Setting benchmarks for modelling gas-surface interactions using coherent control of rotational orientation states

Characterisation of magnetic atomic and molecular beamlines for the extraction of empirical scattering-matrices

A recently developed magnetic molecular interferometry technique allows the experimental determination of how the amplitudes and phases of the molecular wave-function change during the collision of a gas phase molecule with a surface. This information, quantified by a scattering-matrix, provides a very stringent benchmark for developing accurate theoretical models as they can also be determined from scattering calculations and are particularly sensitive to the underlying interaction potential. However, the value of this comparison is necessarily limited by the accuracy with which an empirical scattering-matrix can be extracted from the experimental data. This paper presents the methods used to analyse the measurements and uses simulations to determine how various uncertainties in modelling the different magnetic elements which make up the beamline of the apparatus affect the accuracy with which the scattering-matrix can be extracted. It is shown that when signals have a noise level which corresponds to on the order of 1% of the oscillation amplitude, the uncertainties in the modelling do not significantly affect the ability to extract the scattering-matrix elements, with the error in the extracted values increasing to a few percent as the noise in the signals is increased to 10% of the oscillation amplitude. This therefore gives an estimate of the accuracy of the parameters that can be obtained from future measurements.

Hydrogen atom scattering at the Al2O3(0001) surface: a combined experimental and theoretical study

Investigating atom-surface interactions is the key to an in-depth understanding of chemical processes at interfaces, which are of central importance in many fields - from heterogeneous catalysis to corrosion. In this work, we present a joint experimental and theoretical effort to gain insights into the atomistic details of hydrogen atom scattering at the α-Al2O3(0001) surface. Surprisingly, this system has been hardly studied to date, although hydrogen atoms as well as α-Al2O3 are omnipresent in catalysis as reactive species and support oxide, respectively. We address this system by performing hydrogen atom beam scattering experiments and molecular dynamics (MD) simulations based on a high-dimensional machine learning potential trained to density functional theory data. Using this combination of methods we are able to probe the properties of the multidimensional potential energy surface governing the scattering process. Specifically, we compare the angular distribution and the kinetic energy loss of the scattered atoms obtained in experiment with a large number of MD trajectories, which, moreover, allow to identify the underlying impact sites at the surface.

Stereodynamics of adiabatic and non-adiabatic energy transfer in a molecule surface encounter

Molecular energy transfer and reactions at solid surfaces depend on the molecular orientation relative to the surface. While such steric effects have been largely understood in electronically adiabatic processes, the orientation-dependent energy transfer in NO scattering from Au(111) was complicated by electron-mediated nonadiabatic effects, thus lacking a clear interpretation and posing a great challenge for theories. Herein, we investigate the stereodynamics of adiabatic and nonadiabatic energy transfer via molecular dynamics simulations of NO(v = 3) scattering from Au(111) using realistic initial orientation distributions based on accurate neural network fitted adiabatic potential energy surface and electronic friction tensor. Our results reproduce the observed stronger vibrational relaxation for N-first orientation and enhanced rotational rainbow for O-first orientation, and demonstrate how adiabatic anisotropic interactions steer molecules into the more attractive N-first orientation to experience more significant energy transfer. Remaining disagreements with experiment suggest the direction for further developments of nonadiabatic theories for gas-surface scattering.

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.

Multiple echoes in beam spin-echo spectroscopy and their effect on measurements of ultra-fast dynamics

Helium (³He) spin-echo is a powerful experimental technique used to probe ultra-fast atomic scale surface dynamics. The analysis of these measurements is typically performed assuming there is only a single spin-echo condition, expected to produce a constant signal for pure elastic scattering, a monotonically decaying signal for quasi-elastic scattering and oscillations from inelastic scattering events. In the present work, we show that there are in fact four spin-echoes which must be correctly accounted for, and that even in the case of elastic scattering these additional echoes lead to oscillations which could mistakenly be interpreted as being due to inelastic scattering. We demonstrate that it is possible to accurately simulate the experimental data by propagating the³He through the measured magnetic field profile of the apparatus and considering the geometry of the machine, allowing the effect of these additional echoes to be disentangled from inelastic scattering events in future³He spin-echo measurements.

