The dissociation of diatomic molecules at surfaces

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.