Surface temperature dependence of rotational excitation of H(2) scattered from Pd(111)

Grazing incidence fast atom and molecule diffraction: theoretical challenges

This perspective article reviews the state-of-the-art of grazing incidence fast atom and molecule diffraction (GIFAD and GIFMD) simulations and addresses the main challenges that theorists, aiming to provide useful inputs in this topic, are facing. We first discuss briefly the methods used to build accurate potential energy surfaces describing the interaction between the projectile and the surface. Subsequently, we focus on the dynamics simulation methods for GIFAD, a phenomenon that has received a lot of experimental attention since 2007, when the first measurements were published. Following this experimental effort, theorists have developed and adapted a bunch of methods able to simulate, analyze and extract information from the experimental outputs. We review these methods, from the very simple ones based on classical dynamics to the full quantum ones, paying special attention to more versatile semiclassical approaches, which include quantum ingredients in the dynamics at a computational cost only slightly higher than that required in classical dynamics. Within the semiclassical framework it is possible, for example, to include in the dynamics the surface phonons and the projectile coherence, two factors that may have a relevant influence on the experimental measurements, at a reasonable computational cost. Finally, we address GIFMD, a phenomenon that has received much less attention and for which there is still a lot of room for research. We review the few examples of GIFMD available in the literature, and we discuss new phenomena associated with the molecular internal degrees of freedom, which may have some impact in other closely related fields, such as molecular reactivity on metal surfaces. Finally, we point out opened questions, raised from the comparisons between theoretical and experimental results, which claim for further experimental efforts.

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.

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.

Experimental and theoretical study of rotationally inelastic diffraction of H2(D2) from methyl-terminated Si(111)

Fundamental details concerning the interaction between H2 and CH3-Si(111) have been elucidated by the combination of diffractive scattering experiments and electronic structure and scattering calculations. Rotationally inelastic diffraction (RID) of H2 and D2 from this model hydrocarbon-decorated semiconductor interface has been confirmed for the first time via both time-of-flight and diffraction measurements, with modest j = 0 → 2 RID intensities for H2 compared to the strong RID features observed for D2 over a large range of kinematic scattering conditions along two high-symmetry azimuthal directions. The Debye-Waller model was applied to the thermal attenuation of diffraction peaks, allowing for precise determination of the RID probabilities by accounting for incoherent motion of the CH3-Si(111) surface atoms. The probabilities of rotationally inelastic diffraction of H2 and D2 have been quantitatively evaluated as a function of beam energy and scattering angle, and have been compared with complementary electronic structure and scattering calculations to provide insight into the interaction potential between H2 (D2) and hence the surface charge density distribution. Specifically, a six-dimensional potential energy surface (PES), describing the electronic structure of the H2(D2)/CH3-Si(111) system, has been computed based on interpolation of density functional theory energies. Quantum and classical dynamics simulations have allowed for an assessment of the accuracy of the PES, and subsequently for identification of the features of the PES that serve as classical turning points. A close scrutiny of the PES reveals the highly anisotropic character of the interaction potential at these turning points. This combination of experiment and theory provides new and important details about the interaction of H2 with a hybrid organic-semiconductor interface, which can be used to further investigate energy flow in technologically relevant systems.

Towards bond selective chemistry from first principles: methane on metal surfaces

Controlling bond-selective chemical reactivity is of great importance and has a broad range of applications. Here, we present a molecular dynamics study of bond selective reactivity of methane and its deuterated isotopologues (i.e., CH(4-x)D(x), x=0,1,2,3,4) on Ni(111) and Pt(111) from first principles calculations. Our simulations allow for reproducing the full C-H bond selectivity recently achieved experimentally via mode-specific vibrational excitation and explain its origin. Moreover, we also predict the hitherto unexplored influence of the molecular translational energy on such a selectivity as well as the conditions under which the full selectivity can be realized for the a priori less active C-D bond.