Measuring surface phonons using molecular spin-echo

A new method to measure surface phonons with a molecular beam is presented. The method extends the principles of ³He spin-echo spectroscopy, to the more complex case of a molecular beam exchanging energy with the surface. Measurements are presented for inelastic scattering of D₂ from a Cu(111) surface. Similarly to helium spin-echo, experiments can be performed along optimal tilted projections making it possible to resolve energy peaks with a high energy resolution which is not restricted by the spread of energies of the incident beam. Two analysis methods for these molecular spin echo experiments are presented. A classical approach, analogous to that used for helium spin-echo, explains the most dominant excitation peaks measured, whereas a semi-classical approach allows us to identify smaller peaks which are related to the complexity of the multiple spin-rotation states which exist for molecules.

Accurate Description of the Quantum Dynamical Surface Temperature Effects on the Dissociative Chemisorption of H2 from Cu(111)

Accurately describing surface temperature effects for the dissociative scattering of H2 on a metal surface on a quantum dynamical level is currently one of the open challenges for theoretical surface scientists. We present the first quantum dynamical (QD) simulations of hydrogen dissociating on a Cu(111) surface which accurately describe all relevant surface temperature effects, using the static corrugation model (SCM). The reaction probabilities we obtain show very good agreement with those found using quasi-classical dynamics (QCD), both for individual surface slabs and for an averaged, thus Monte-Carlo sampled, set of thermally distorted surface configurations. Rovibrationally elastic scattering probabilities show a much clearer difference between the QCD and QD results, which appears to be traceable back towards thermally distorted surface configurations with very low dissociation probabilities and underlines the importance of investigating more observables than just dissociation. By reducing the number of distorted surface atoms included in the dynamical model, we also show that only including one, or even three, surface atoms is generally not enough to accurately describe the effects of surface temperature on dissociation and elastic scattering. These results are a major step forward in accurately describing hydrogen scattering from a thermally excited Cu(111) surface, and open up a pathway to better describe reaction and scattering from other relevant crystal facets, such as stepped surfaces, at moderately elevated surface temperatures where quantum effects are expected to play a more important role in the dissociation of H2 on Cu.

Stopping molecular rotation using coherent ultra-low-energy magnetic manipulations

Rotational motion lies at the heart of intermolecular, molecule-surface chemistry and cold molecule science, motivating the development of methods to excite and de-excite rotations. Existing schemes involve perturbing the molecules with photons or electrons which supply or remove energy comparable to the rotational level spacing. Here, we study the possibility of de-exciting the molecular rotation of a D₂ molecule, from J = 2 to the non-rotating J = 0 state, without using an energy-matched perturbation. We show that passing the beam through a 1 m long magnetic field, which splits the rotational projection states by only 10⁻¹²eV, can change the probability that a molecule-surface collision will stop a molecule from rotating and lose rotational energy which is 9 orders larger than that of the magnetic manipulation. Calculations confirm that different rotational orientations have different de-excitation probabilities but underestimate rotational flips (∆m_J\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ne$$\end{document}≠0), highlighting the importance of the results as a sensitive benchmark for further developing theoretical models of molecule-surface interactions.

Manipulating the rotational motions of molecules may provide a tool for controlling chemical processes. Here the authors demonstrate that the rotation of a D₂ molecule can be stopped, upon collision with a metal surface, by a magnetic field that affects the rotational levels to a much smaller extent than the energy difference upon de-excitation.

Surface electronic corrugation of a one-dimensional topological metal: Bi(114)

The surface of Bi(114) is a striking example where the reduced dimensionality gives rise to structural rearrangement and new states at the surface. Here, we present a study of the surface structure and electronic corrugation of this quasi one-dimensional topological metal based on helium atom scattering (HAS) measurements. In contrast to low-index metal surfaces, upon scattering from the stepped (114) truncation of Bi, a large proportion of the incident beam is scattered into higher order diffraction channels which in combination with the large surface unit cell makes an analysis challenging. The surface electronic corrugation of Bi(114) is determined, using measurements upon scattering normal to the steps, together with quantum mechanical scattering calculations. Therefore, minimisation routines that vary the shape of the corrugation are employed, in order to minimise the deviation between the calculations and experimental scans. Furthermore, we illustrate that quantum mechanical scattering calculations can be used to determine the orientation of the in- and outgoing beam with respect to the stepped surface structure.

