Inverted vibrational distributions from N2 recombination at Ru(001): Evidence for a metastable molecular chemisorption well

Neural Network Sampling of the Free Energy Landscape for Nitrogen Dissociation on Ruthenium

In heterogeneous catalysis, free energy profiles of reactions govern the mechanisms, rates, and equilibria. Energetics are conventionally computed using the harmonic approximation (HA), which requires determination of critical states a priori. Here, we use neural networks to efficiently sample and directly calculate the free energy surface (FES) of a prototypical heterogeneous catalysis reaction-the dissociation of molecular nitrogen on ruthenium-at density-functional-theory-level accuracy. We find that the vibrational entropy of surface atoms, often neglected in HA for transition metal catalysts, contributes significantly to the reaction barrier. The minimum free energy path for dissociation reveals an "on-top" adsorbed molecular state prior to the transition state. While a previously reported flat-lying molecular metastable state can be identified in the potential energy surface, it is absent in the FES at relevant reaction temperatures. These findings demonstrate the importance of identifying critical points self-consistently on the FES for reactions that involve considerable entropic effects.

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.

Analysis of Energy Dissipation Channels in a Benchmark System of Activated Dissociation: N2 on Ru(0001)

The excitation of electron-hole pairs in reactive scattering of molecules at metal surfaces often affects the physical and dynamical observables of interest, including the reaction probability. Here, we study the influence of electron-hole pair excitation on the dissociative chemisorption of N2 on Ru(0001) using the local density friction approximation method. The effect of surface atom motion has also been taken into account by a high-dimensional neural network potential. Our nonadiabatic molecular dynamics simulations with electronic friction show that the reaction of N2 is more strongly affected by the energy transfer to surface phonons than by the energy loss to electron-hole pairs. The discrepancy between the computed reaction probabilities and experimental results is within the experimental error both with and without friction; however, the incorporation of electron-hole pairs yields somewhat better agreement with experiments, especially at high collision energies. We also calculate the vibrational efficacy for the N2 + Ru(0001) reaction and demonstrate that the N2 reaction is more enhanced by exciting the molecular vibrations than by adding an equivalent amount of energy into translation.

Accurate Neural Network Description of Surface Phonons in Reactive Gas-Surface Dynamics: N2 + Ru(0001)

Ab initio molecular dynamics (AIMD) simulations enable the accurate description of reactive molecule-surface scattering especially if energy transfer involving surface phonons is important. However, presently, the computational expense of AIMD rules out its application to systems where reaction probabilities are smaller than about 1%. Here we show that this problem can be overcome by a high-dimensional neural network fit of the molecule-surface interaction potential, which also incorporates the dependence on phonons by taking into account all degrees of freedom of the surface explicitly. As shown for N₂ + Ru(0001), which is a prototypical case for highly activated dissociative chemisorption, the method allows an accurate description of the coupling of molecular and surface atom motion and accurately accounts for vibrational properties of the employed slab model of Ru(0001). The neural network potential allows reaction probabilities as low as 10^-5 to be computed, showing good agreement with experimental results.

Dissociative dynamics of O2 on Ag(110)

The dissociative dynamics of O₂ on Ag(110) is studied using classical (CT) and quasiclassical (QCT) trajectory calculations performed on an accurate multidimensional DFT potential energy surface.

Towards chemically accurate simulation of molecule-surface reactions

This perspective addresses four challenges facing theorists whose aim is to make quantitatively accurate predictions for reactions of molecules on metal surfaces, and suggests ways of meeting these challenges, focusing on dissociative chemisorption reactions of H(2), N(2), and CH(4). Addressing these challenges is ultimately of practical importance to a more accurate description of overall heterogeneously catalysed reactions, which play a role in the production of more than 90% of man-made chemicals. One challenge is to describe the interaction of a molecule with a metal surface with chemical accuracy, i.e., with errors in reaction barrier heights less than 1 kcal mol(-1). In this framework, the potential of a new implementation of specific reaction parameter density functional theory (SRP-DFT) will be discussed, with emphasis on applications to reaction of H(2) with metal surfaces. Two additional challenges are to come up with improved descriptions of the effects of phonons and electron-hole pairs on reaction of molecules like N(2) on metal surfaces. Phonons can be tackled using sudden approximations in quantum dynamics, and through Ab Initio Molecular Dynamics (AIMD) calculations using classical dynamics. To additionally achieve an accurate description of the effect of electron-hole pair excitation on dissociative chemisorption within a classical dynamics framework, it may be possible to combine AIMD with electronic friction. The fourth challenge we will consider is how to achieve an accurate quantum mechanical description of the dissociative chemisorption of a polyatomic molecule, like methane, on a metal surface. A method of potential interest is the Multi-Configuration Time-Dependent Hartree (MCTDH) method.