Surface temperature effects on the dynamics of N2 Eley-Rideal recombination on W(100)

Quasiclassical trajectories simulations are performed to study the influence of surface temperature on the dynamics of a N atom colliding a N-preadsorbed W(100) surface under normal incidence. A generalized Langevin surface oscillator scheme is used to allow energy transfer between the nitrogen atoms and the surface. The influence of the surface temperature on the N(2) formed molecules via Eley-Rideal recombination is analyzed at T = 300, 800, and 1500 K. Ro-vibrational distributions of the N(2) molecules are only slightly affected by the presence of the thermal bath whereas kinetic energy is rather strongly decreased when going from a static surface model to a moving surface one. In terms of reactivity, the moving surface model leads to an increase of atomic trapping cross section yielding to an increase of the so-called hot atoms population and a decrease of the direct Eley-Rideal cross section. The energy exchange between the surface and the nitrogen atoms is semi-quantitatively interpreted by a simple binary collision model.

SIX-DIMENSIONAL DYNAMICS OF DISSOCIATIVE CHEMISORPTION OF H2 ON METAL SURFACES

The theory of time-dependent quantum dynamics of dissociative chemisorption of hydrogen on metal surfaces is reviewed, in the framework of electronically adiabatic scattering from static surfaces. Four implementations of the time-dependent wave packet (TDWP) method are discussed. In the direct product pseudo-spectral and the spherical harmonics pseudo-spectral methods, no use is made of the symmetry associated with the surface unit cell. This symmetry is exploited by the symmetry adapted wave packet and the symmetry adapted pseudo-spectral (SAPS) method, which are efficient for scattering at normal incidence. The SAPS method can be employed for potential energy surfaces of general form.

Comparison to experiment shows that the TDWP method yields good, but not yet excellent, quantitative accuracy for dissociation of (ν = 0, j = 0) H 2 if the calculations are based on accurately fitted density functional theory calculations that are performed using the generalized gradient approximation. The influence of the molecule's vibration (rotation) is well (reasonably well) described. The theory does not yet yield quantitatively accurate results for rovibrationally inelastic scattering. The theory has helped with the interpretation of existing experimental results, for instance, by solving a parodox regarding the corrugation of Pt(111) as seen by reacting and scattering H 2. The theory has also provided some exciting new predictions, for instance, concerning where on the surface of Cu(100) H2 reacts depending on its vibrational state. Future theoretical studies of H 2 reacting on metal surfaces will likely be aimed at validating GGAs for molecule-surface interactions, and understanding trends in collisions of H 2 with complex metal surfaces.

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.

Experimental evidence of dynamic trapping in the scattering of H2 from Pd(110)

We have performed H2(D2) diffraction experiments on a Pd(110) surface using two different high-sensitivity set-ups. We have found that, although the total reflectivity of Pd(110) is comparable to that observed in other reactive systems, the corresponding H2(D2) diffraction patterns are quite different: no diffraction peak, including the specular one, is observed on Pd(110). This unexpected result is the consequence of dynamic trapping. Such interpretation is supported by classical dynamics calculations based on accurate ab initio potential energy surfaces.

Reactive and Nonreactive Scattering of H2 from a Metal Surface Is Electronically Adiabatic

The Born-Oppenheimer approximation of uncoupled electronic and nuclear motion is a standard tool of the computational chemist. However, its validity for molecule-metal surface reactions, which are important to heterogeneous catalysis, has been questioned because of the possibility of electron-hole pair excitations. We have performed experiments and calculations on the scattering of molecular hydrogen from a catalytically relevant metal surface, obtaining absolute probabilities for changes in the molecule's velocity parallel to the representative Pt(111) surface. The comparison for in-plane and out-of-plane scattering and results for dissociative chemisorption in the same system show that for hydrogen-metal systems, reaction and diffractive scattering can be accurately described using the Born-Oppenheimer approximation.