Focusing and spin polarization of atomic hydrogen beam

We have developed a spin-polarized-hydrogen beam with a hexapole magnet. By combining the beam chopper and pulsed laser ionization detection, the time-of-flight of the hydrogen beam was measured, and the dependence of the beam profile on the velocity was acquired, which was consistent with the beam trajectory simulations. The spin polarization of the beam was analyzed by using the Stern-Gerlach-type magnet in combination with the spatial scan of the detection laser. The spin polarization was about 95% at a focusing condition due to the hexapole magnet. The polarization was, on the other hand, reduced to about 70% for the beam at higher velocities, which is consistent with simulation results.

Survival of rotational alignment in H2 scattering from Si(100)

We report a state-prepared, state-resolved study of rotational scattering of a diatomic molecule from a solid surface. Specifically, H₂ molecules with 80 meV kinetic energy are rotationally aligned in the j = 3 rotational state via stimulated Raman pumping and then scattered from a Si(100) surface at normal incidence. The rotational alignment of the scattered molecules is determined by measuring, for both the incident and scattered molecules, the ionization yield of a probe laser, tuned to selectively ionize molecules in the j = 3 rotation level, as the probe laser polarization is rotated. The measurement is performed for two initial rotational alignments: a "helicoptering" alignment with the bonds constrained to lie primarily parallel to the surface and a "cartwheeling" alignment with the bonds lying primarily normal to the surface. For both initial alignments, the modulation of the probe ionization yield with laser polarization for the scattered molecules is pronounced, although significantly weaker than the modulation measured for the incident molecules. This indicates a significant modification but not a complete elimination of the initial alignment. The modulation is found to be stronger for the scattered molecules originating in the cartwheeling alignment than for the helicoptering alignment. These results contribute toward an improved understanding of the role of rotational motion in molecule-surface dynamics.

Low-energy electron ionization mass spectrometer for efficient detection of low mass species

The design of a high-efficiency mass spectrometer is described, aimed at residual gas detection of low mass species using low-energy electron impact, with particular applications in helium atom microscopy and atomic or molecular scattering. The instrument consists of an extended ionization volume, where electrons emitted from a hot filament are confined using a solenoidal magnetic field to give a high ionization probability. Electron space charge is used to confine and extract the gas ions formed, which are then passed through a magnetic sector mass filter before reaching an ion counter. The design and implementation of each of the major components are described in turn, followed by the overall performance of the detector in terms of mass separation, detection efficiency, time response, and background count rates. The linearity of response with emission current and magnetic field is discussed. The detection efficiency for helium is very high, reaching as much as 0.5%, with a time constant of (198 ± 6) ms and a background signal equivalent to an incoming helium flux of (8.7 ± 0.2) × 10⁶ s^-1.

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.

Molecular spin echoes; multiple magnetic coherences in molecule surface scattering experiments

In this paper we demonstrate that a molecular beam of hydrogen molecules can be magnetically manipulated to produce multiple coherences in the molecular interference pattern. Unlike spin 1/2 magnetic beam experiments, i.e., neutron and helium spin echo, the nuclear and rotational magnetic moments in a molecule are strongly coupled. We show experimentally and theoretically that this coupling leads to multiple magnetic field conditions under which the magnetic moment of molecules travelling with different speeds can be coherently refocussed. We also demonstrate that these multiple coherence signals are extremely sensitive to the scattering event, opening up new possibilities for measuring molecule-surface interactions.

Time-of-flight measurements of the low-energy scattering of CH4 from Ir(111)

We have measured high-resolution time-of-flight (TOF) spectra of methane scattered from an Ir(111) surface at an incident energy of 81 meV. The angular distributions of scattered CH₄ reveal the presence of a sharp and intense specular peak in addition to sharp features corresponding to rotationally inelastic diffraction (RID) peaks along the two main symmetry directions of Ir(111). TOF spectra have been recorded at several RID positions for the two high-symmetry directions. The data show that the scattering dynamics of CH₄ is more complex than the one reported for H₂/D₂, where energy losses in TOF correspond to the expected excitation/deexcitation RID energy transitions. For CH₄, this is the case only for RID peaks showing up far from the specular peak, whereas those appearing close to the specular position present different behaviors, depending on the incident direction. The results are compared with Ne scattering TOF data, which allows to assess the relevance of multiphonon scattering in the energy-exchange process. Finally, we report experimental evidence of selective adsorption resonances detected with CH₄ beams. This will allow characterizing the CH₄-metal surface physisorption well by measuring angular distributions with CH₄ beams.

