Recent experiments have provided direct evidence for the excitation of electronhole pairs during the adsorption of atoms on metal surfaces. The excitation of electron-hole pairs is an inherently non-adiabatic process which is often ignored in standard theoretical treatments of surface phenomena, using tools such as density functional theory (DFT), as the Born-Oppenheimer approximation cannot be used. To obtain a theoretical model for the electronic excitation process it is therefore necessary to go beyond conventional methods. Previous theoretical descriptions have used a nearly-adiabatic approximation to describe electronic excitations. However, these methods have been found to fail in situations where an adsorbing atom undergoes a transition between a spin-polarised and unpolarised state. In this thesis we develop a fully non-adiabatic theory using a simple description of the adsorbate-metal interaction; the time-dependent, mean-field Newns- Anderson model. This model describes a simple electronic system in which a band of metal states interacts with a single atomic orbital, which can undergo a ‘spin-transition’. We derive expressions describing the time-dependent transfer of charge and energy between the adsorbate and surface, as well as the spectrum of electronic excitations generated. Each of these results describe the evolution of the electronic system in terms of a simple set of parameters. These results are demonstrated using a set of example parameter variations to explore the impact of variables such as adsorbate speed and the temperature of the system. A set of parameter variations describing the interaction of hydrogen isotopes with copper and silver surfaces are obtained from DFT calculations. These parameters are used to drive our model through a single approach of the adsorbate to the surface. We find the results of these calculations to be in good agreement with reported experimental results. Our conclusions, and some possible directions for further work, are summarised in the final chapter.