The role of molecular rotation in activated dissociative adsorption on metal surfaces

The role of molecular rotation in dissociative adsorption of H2 on the activated NiAl(110) metal surface is systematically investigated by means of classical dynamics calculations performed on ab initio six-dimensional potential energy surfaces. The calculations show that molecules rotate abruptly when they are close to the surface and that this rotation allows the molecules to adopt the orientation that is more convenient for dissociation (i.e., nearly parallel to the surface). Also, in reactive sectors of the NiAl(110) unit cell, there is an "angular threshold" below which molecules cannot dissociate. This angular threshold goes down as the incidence energy increases, which explains the rise of the dissociation probability and the fact that it reaches a value close to 1 at incidence energies of the order of 2 eV. The fact that switching on molecular rotation favors dissociation establishes a competition between dissociation and rotational excitation of reflected molecules above the dissociation threshold. Measurements on rotational excitation might thus bring indirect evidence on the dissociation dynamics. Sample calculations for nonactivated Pd(111) and activated Cu(110) metal surfaces suggest that some of these conclusions may be of general validity.

Rotational effects in the dissociative adsorption of H2 on the Pt211 stepped surface

Rotational effects in the dissociative adsorption of H2 on the Pt211 stepped surface have been studied using classical trajectory calculations on a six-dimensional, density-functional theory potential-energy surface. Reaction of rotating molecules via an indirect trapping mechanism exhibits an unexpected nonmonotonic dependence on the initial rotational quantum number J. Indirect reaction is first quenched with increasing J but is enhanced again for high J initial states. The quenching is attributed to rotational-to-translational energy transfer, which facilitates escape from the chemisorption wells responsible for molecular trapping. For high J, rotational and translational motions decouple, and the energy transfer is no longer possible, which leads again to trapping. Degeneracy-resolved calculations show that for high initial J, molecules rotating in a "cartwheel" fashion (mJ=0) are more likely to become trapped and react indirectly than "helicoptering" molecules (mJ=J). Experimental confirmation of this finding would lend strong support to the existence of the chemisorption wells that trap molecules prior to reaction.

Off-normal incidence dissociative sticking of H2 on Cu(100) studied using six-dimensional quantum calculations

Six-dimensional quantum calculations of the sticking probability for H2 hitting a Cu(100) surface with off-normal incidence are presented. The multiconfiguration time-dependent Hartree approach is employed for an efficient wave-packet propagation. The sticking probability is calculated for different initial momenta parallel to the surface. In contrast with the picture described in the literature, the sticking probability was found to depend on the parallel momentum. The results are explained by the topology of the potential-energy surface, which shows significant corrugation with a moderate variation of the barrier height with the surface site.

State-to-state scattering of D2 from Cu(100) and Pd(111)

Results from state resolved experiments are presented for the interaction of D2(v=1,J=2) with Cu(100) and Pd(111). The reflected molecules were probed using quantum state specific spectroscopy. For D2 scattered from Cu(100) the vibrational survival probability and some transition inelastic probabilities were measured for incident energies from 70-200 meV. The survival probability was found to be larger then that found previously for H2(v=1) scattered from the same surface; these differences are discussed in terms of the lower zero point energy and smaller vibrational energy spacings of D2. D2 translational energy exchange was studied for several different scattering channels and interpreted using simple classical calculations. The survival probability was also measured for D2(v=1) scattered from Pd(111) at one incident energy. Pd is reactive for D2 dissociation and this survival probability was measured to be small and also to be much smaller than that for H2(v=1) under similar conditions. Vibrational relaxation channels were studied for D2 scattering from both Cu(100) and Pd(111). The vibrational relaxation probability on both surfaces was also found to be smaller than that measured for comparable channels for H2. The smaller survival probability and vibrational relaxation probability for D2 on Pd(111) cannot be easily accounted for by the difference in zero point energy and vibrational energy spacings.

