We have studied theoretically the dynamics of H adsorption on and adsorption in Cu(111) using a classical molecular dynamics approach. A key ingredient of this study is plane-wave and pseudopotential calculations of potential energy curves for the major high symmetry sites. These calculations are based on functional theory and the generalized gradient approximation. The extracted chemisorption bond parameters from the energy curves are in good agreement with available experimental data. We find that the calculated energy barriers for absorption of an adsorbed atom are lowered dramatically by relaxation of the Cu atoms, these barriers are so low that, even in the rigid surface lattice situation, the absorption of an incident H atom is non-activated for impacts close to the so-called fcc and hep hollow sites. The model interaction potential that we have used in the dynamics calculations is determined from the calculated potential energy curves and its form is taken from a semi-empirical effective medium theory for binary compounds. The main results of the dynamics calculations are: the relaxations and thermal fluctuations of the Cu atom do not affect the absorption of H in the surface; the energy transfer to the phonons is rather inefficient so the H atom has to make a large number of collisions with the surface atoms before it sticks either in the surface adsorption well or in the subsurface absorption well: a simple estimation shows that the energy transfer to electron-hole pairs can be as efficient as the energy transfer to phonons; our results are consistent with experiments, which indicate that subsurface sites can be populated by an incident atomic H beam and show that the scattering probability is small. (C) 1998 Elsevier Science B.V.