovibrational state from 9D quantum dynamics calculations are quite different from the site-specific results from the seven-dimensional (7D) calculations, indicating the importance of full-dimensional quantum dynamics to quantitatively characterize this gas-surface reaction. It is found that the validity of the site-averaging approximation with exact potential holds well, where the site-averaging dissociation probability over 15 fixed impact sites obtained from 7D quantum dynamics calculations can accurately approximate the 9D dissociation probability for H₂O in the ground rovibrational state.

Rotational and steric effects in water dissociative chemisorption on Ni(111)

Powerful laser techniques have recently enabled quantum-state resolved molecular beam experiments for investigating gas-surface reactions, which have unveiled intriguing vibrational, rotational, and also steric effects. For reactions involving polyatomic molecules, e.g., the dissociative chemisorption of methane and water, the rotational and related steric effects are far less understood despite a large body of theoretical work having been able to reproduce the observed vibrational mode specificity and related bond selectivity semi-quantitatively or even within chemical accuracy. Herein, we report a high dimensional quantum dynamics study of water dissociation on Ni(111) on a first-principles potential energy surface, focusing on the reactivities of D2O in various rotational quantum states with different spatial orientations. Through an accurate quantum mechanical description of this asymmetric top, remarkable dependence of the reactivity on the orientation is observed. This dependence is site specific and rotational state specific. These single site rotational and steric effects are partially justified by a sudden model on the basis of the overlap between the rotational wavefunctions and the angular potential near the transition state, but rotational steering also plays a significant role which complicates the dynamics. Although site averaging weakens the influence of initial rotational excitations and leads to minor effects to the reactivity, steric effects are predicted to be observable if the water molecule is selectively excited and aligned by a linearly polarized laser.

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.

Evidence for Electron-Hole Pair Excitation in the Associative Desorption of H2 and D2 from Au(111)

The dissociative adsorption reaction of hydrogen on noble metals is believed to be well-described within the Born-Oppenheimer approximation. In this work, we have experimentally derived translational energy distributions for selected quantum states of H₂ and D₂ formed in associative desorption reactions at a Au(111) surface. Using the principle of detailed balance, we compare our results to theory carried out at the same level of sophistication as was done for the reaction on copper. The theory predicts translational excitation that is much higher than is seen in experiment and fails to reproduce the experimentally observed isotope effect. The large deviations between experiment and theory are surprising because, for the same reactions occurring on Cu(111), a similar theoretical strategy agreed with experiment, yielding "chemical accuracy". We argue that electron-hole pair excitation is more important for the reaction on gold, an effect that may be related to the reaction's later transition state.

Dissociative chemisorption of methane on Ni(111) using a chemically accurate fifteen dimensional potential energy surface

A new chemically accurate potential energy surface for the dissociative chemisorption of methane on the rigid Ni(111) surface.

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.

Mode specificity of the dissociative chemisorption of HOD on rigid Cu(111): an approximate full-dimensional quantum dynamics study

The approximate 9D dissociation probabilities for HOD/Cu(111) are obtained to investigate the influence of the mode specificity on reaction dynamics.

Towards an accurate specific reaction parameter density functional for water dissociation on Ni(111): RPBE versus PW91

Approximated nine dimensional quantum dynamics on a new potential energy surface for water dissociation on Ni(111) computed using the RPBE functional.

Dynamics of water dissociative chemisorption on Ni(111): effects of impact sites and incident angles

The dissociative chemisorption of water on rigid Ni(111) is investigated using a quasiclassical trajectory method on a nine-dimensional global potential energy surface based on a faithful permutation invariant fit of ∼25 000 density functional theory points. This full-dimensional model not only confirms the validity of our earlier reduced-dimensional model with 6 degrees of freedom, but also allows the examination of the influence of impact sites and incident angles. It is shown that the reactivity depends on the site of impact in a complex fashion controlled by the topography of the potential energy surface rather than the barrier height alone. In addition, the reaction is promoted by momenta both parallel and perpendicular to the surface, as predicted by the recently proposed sudden vector projection model.

Six-dimensional quantum dynamics of dissociative chemisorption of H2 on Co(0001) on an accurate global potential energy surface

Six-dimensional quantum dynamics of hydrogen dissociative chemisorption on Co(0001) is investigated on a DFT based potential energy surface.

The sudden vector projection model for reactivity: mode specificity and bond selectivity made simple

CONSPECTUS: Mode specificity is defined by the differences in reactivity due to excitations in various reactant modes, while bond selectivity refers to selective bond breaking in a reaction. These phenomena not only shed light on reaction dynamics but also open the door for laser control of reactions. The existence of mode specificity and bond selectivity in a reaction indicates that not all forms of energy are equivalent in promoting the reactivity, thus defying a statistical treatment. They also allow the enhancement of reactivity and control product branching ratio. As a result, they are of central importance in chemistry. This Account discusses recent advances in our understanding of these nonstatistical phenomena. In particular, the newly proposed sudden vector projection (SVP) model and its applications are reviewed. The SVP model is based on the premise that the collision in many direct reactions is much faster than intramolecular vibrational energy redistribution in the reactants. In such a sudden limit, the coupling of a reactant mode with the reaction coordinate at the transition state, which dictates its ability to promote the reaction, is approximately quantified by the projection of the former onto the latter. The SVP model can be considered as a generalization of the venerable Polanyi's rules, which are based on the location of the barrier. The SVP model is instead based on properties of the saddle point and as a result capable of treating the translational, rotational, and multiple vibrational modes in reactions involving polyatomic reactants. In case of surface reactions, the involvement of surface atoms can also be examined. Taking advantage of microscopic reversibility, the SVP model has also been used to predict product energy disposal in reactions. This simple yet powerful rule of thumb has been successfully demonstrated in many reactions including uni- and bimolecular reactions in the gas phase and gas-surface reactions. The success of the SVP model underscores the importance of the transition state in controlling mode-specific and bond-selective chemistry.