Green's function techniques and tight-binding Hamiltonians provide a very versatile approach to the electronic properties of surfaces, as demonstrated in the pioneering work of Professor Kouteck. Here we show that the same general approach is useful for studies of atomic and molecular motion at surfaces; i.e., one can reliably perform molecular dynamics simulations of the various processes that occur when atoms, atomic clusters, or molecules impinge on a solid surface. 1988, Pergamon Press plc. All rights reserved.