  Due to the improvement of computer power and the development of efficient
algorithms it is now possible to combine high-dimensional quantum dynamical
calculations of the dissociative adsorption of molecular beams with reliable
ab-initio potential energy surfaces (PES). In this brief review two recent
examples of such studies of the systems H_2/Cu(111), where adsorption is
hindered by a noticeable energy barrier, and H_2/Pd(100), where activated as
well as non-activated paths to adsorption exist, are presented. The effect of
lateral surface corrugations on the sticking probability in the tunneling and
the classical regime and the role of additional parallel momentum are discussed
in the context of the H_2/Cu(111) results. For the system H_2/Pd(100) it is
shown that the initial decrease of the sticking probability with increasing
kinetic energy, which is usually attributed to a precursor mechanism, can be
explained by dynamical steering. In addition, the influence of rotation on the
adsorption and desorption dynamics is examined.
