Methane dissociation on Ni(111): The effects of lattice motion and relaxation on reactivity

Best-of-Both-Worlds Predictive Approach to Dissociative Chemisorption on Metals

Predictive capability, accuracy, and affordability are essential features of a theory that is capable of describing dissociative chemisorption on a metal surface. This type of reaction is important for heterogeneous catalysis. Here we present an approach in which we use diffusion Monte Carlo (DMC) to pin the minimum barrier height and construct a density functional that reproduces this value. This predictive approach allows the construction of a potential energy surface at the cost of density functional theory while retaining near DMC accuracy. Scrutinizing effects of energy dissipation and quantum tunneling, dynamics calculations suggest the approach to be of near chemical accuracy, reproducing molecular beam sticking experiments for the showcase H2 + Al(110) system to ∼1.4 kcal/mol.

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.

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...

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.

The dissociation and recombination rates of CH4 through the Ni(111) surface: The effect of lattice motion

Methane dissociation is a prototypical system for the study of surface reaction dynamics. The dissociation and recombination rates of CH₄ through the Ni(111) surface are calculated by using the quantum instanton method with an analytical potential energy surface. The Ni(111) lattice is treated rigidly, classically, and quantum mechanically so as to reveal the effect of lattice motion. The results demonstrate that it is the lateral displacements rather than the upward and downward movements of the surface nickel atoms that affect the rates a lot. Compared with the rigid lattice, the classical relaxation of the lattice can increase the rates by lowering the free energy barriers. For instance, at 300 K, the dissociation and recombination rates with the classical lattice exceed the ones with the rigid lattice by 6 and 10 orders of magnitude, respectively. Compared with the classical lattice, the quantum delocalization rather than the zero-point energy of the Ni atoms further enhances the rates by widening the reaction path. For instance, the dissociation rate with the quantum lattice is about 10 times larger than that with the classical lattice at 300 K. On the rigid lattice, due to the zero-point energy difference between CH₄ and CD₄, the kinetic isotope effects are larger than 1 for the dissociation process, while they are smaller than 1 for the recombination process. The increasing kinetic isotope effect with decreasing temperature demonstrates that the quantum tunneling effect is remarkable for the dissociation process.

Methane dissociation on Ni(111): A fifteen-dimensional potential energy surface using neural network method

In the present work, we develop a highly accurate, fifteen-dimensional potential energy surface (PES) of CH4 interacting on a rigid flat Ni(111) surface with the methodology of neural network (NN) fit to a database consisted of about 194 208 ab initio density functional theory (DFT) energy points. Some careful tests of the accuracy of the fitting PES are given through the descriptions of the fitting quality, vibrational spectrum of CH4 in vacuum, transition state (TS) geometries as well as the activation barriers. Using a 25-60-60-1 NN structure, we obtain one of the best PESs with the least root mean square errors: 10.11 meV for the entrance region and 17.00 meV for the interaction and product regions. Our PES can reproduce the DFT results very well in particular for the important TS structures. Furthermore, we present the sticking probability S0 of ground state CH4 at the experimental surface temperature using some sudden approximations by Jackson's group. An in-depth explanation is given for the underestimated sticking probability.

Quantum dynamics of polyatomic dissociative chemisorption on transition metal surfaces: mode specificity and bond selectivity

Recent advances in quantum dynamical characterization of polyatomic dissociative chemisorption on accurate global potential energy surfaces are critically reviewed.

Reaction Rate Constants of CH4(ads) ⇌ CH3(ads) + H(ads) on Ni(111): The Effect of Lattice Motion

Methane dissociation on metal surfaces is of great commercial importance. The dissociation and recombination rate constants of CH4 on Ni(111) are calculated using the quantum instanton approach with the path integral Monte Carlo method. The Ni(111) lattice is treated rigidly, classically, and quantum mechanically to reveal the effects of lattice motion and quantum tunneling. For the dissociation of CH4, the rates have the smallest value on the rigid lattice, while they possess the largest value on the quantum lattice. For instance, at 300 K, the rates on the classical and quantum lattices are 5 and 12 times larger than that on the rigid lattice, respectively. The curve of the Arrhenius plot for the dissociation rates on the rigid lattice demonstrates that the quantum tunneling effect of the ruptured H atom is remarkable, while the nearly invariable dissociation rates at low temperatures on the quantum lattice confirm that the thermally assisted tunneling should be dominant at low temperatures. For the recombination of CH4, the quantum lattice still has rates that are much larger than that of the rigid lattice. For instance, the ratio of the recombination rates on the quantum and rigid lattices is 12 at 300 K. The quantum tunneling effect seems to play a minor role in the recombination rates on the rigid lattice; however, the thermally assisted tunneling is still very significant for the recombination process.

Ab Initio Molecular Dynamics Calculations versus Quantum-State-Resolved Experiments on CHD3 + Pt(111): New Insights into a Prototypical Gas-Surface Reaction

The dissociative chemisorption of methane on metal surfaces is of fundamental and practical interest, being a rate-limiting step in the steam reforming process. The reaction is best modeled with quantum dynamics calculations, but these are currently not guaranteed to produce accurate results because they rely on potential energy surfaces based on untested density functionals and on untested dynamical approximations. To help overcome these limitations, here we present for the first time statistically accurate reaction probabilities obtained with ab initio molecular dynamics (AIMD) for a polyatomic gas-phase molecule reacting with a metal surface. Using a general purpose density functional, the AIMD reaction probabilities are in semiquantitative agreement with new quantum-state-resolved experiments on CHD3 + Pt(111). The comparison suggests the use of the sudden approximation for treating the rotations even though CHD3 has large rotational constants and yields an estimated reaction barrier of 0.9 eV for CH4 + Pt(111).

Enhancing dissociative chemisorption of H2O on Cu(111) via vibrational excitation

The dissociative chemisorption of water is an important step in many heterogeneous catalytic processes. Here, the mode selectivity of this process was examined quantum mechanically on a realistic potential energy surface determined by fitting planewave density functional calculations spanning a large configuration space. The quantum dynamics of the surface reaction were characterized by a six-dimensional model including all important internal coordinates of H(2)O and its distance to the surface. It was found that excitations in all three vibrational modes are capable of enhancing reactivity more effectively than increasing translational energy, consistent with the "late" transition state in the reaction path.

Methane dissociation on Ni(111): a new understanding of the lattice effect

The nature of the lattice motion during the dissociation of methane on Ni(111) is analyzed in great detail, and various models for including lattice effects are explored. It is shown that the thermal vibrations of the lattice strongly modify the reactivity, but that the lattice motion is relatively unperturbed by the incident molecule during the collision, in contrast with several earlier predictions. Based on these studies we propose a new model to describe the effects of lattice motion, which agrees well with exact quantum calculations.

Density functional theory for transition metals and transition metal chemistry

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.