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.