We present an exposition of the various theoretical models currently in use for describing the dynamics of molecular dissociation at surfaces. We begin by outlining the representations of the nuclear and electronic dynamics and how these define the potential energy surfaces for the interactions. Strategies for solving the nuclear motion follow with particular emphasis being paid to a quantum description on the electronic ground state which is in line with experiments employing hyperthermal molecular beams. These can be performed in either a time-dependent or time-independent fashion and both approaches are considered. Following this, the methods that have been developed for treating the dissipative motion as the molecule nears the surface are presented. This is divided into energy loss to the electronic subsystem and to the substrate atomic vibrations. The final part of the review shows how the results of theoretical simulations have been usefully applied to rationalize data obtained from molecular beam scattering experiments.

https://iopscience.iop.org/article/10.1088/0034-4885/58/12/001/pdf

The dissociation of diatomic molecules at surfaces

We have determined the dependence of the dissociative adsorption probability in the zero coverage limit, S0, for H2 on Cu(111) as a function of translational energy, Ei, and incidence angle, θi, vibrational state, v, and rotational state, J We have also obtained information on the effect of surface temperature, Ts, on this probability These results have been obtained by combining the findings of two separate experiments We have obtained the form of the dependence of S0 on Ei at Ts=925 K for a range of quantum states from desorption experiments via the principle of detailed balance We have obtained absolute S0 values from direct molecular beam adsorption experiments, which reveal that S0 scales with the so‐called ‘‘normal energy,’’ En=Ei cos2 θi The desorption experiments provide detailed information for J=0 to 10 of H2(v=0) and for J=0 to 7 of H2(v=1) The beam experiments additionally provide information on the adsorption of H2(v=2), averaged over J All measurements are consistent with adsorption functions with an s‐shaped form, which can be described by S0=A(1+erf(x))/2, where x=(En−E0)/W Values of W are ∼016 and 013 eV for v=0 and v=1, respectively, at Ts=925 K, falling by about 005 eV for Ts=120 K, and with only a slight dependence on J Values of A are insensitive to v and J, with a value of ∼025 S(En,v,J) curves are thus similar for different v and J, but shifted in EnIn contrast, we find that the values of E0, which determine the mid‐point of the curves, have a strong dependence on v and J Specifically, E0 for H2(v=0) molecules is about 06 eV, falling to 03 and 01 eV for H2(v=1) and H2(v=2), respectively Translational energy is thus about twice as effective as vibrational energy in promoting dissociation E0 rises with increasing J at low J, before falling at high J, indicating that rotational motion hinders adsorption for low rotational states (J<4), and enhances adsorption for high rotational states (J≳4) Results are compared with similar studies on the D2/Cu(111) system and with recent calculations Finally, these results are used to predict the dependence of the rate of dissociation on temperature for a ‘‘bulb’’ experiment with ambient hydrogen gas in contact with a Cu(111) surface This simulation yields an activation energy of 047 eV for temperatures close to 800 K, compared to a literature value of 04 eV from experiment Analysis of the temperature dependence reveals that the dominant reason for the increase in rate at high temperature is the increase in population of the high energy tail of the translational energy distribution

Quantum‐state‐specific dynamics of the dissociative adsorption and associative desorption of H2 at a Cu(111) surface

This computational study is motivated by the apparent conflict between an experiment on dissociation of H2 and D2 on Pt(111), which suggests a rather corrugated potential energy surface (PES) for the H2/Pt(111) system, and an experiment showing only weak nonzero-order diffraction of HD scattering from Pt(111). In the calculations we have used density functional theory (DFT) within the generalized gradient approximation (GGA), including scalar relativistic effects and modelling the Pt(111) surface as a slab. We have found that the H2/Pt(111) PES is both energetically and geometrically corrugated. We have also found that there are reaction paths without or with very low barriers leading to dissociation of H2 on the Pt(111) surface, but that there are other reaction paths with substantial barriers. By performing extensive calculations on H interacting with a Pt(111) surface we have shown that a DFT/GGA approach that includes scalar relativistic effects is capable of describing the interaction between a hydro...

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Atomic and molecular hydrogen interacting with Pt(111).

Here, we give a full account of a large collaborative effort toward an atomic-scale understanding of modern industrial ammonia production over ruthenium catalysts We show that overall rates of ammonia production can be determined by applying various levels of theory (including transition state theory with or without tunneling corrections, and quantum dynamics) to a range of relevant elementary reaction steps, such as N(2) dissociation, H(2) dissociation, and hydrogenation of the intermediate reactants A complete kinetic model based on the most relevant elementary steps can be established for any given point along an industrial reactor, and the kinetic results can be integrated over the catalyst bed to determine the industrial reactor yield We find that, given the present uncertainties, the rate of ammonia production is well-determined directly from our atomic-scale calculations Furthermore, our studies provide new insight into several related fields, for instance, gas-phase and electrochemical ammonia synthesis The success of predicting the outcome of a catalytic reaction from first-principles calculations supports our point of view that, in the future, theory will be a fully integrated tool in the search for the next generation of catalysts

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Predicting Catalysis: Understanding Ammonia Synthesis from First-Principles Calculations

Probing catalytic reactions at surfaces

Molecular beam techniques have been utilized to measure the dissociative chemisorption probability at zero surface coverage S0 for D2(H2) on Pt(111) as a function of initial energy Ei, angle of incidence θi, surface temperature Ts, isotopic mass and nozzle temperature Tn. S0 shows a large increase with translational energy, but no threshold in Ei, a peaking at θi=0°, and an independence with Ts, isotope and Tn. These results are interpreted in terms of direct dissociative chemisorption on the Pt(111) terraces. The dynamical picture that emerges is that although there is no significant barrier to dissociation along the minimum energy path, barriers do exist along nonoptimal reactive trajectories. Thus, the ‘‘translational activation’’ and other dynamical observations are intimately related to the multidimensional aspects of the dissociative potential energy surface. Some aspects of the dissociative chemisorption, however, still seem somewhat surprising within this general description.

J. K. Brown

Papers

Molecular beam studies of H2 and D2 dissociative chemisorption on Pt(111)