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

Best-of-both-worlds computational approaches to difficult-to-model dissociation reactions on metal surfaces

The accurate modeling of dissociative chemisorption of molecules on metal surfaces presents an exciting scientific challenge to theorists, and is practically relevant to modeling heterogeneously catalyzed reactive processes in computational catalysis. The first important scientific challenge in the field is that accurate barriers for dissociative chemisorption are not yet available from first principles methods. For systems that are not prone to charge transfer (for which the difference between the work function of the surface and the electron affinity of the molecule is larger than 7 eV) this problem can be circumvented: chemically accurate barrier heights can be extracted with a semi-empirical version of density functional theory (DFT). However, a second important challenge is posed by systems that are prone to (full or partial) electron transfer from the surface to the molecule. For these systems the Born-Oppenheimer approximation breaks down, and currently no method of established accuracy exists for modeling the resulting effect of non-adiabatic energy dissipation on the dissociative chemisorption reaction. Because two problems exist for this class of reactions, a semi-empirical approach to computing barrier heights, which would demand that computed and experimental dissociative chemisorption probabilities match, is unlikely to work. This Perspective presents a vision on how these two problems may be solved. We suggest an approach in which parameterized density functionals are used as in the previous semi-empirical approach to DFT, but in which the parameters are based on calculations with first principles electronic structure methods. We also suggest that the diffusion Monte-Carlo (DMC) and the random phase approximation (RPA) probably are the best two first principles electronic structure methods to pursue in the framework of the approach that we call first-principles based DFT (FPB-DFT) - providing DMC and the RPA with a steppingstone towards benchmarking and future applications in computational catalysis. Probably the FPB density functional is best based on screened hybrid exchange in combination with non-local van der Waals correlation. We also propose a new electronic friction method called scattering potential friction (SPF) that could combine the advantages and avoid the disadvantages of the two main existing electronic friction approaches for describing non-adiabatic effects: by extracting an electronic scattering potential from a DFT calculation for the full molecule-metal surface system, it might be possible to compute friction coefficients from scattering phase shifts in a computationally convenient and robust fashion. Combining the FPB-DFT and SPF methods may eventually result in barrier heights of chemical accuracy for the difficult-to-model class of systems that are prone to charge transfer. This should also enable the construction of a representative database of barrier heights for dissociative chemisorption on metal surfaces. Such a database would allow testing new density functionals, or, more generally, new electronic structure approaches on a class of reactions that is of huge importance to the chemical industry. Additionally, the difficult-to-model sub-class of systems we focus on is essential to sustainable chemistry and important for a sustainable future. Adding the database envisaged to large databases already existing but mostly addressing gas phase chemistry will enable testing density functionals that have a claim to universality, i.e., to be good for all chemical systems of importance. We also make a suggestion for how to develop such a generally applicable functional, which should have the correct asymptotic dependence of the exchange contribution to the energy in both the gas phase and the metal. Finally we suggest some improvements in the representation of potential energy surfaces and in dynamics methods that would help with the validation of the proposed methods.

Molecular Dynamics Simulations of Nitric Oxide Scattering Off Graphene

We performed classical molecular dynamics simulations to model the scattering process of nitric oxide, NO, off graphene supported on gold. This is motivated by our desire to probe the energy transfer in collisions with graphene. Since many of these collision systems comprising of graphene and small molecules have been shown to scatter non-reactively, classical molecular dynamics appear to describe such systems sufficiently. We directed thousands of trajectories of NO molecules onto graphene along the surface normal, while varying impact position, but also speed, orientation, and rotational excitation of the nitric oxide, and compare the results with experimental data. While experiment and theory do not match quantitatively, we observe agreement that the relative amount of kinetic energy lost during the collision increases with increasing initial kinetic energy of the NO. Furthermore, while at higher collision energies, all NO molecules lose some energy, and the vast majority of NO is scattered back, in contrast at low impact energies, the fraction of those nitric oxide molecules that are trapped at the surface increases, and some NO molecules even gain some kinetic energy during the collision process. The collision energy seems to preferentially go into the collective motion of the carbon atoms in the graphene sheet.

Time-dependent density functional theory calculations of electronic friction in non-homogeneous media

The excitation of low-energy electron-hole pairs is one of the most relevant processes in the gas-surface interaction. An efficient tool to account for these excitations in simulations of atomic and molecular dynamics at surfaces is the so-called local density friction approximation (LDFA). The LDFA is based on a strong approximation that simplifies the dynamics of the electronic system: a local friction coefficient is defined using the value of the electronic density for the unperturbed system at each point of the dynamics. In this work, we apply real-time time-dependent density functional theory to the problem of the electronic friction of a negative point charge colliding with spherical jellium metal clusters. Our non-adiabatic, parameter-free results provide a benchmark for the widely used LDFA approximation and allow the discussion of various processes relevant to the electronic response of the system in the presence of the projectile.

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.

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.

Ab initio molecular dynamics of hydrogen on tungsten surfaces

The dissociation process of hydrogen molecules on W(110) was studied using density functional theory and classical molecular dynamics. We have calculated the dissociation probability for molecules with energies below 300 meV and analyzed the dynamics of the adsorption process. Our results show that the fate of each trajectory is determined at distances relatively far from the surface, at roughly 2-2.5 Å. This distance varies slightly with the initial kinetic energy of the molecule. Part of our simulations include van der Waals dispersion effects in the interaction between molecule and surface. We present a comparison between these results and other theoretical and experimental results previously published. The inclusion of the van der Waals term provokes an increase in the far-distance attraction that is compensated by a stronger repulsion at short distances. The combination of both effects appreciably decreases the value of the dissociation probability. The successful comparison of our results with experimental information confirms that the methodology employed can be considered as a rich and accurate instrument to study the dissociation of hydrogen on surfaces.

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.