Dynamics of Reactions at Surfaces

Abstract

Chemical reactions correspond to dynamical events involving bond-making and bond-breaking processes [1]. In the previous chapter we have seen how the energetics of catalytic reactions can be determined from first principles using electronic structure theory. Due to the constant improvement in the computer power and the development of efficient algorithms for electronic structure calculations, mainly based on density functional theory (DFT), it has become possible to map out entire potential energy surfaces (PES) of complex catalytic reactions [2, 3]. However, this static information is often not sufficient to really understand how a reaction proceeds. Furthermore, in the experiment the potential energy surface is never directly measured but just reaction rates and probabilities which are a consequence of the interaction potential. Thus for a true detailed understanding of reaction mechanisms dynamical simulations can be very helpful. Calculating the time evolution of processes also allows a genuine comparison between theory and experiment since experimentally accessible quantities such as reaction or adsorption probabilities can be directly derived from the simulations. Thereby dynamical simulations also provide a reliable check of the accuracy of the calculated PES on which the dynamical simulations are based. In Fig. 1, a schematic two-dimensional PES is shown as a function of the distance of the reactants from a catalyst surface and of some molecular coordinate. It provides an illustration how a catalyst works. A reaction might be hindered by a relatively large barrier in the gas phase or in solution. However, for the adsorbed reactants, the barrier can be much lower. Thus the catalyst provides a detour in the multi-dimensional configuration space with a barrier that can be much more easily traversed. It should be noted that the catalyst not only provides reaction routes with smaller barriers, but the catalyst also acts as a thermal bath that can provide and dissipate energy. Therefore many details of heterogeneous catalytic reactions can be understood based on concepts derived from equilibrium thermodynamics. For example, rate constants can be estimated based on transition state theory [4] where the assumption of strong friction is crucial [5]. This also means that the activity and selectivity of a heterogeneous catalytic reactions depend much more strongly on activation barrier heights, which enter the reaction rate constants exponentially, than on dynamical effects. This means that the length and the curvature of the detour in the multi-dimensional configuration space illustrated in Fig. 1 hardly matters, it is just the reduction in the activation barrier height on the FIG. 1: Schematic illustration of the role of a catalyst employing a two-dimensional representation of the potential energy surface. A catalyst provides a detour in the multi-dimensional PES (dashed line) with a lower activation barrier for the adsorbed species than in the gas phase (or in solution).