Anomalous KCl(001) Surface Corrugation from Fast He Diffraction at Very Grazing Incidence

Reply to the 'Comment on "Perturbation theory of scattering for grazing-incidence fast-atom diffraction"' by G. A. Bocan, H. Breiss, S. Szilasi, A. Momeni, E. M. S. Casagrande, E. A. Sánchez, M. S. Gravielle and H. Khemliche, Phys. Chem. Chem. Phys., 2023, , DOI: 10.1039/D3CP02486E

In this Reply, we show that criticisms of perturbation theory for grazing-incidence fast-atom diffraction (GIFAD) are ill-founded. We show explicitly that our formulation (W. Allison, S. Miret-Artés and E. Pollak, Phys. Chem. Chem. Phys., 2022, 24, 15851) provides a similar precision in describing the observed phenomena as ab initio potentials. Since that is the main criterion to distinguish between methods, it seems reasonable to conclude that the perturbation approach using a Morse-type potential reproduces the essential aspects of the dynamics correctly. In addition we expand on the historical context and summarize the physical insights provided by our methods.

Comment on "Perturbation theory of scattering for grazing-incidence fast-atom diffraction", by W. Allison, S. Miret-Artés and E. Pollak, Phys. Chem. Chem. Phys., 2022, , 15851

In this comment we discuss some aspects of Phys. Chem. Chem. Phys., 2022, 24, 15851, by Allison et al., an article intensely motivated by our study of grazing incidence fast atom diffraction (GIFAD) for He-KCl(001) [G. A. Bocan, H. Breiss, S. Szilasi, A. Momeni, M. E. Staicu Casagrande, M. S. Gravielle, E. A. Sánchez and H. Khemliche, Phys. Rev. Lett., 2020, 125, 096101; G. A. Bocan, H. Breiss, S. Szilasi, A. Momeni, M. E. Staicu Casagrande, E. A. Sánchez, M. S. Gravielle and H. Khemliche, Phys. Rev. B, 2021, 104, 235401]. In particular, (a) we show that, contrary to first order perturbation prediction, the surface corrugation is not proportional to the tangent of the rainbow angle and, (b) we analyze whether a Morse-like formula, like the one Allison et al. use, is able to reproduce the atom-surface potential derived from density functional theory (DFT) calculations. In addition, we give some clarifications regarding specific remarks the authors made about our articles.

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.

Perturbation theory of scattering for grazing-incidence fast-atom diffraction

Recent grazing-incidence, fast atom diffraction (GIFAD) experiments have highlighted the well known observation that the distance between classical rainbow angles depends on the incident energy. The GIFAD experiments imply an incident vertical scattering angle, facilitating an analytic analysis using classical perturbation theory, which leads to the conclusion that the so called "dynamic corrugation" amplitude, as defined by Bocan et al., Phys. Rev. Lett., 2020 125, 096101 is, within first-order perturbation theory, proportional to the tangent of the rainbow angle. Therefore it provides no further information about the interaction than is gleaned from the rainbow angle and its energy dependence. Perhaps more importantly, the resulting analytic theory reveals how the energy dependence of rainbow angles may be inverted into information on the force field governing the interaction of the incident projectile with the surface.

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.

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.