  We study the dynamics of a dimer moving on a periodic one-dimensional
substrate as a function of the initial kinetic energy at zero temperature. The
aim is to describe, in a simplified picture, the microscopic dynamics of
diatomic molecules on periodic surfaces, which is of importance for thin film
formation and crystal growth. We find a complex behaviour, characterized by a
variety of dynamical regimes, namely oscillatory, ``quasi-diffusive'' (chaotic)
and drift motion. Parametrically resonant excitations of internal vibrations
can be induced both by oscillatory and drift motion of the centre of mass. For
weakly bound dimers a chaotic regime is found for a whole range of velocities
between two non-chaotic phases at low and high kinetic energy. The chaotic
features have been monitored by studying the Lyapunov exponents and the power
spectra. Moreover, for a short-range interaction, the dimer can dissociate due
to the parametric excitation of the internal motion.