Mechanisms of H2 dissociative adsorption on the Pt(211) stepped surface

We utilize classical trajectory calculations to study the reaction dynamics of the dissociative adsorption of H2 on the stepped Pt(211) surface. The potential-energy surface has been obtained through an accurate interpolation of density-functional theory data at the generalized gradient approximation level, using the corrugation reduction procedure. New techniques for visualizing the collective dynamics of trajectories are introduced to elucidate the reaction mechanisms involved. Reaction exhibits a nonmonotonic dependence on collision energy, first decreasing with energy, and then increasing. A strong component of direct nonactivated reaction exists at the top edge of the step over the entire range of energies. The inverse relationship between reaction and collision energy at low energies is attributed to trapping in weak chemisorption wells. These wells also influence the direct reaction at the step, leading to a strong asymmetric dependence on incidence angle. Reaction on the terrace is activated, and only contributes significantly at high energies. Agreement with experiments on Pt(533) [A. T. Gee, B. E. Hayden, C. Mormiche, and T. S. Nunney, J. Chem. Phys. 112, 7660 (2000); Surf. Sci. 512, 165 (2002)] is good, and we are able to suggest new interpretations of the experimental data.

A classical dynamics method for H2 diffraction from metal surfaces

We present a discretization method that allows one to interpret measurements on diffraction of diatomic molecules from solid surfaces using six-dimensional (6D) classical trajectory calculations. It has been applied to the D2NiAl(110) and H2Pd(111) systems (which are models for activated and nonactivated dissociative chemisorption, respectively) using realistic potential energy surfaces obtained from first principles. Comparisons with experimental results and 6D quantum dynamical calculations show that, in general, the method is able to predict the relative intensity of the most important diffraction peaks. We therefore conclude that classical mechanics can be an efficient guide for experimentalists in the search for the most significant diffraction channels.

Trapping, molecular adsorption, and precursors for nonactivated chemisorption

Many fundamental questions are still unanswered regarding the very existence of precursor states and the microscopic mechanism of its population in the case of dissociative adsorption of light molecules on metal surfaces. We report results of classical trajectory calculations for H(2)/Pd(110) based on a six-dimensional potential energy surface obtained from ab initio calculations and a generalized Langevin oscillator model to account for energy exchange with the surface and dissipation. A quantitative characterization of the dynamic process is obtained which elucidates the respective roles played by direct dissociation, dynamic trapping, and precursor mediated adsorption. We predict the existence of H2 molecular chemisorption and provide the precise adsorption conditions for its experimental observation.

Theoretical analysis of the relation between H2 dissociation and reflection on Pd surfaces

We study the scattering of H2 (v=0, J=0) molecules by the Pd(110) surface using classical trajectory methods. We show that the dissociative adsorption probability barely depends on incidence angle (total energy scaling) up to an impact energy of 200 meV. This is the consequence of a "loss of memory" of the initial incidence angle, mostly due to dynamic trapping, which also reflects itself in a cosinelike angular distribution of reflected molecules. Consequently, a cosinelike distribution can be the result of a subpicosecond process that involves neither energy dissipation to the surface nor transient thermal accommodation.

Energy loss of atoms at metal surfaces due to electron-hole pair excitations: first-principles theory of "chemicurrents"

A method is presented for calculating electron-hole pair excitation due to an incident atom or molecule interacting with a metal surface. Energy loss is described using an ab initio approach that obtains a position-dependent friction coefficient for an adsorbate moving near a metal surface from a total energy pseudopotential calculation. A semiclassical forced oscillator model is constructed to describe excitation of the electron gas due to the incident molecule. This approach is applied to H and D atoms incident on a Cu(111) surface, and we obtain theoretical estimates of the "chemicurrents" measured by Nienhaus et al. [Phys. Rev. Lett. 82, 446 (1999)] for these atoms incident on the surface of a Schottky diode.