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.

Six-dimensional quantum dynamics study for the dissociative chemisorption of H2 on pure and alloyed AgAu surfaces

The 6D time-dependent wave packet calculations were performed to explore H2 dissociation on Ag, Au, and two AgAu alloy surfaces, using four newly fitted potential energy surfaces based on the neural network fitting to density functional theory energy points. The ligand effect resulting from the Ag-Au interaction causes a reduction in the barrier height for H2+Ag/Au(111) compared to H2+Ag(111). However, the scenario is reversed for H2+Au/Ag(111) and H2+Au(111). The 6D dissociation probabilities of H2 on Ag/Au(111) surfaces are significantly higher than those on the pure Ag(111) surface, but the corresponding results for H2 on Au/Ag(111) surfaces are substantially lower than those on the pure Au(111) surface. The reactivity of H2 on Au(111) is larger than that on Ag(111), despite Ag(111) having a slightly lower static barrier height. This can be attributed to the exceptionally small dissociation probabilities at the hcp and fcc regions, which are at least 100 times smaller compared to those at the bridge or top site for H2+Ag(111). Due to the late barrier being more pronounced, the vibrational excitation of H2 on Ag(111) is more effective in promoting the reaction than on Au(111). Moreover, a high degree of alignment dependence is detected for the four reactions, where the H2 dissociation has the highest probability at the helicopter alignment, as opposed to the cartwheel alignment.

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.

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.

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.