  The energetics of H$_2$ interacting with the Si(100) surface is studied by
means of {\em ab initio} total energy calculations within the framework of
density functional theory. We find a direct desorption pathway from the
mono-hydride phase which is compatible with experimental activation energies
and demonstrate the importance of substrate relaxation for this process. Both
the transition state configuration and barrier height depend crucially on the
degree of buckling of the Si dimers on the Si(100) surface. The adsorption
barrier height on the clean surface is governed by the buckling via its
influence on the surface electronic structure. We discuss the consequences of
this coupling for adsorption experiments and the relation between adsorption
and desorption.