Atom-surface van der Waals potentials of topological insulators and semimetals from scattering measurements

The phenomenology of resonant scattering has been known since the earliest experiments upon scattering of atomic beams from surfaces and is a means of obtaining experimental information about the fundamentals of weak adsorption systems in the van der Waals regime. We provide an overview of the experimental approach based on new experimental data for the He-Sb₂Te₃(111) system, followed by a comparative overview and perspective of recent results for topological semimetal and insulator surfaces. Moreover, we shortly discuss the perspectives of calculating helium-surface interaction potentials from ab initio calculations. Our perspective demonstrates that atom-surface scattering provides direct experimental information about the atom-surface interaction in the weak physisorption regime and can also be used to determine the lifetime and mean free path of the trapped atom. We further discuss the effects of elastic and inelastic scattering on the linewidth and lifetime of the trapped He atom with an outlook on future developments and applications.

Material properties particularly suited to be measured with helium scattering: selected examples from 2D materials, van der Waals heterostructures, glassy materials, catalytic substrates, topological insulators and superconducting radio frequency materials

Helium Atom Scattering (HAS) and Helium Spin-Echo scattering (HeSE), together helium scattering, are well established, but non-commercial surface science techniques. They are characterised by the beam inertness and very low beam energy (<0.1 eV) which allows essentially all materials and adsorbates, including fragile and/or insulating materials and light adsorbates such as hydrogen to be investigated on the atomic scale. At present there only exist an estimated less than 15 helium and helium spin-echo scattering instruments in total, spread across the world. This means that up till now the techniques have not been readily available for a broad scientific community. Efforts are ongoing to change this by establishing a central helium scattering facility, possibly in connection with a neutron or synchrotron facility. In this context it is important to clarify what information can be obtained from helium scattering that cannot be obtained with other surface science techniques. Here we present a non-exclusive overview of a range of material properties particularly suited to be measured with helium scattering: (i) high precision, direct measurements of bending rigidity and substrate coupling strength of a range of 2D materials and van der Waals heterostructures as a function of temperature, (ii) direct measurements of the electron-phonon coupling constant λ exclusively in the low energy range (<0.1 eV, tuneable) for 2D materials and van der Waals heterostructures (iii) direct measurements of the surface boson peak in glassy materials, (iv) aspects of polymer chain surface dynamics under nano-confinement (v) certain aspects of nanoscale surface topography, (vi) central properties of surface dynamics and surface diffusion of adsorbates (HeSE) and (vii) two specific science case examples - topological insulators and superconducting radio frequency materials, illustrating how combined HAS and HeSE are necessary to understand the properties of quantum materials. The paper finishes with (viii) examples of molecular surface scattering experiments and other atom surface scattering experiments which can be performed using HAS and HeSE instruments.

High-Dimensional Atomistic Neural Network Potential to Study the Alignment-Resolved O2 Scattering from Highly Oriented Pyrolytic Graphite

A high dimensional and accurate atomistic neural network potential energy surface (ANN-PES) that describes the interaction between one O₂ molecule and a highly oriented pyrolytic graphite (HOPG) surface has been constructed using the open-source package (aenet). The validation of the PES is performed by paying attention to static characteristics as well as by testing its performance in reproducing previous ab initio molecular dynamics simulation results. Subsequently, the ANN-PES is used to perform quasi-classical molecular dynamics calculations of the alignment-dependent scattering of O₂ from HOPG. The results are obtained for 200 meV O₂ molecules with different initial alignments impinging with a polar incidence angle with respect to the surface normal of 22.5° on a thermalized (110 and 300 K) graphite surface. The choice of these initial conditions in our simulations is made to perform comparisons to recent experimental results on this system. Our results show that the scattering of O₂ from the HOPG surface is a rather direct process, that the angular distributions are alignment dependent, and that the final translational energy of end-on molecules is around 20% lower than that of side-on molecules. Upon collision with the surface, the molecules that are initially aligned perpendicular to the surface become highly rotationally excited, whereas a very small change in the rotational state of the scattered molecules is observed for the initial parallel alignments. The latter confirms the energy transfer dependence on the stereodynamics for the present system. The results of our simulations are in overall agreement with the experimental observations regarding the shape of the angular distributions and the alignment dependence of the in-plane reflected molecules.