Reactive and nonreactive scattering of N2 from Ru(0001): a six-dimensional adiabatic study

We have studied the dissociative chemisorption and scattering of N(2) on and from Ru(0001), using a six-dimensional quasiclassical trajectory method. The potential energy surface, which depends on all the molecular degrees of freedom, has been built applying a modified Shepard interpolation method to a data set of results from density functional theory, employing the RPBE generalized gradient approximation. The frozen surface and Born-Oppenheimer [Ann. Phys. (Leipzig) 84, 457 (1927)] approximations were used, neglecting phonons and electron-hole pair excitations. Dissociative chemisorption probabilities are found to be very small even for translational energies much higher than the minimum reaction barrier, in good agreement with experiment. A comparison to previous low dimensional calculations shows the importance of taking into account the multidimensional effects of N(2) rotation and translation parallel to the surface. The new calculations strongly suggest a much smaller role of nonadiabatic effects than previously assumed on the basis of a comparison between low dimensional results and experiments [J. Chem. Phys. 115, 9028 (2001)]. Also in agreement with experiment, our theoretical results show a strong dependence of reaction on the initial vibrational state. Computed angular scattering distributions and parallel translation energy distributions are in good agreement with experiments on scattering, but the theory overestimates vibrational and rotational excitations in scattering.

Multidimensional effects on dissociation of N2 on Ru(0001)

The applicability of the Born-Oppenheimer approximation to molecule-metal surface reactions is presently a topic of intense debate. We have performed classical trajectory calculations on a prototype activated dissociation reaction, of N2 on Ru(0001), using a potential energy surface based on density functional theory. The computed reaction probabilities are in good agreement with molecular beam experiments. Comparison to previous calculations shows that the rotation of N2 and its motion along the surface affect the reactivity of N2 much more than nonadiabatic effects.

How adiabatic is activated adsorption/associative desorption?

Using density-functional theory we calculate friction coefficients describing the damping of nuclear motion into electron-hole pair excitation for the two best-known examples of activated adsorption: H2 dissociation on a Cu(111) surface and N2 dissociation on a Ru(0001) surface. In both cases, the frictions increase dramatically along the reaction path towards the transition state and can be an order of magnitude larger there than typical in the molecularly adsorbed state. In addition, the frictions for N2/Ru(0001) are typically an order of magnitude larger than for H2/Cu(111). We rationalize these trends in terms of the electron structure as the systems proceed to dissociation along the reaction paths. Combining these friction coefficients with the potential-energy surface in quasiclassical dynamics allows first-principles studies of the importance of the breakdown in the Born-Oppenheimer approximation in describing the chemistry. We find that nonadiabatic effects are minimal for the H2/Cu(111) system, but are quite important for N2/Ru(0001).

The reaction rate for dissociative adsorption of N2 on stepped Ru(0001): Six-dimensional quantum calculations

Quantum-mechanical calculations of the reaction rate for dissociative adsorption of N2 on stepped Ru(0001) are presented. Converged six-dimensional quantum calculations for this heavy-atom reaction have been performed using the multiconfiguration time-dependent Hartree method. A potential-energy surface for the transition-state region is constructed from density-functional theory calculations using Shepard interpolation. The quantum results are in very good agreement with the results of the harmonic transition-state theory. In contrast to the findings of previous model calculations on similar systems, the tunneling effect is found to be small.

Preference for Vibrational over Translational Energy in a Gas-Surface Reaction

State-resolved gas-surface reactivity measurements revealed that vibrational excitation of nu3 (the antisymmetric C-H stretch) activates methane dissociation more efficiently than does translational energy. Methane molecules in the vibrational ground state require 45 kilojoules per mole (kJ/mol) of translational energy to attain the same reactivity enhancement provided by 36 kJ/mol of nu3 excitation. This result contradicts a key assumption underlying statistical theories of gas-surface reactivity and provides direct experimental evidence of the central role that vibrational energy can play in activating gas-surface reactions.

State-resolved dynamics of oxygen atom recombination on polycrystalline Ag

Rotationally resolved, velocity distributions for desorbed O2 molecules formed by O-atom recombination on the surface of a polycrystalline Ag surface are reported. Surface O atoms are generated by oxygen permeation through a 0.25-mm-thick Ag foil heated to 1020 K. Desorbing O2 molecules are probed by (2 + 1) resonant multiphoton ionization via the C 3Pig (3ssigma), v' = 2 <-- <-- X 3Sigmag-, v" = 0 transition and time-of-flight mass spectrometry. Measured velocity distributions are near Maxwell-Boltzmann and yield average translational energies which are significantly lower than the surface temperature ([Et]/2kB approximately 515 K) and essentially independent of rotational excitation. Comparison of the observed C-X (2,0) resonantly enhanced multiphoton ionization spectrum with spectral simulations suggests that the v" = 0 rotational state distribution is more consistent with the surface temperature, but spectral congestion and apparent intensity perturbations prevent a more quantitative analysis. The calculated, sticking curves show a small barrier energy barrier (approximately 10 meV) beyond which sticking decreases. These observations are consistent with low energy desorption and adsorption pathways involving a weakly bound molecular O2 precursor.

Dynamics of high-barrier surface reactions: laser-assisted associative desorption of N2 from Ru(0001)

We have determined the dynamics and energetics of associative desorption of N2 from Ru(0001) using both an experimental technique, laser-assisted associative desorption, and density functional calculations. These show that N2 is preferentially desorbed into very high vibrational states and that the barriers between gas phase N2 and adsorbed N atoms increase from 2 to >3 eV with increasing N coverage on the surface. This experimental technique is found to be quite insensitive to low barrier steps and defects which complicate interpretations from other methods of studying high-barrier surface reactions.