Pronounced out-of-plane diffraction of H2 molecules from a Pd(111) surface

Stereodynamics effects in grazing-incidence fast-molecule diffraction

Grazing-incidence fast-projectile diffraction has been proposed both as a complement and an alternative to thermal-energy projectile scattering, which explains the interest that this technique has received in recent years, especially in the case of atomic projectiles. On the other hand, despite the richer physics involved, molecular projectiles have received much less attention. In this work, we present a theoretical study of grazing-incidence fast-molecule diffraction of H₂ from KCl(001) using a six-dimensional density functional theory based potential energy surface and a time-dependent wavepacket propagation method. The analysis of the computed diffraction patterns as a function of the molecular alignment, and their comparison with the available experimental data, where the initial distribution of rotational states in the molecule is not known, reveals a puzzling stereodynamics effect of the diffracted projectiles: diffracted molecules aligned perpendicular, or quasi perpendicular, to the surface reproduce rather well the experimental diffraction pattern, whereas those molecules aligned parallel to or tilted with respect to the surface do not behave as in the experiments. These results call for more detailed investigations of the molecular beam generation process.

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.

Temperature dependence in fast-atom diffraction at surfaces

Grazing incidence fast atom diffraction at crystal surfaces (GIFAD or FAD) has demonstrated coherent diffraction both at effective energies close to one eV (λ_⊥ ≈ 14 pm for He) and at elevated surface temperatures offering high topological resolution and real time monitoring of growth processes. This is explained by a favorable Debye-Waller factor specific to the multiple collision regime of grazing incidence. This paper presents the first extensive evaluation of the temperature behavior between 177 and 1017 K on a LiF surface. Similarly to diffraction at thermal energies (TEAS), an exponential attenuation of the elastic intensity is observed but, contrarily to TEAS, the maximum coherence is not directly reduced by the attraction forces that increase the effective impact energy. It is more influenced by the surface stiffness and appears very sensitive to surface defects.

Grazing incidence fast atom diffraction, similarities and differences with thermal energy atom scattering (TEAS)

Grazing incidence fast atom diffraction (GIFAD) at surfaces has made rapid progress and has established itself as a surface analysis tool where effective energy E_⊥ of the motion towards the surface is in the same range as that in thermal energy atom scattering (TEAS). To better compare the properties of both techniques, we use the diffraction patterns of helium and neon atoms impinging on a LiF (001) surface as a model system. E-Scan, θ-scan, and φ-scan are presented where the primary beam energy E is varied between a few hundred eV up to five keV, the angle of incidence θ_i between 0.2 and 2° and the azimuthal angle φ_i around 360°. The resulting diffraction charts are analyzed in terms of high and low values of effective energy E_⊥. The former provides high resolution at the positions of the surface atoms and the attached repulsive interaction potentials while the second is sensitive to the attractive forces towards the surface. The recent progress of inelastic diffraction is briefly presented.

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.

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

When elementary reactive processes occur at such low energies that only a few states of reactants and/or products are available, quantum effects strongly manifest and the standard description of the dynamics within the classical framework fails. We show here, for H₂ scattering on Pd(111), that by pseudoquantizing in the spirit of Bohr the relevant final actions of the system, along with adequately treating the diffraction-mediated trapping of the incoming wave, classical simulations achieve an unprecedented agreement with state-of-the-art quantum dynamics calculations.

Exploring surface landscapes with molecules: rotationally induced diffraction of H2 on LiF(001) under fast grazing incidence conditions

Atomic diffraction by surfaces under fast grazing incidence conditions has been used for almost a decade to characterize surface properties with more accuracy than with more traditional atomic diffraction methods. From six-dimensional solutions of the time-dependent Schrödinger equation, we show that diffraction of H₂ molecules under fast grazing incidence conditions could be even more informative for the characterization of ionic surfaces, due to the large anisotropic electrostatic interaction between the quadrupole moment of the molecule and the electric field created by the ionic crystal. Using the LiF(001) surface as a benchmark, we show that fast grazing incidence diffraction of H₂ strongly depends on the initial rotational state of the molecule, while rotationally inelastic processes are irrelevant. We demonstrate that, as a result of the anisotropy of the impinging projectile, initial rotational excitation leads to an increase in intensity of high-order diffraction peaks at incidence directions that satisfy precise symmetry constraints, thus providing a more detailed information on the surface characteristics than that obtained from low-order atomic diffraction peaks under fast grazing incidence conditions. As quadrupole-ion surface potentials are expected to accurately represent the interaction between H₂ and any surface with a marked ionic character, our analysis should be of general applicability to any of such surfaces. Finally, we show that a density functional theory description of the molecule-ion surface potential catches the main features observed experimentally.

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.

Transient quantum trapping of fast atoms at surfaces

We report on the experimental observation and theoretical study of the bound state resonances in fast atom diffraction at surfaces. In our studies, the 4He atom beam has been scattered from a high-quality LiF(001) surface at very small grazing incidence angles. In this regime, the reciprocal lattice vector exchange with the surface allows transient trapping of the 0.3-0.5 keV projectiles into the quasistationary states bound by the attractive atom-surface potential well which is only 10 meV deep. Analysis of the linewidths of the calculated and measured resonances reveals that prior to their release, the trapped projectiles preserve their coherence over travel distances along the surface as large as 0.2  μm, while being in average only at some angstroms in front of the last atomic plane.

High resolution imaging of superficial mosaicity in single crystals using grazing incidence fast atom diffraction

A new table top technique is used to simultaneously analyze the local morphology of crystalline surfaces as well as the misalignment of large scale domains at the topmost surface layer. The approach is based on fast atom diffraction at grazing incidence (GIFAD); the diffraction pattern yields the structural characteristics and the topology of the surface electronic density with atomic resolution. If superficial mosaicity is present, diffraction patterns arising from each mosaic domain can be distinguished, providing high sensitivity to the properties of each of the domains. Taking NaCl(001) as an example, we observe a discrete tilt angle distribution of the mosaic domains following an arithmetic progression with a 0.025° ± 0.005° difference; a twist mosaic angle of 0.09° ± 0.01° is also observed.

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.

Dynamics simulation of N(2) scattering onto W(100,110) surfaces: A stringent test for the recently developed flexible periodic London-Eyring-Polanyi-Sato potential energy surface

An efficient method to construct the six dimensional global potential energy surface (PES) for two atoms interacting with a periodic rigid surface, the flexible periodic London-Eyring-Polanyi-Sato model, has been proposed recently. The main advantages of this model, compared to state-of-the-art interpolated ab initio PESs developed in the past, reside in its global nature along with the small number of electronic structure calculations required for its construction. In this work, we investigate to which extent this global representation is able to reproduce the fine details of the scattering dynamics of N(2) onto W(100,110) surfaces reported in previous dynamics simulations based on locally interpolated PESs. The N(2)/W(100) and N(2)/W(110) systems are chosen as benchmarks as they exhibit very unusual and distinct dissociative adsorption dynamics although chemically similar. The reaction pathways as well as the role of dynamic trapping are scrutinized. Besides, elastic/inelastic scattering dynamics including internal state and angular distributions of reflected molecules are also investigated. The results are shown to be in fair agreement with previous theoretical predictions.

Molecular effects in H2 scattering from metal surfaces at grazing incidence

Collisions of fast atoms with surfaces at grazing incidence have been recently proposed as a promising new tool to determine surface parameters with unprecedented accuracy. Here we show, by means of classical dynamics calculations performed with first-principles six-dimensional potential energy surfaces for H2/NiAl(110) and H2/Pd(111) that, under grazing incidence conditions, fast light molecular projectiles are also useful to determine sticking probabilities at thermal energies, from the threshold up to the saturation limit. Thus they are the ideal complement to traditional experiments at thermal energies to determine sticking curves up to the saturation limit.

Quantum scattering of fast atoms and molecules on surfaces

We present evidence for the diffraction of light keV atoms and molecules grazingly scattered on LiF(001) and NaCl(001) surfaces. At such energies, the de Broglie wavelength is 2 orders of magnitude smaller that the mean thermal atomic displacement in the crystal. Thus, no coherent scattering was expected and interaction of keV atoms with surfaces is routinely treated with classical mechanics. We show here that well-defined diffraction patterns can be observed indicating that, for grazing scattering, the pertinent wavelength is that associated with the slow motion perpendicular to the surface. The experimental data are well reproduced by an ab initio calculation.

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.

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.

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.

In-plane and out-of-plane diffraction of H(2) from metal surfaces

We have measured in-plane and out-of-plane diffraction of H2 and D2 molecular beams scattered by reactive Pd(111) and nonreactive NiAl(110) surfaces at 140-150 meV. A comparison with six-dimensional quantum dynamics and classical trajectory calculations shows for the first time that accurate diffraction patterns can be obtained from state-of-the-art potential energy surfaces based on density functional theory. Our measurements show that, at general incidence conditions, out-of-plane diffraction is much more important than was assumed in previous experiments.