  We present a theory for analyzing residence times of single molecules in a
fixed detection area of a scanning tunneling microscope (STM). The approach is
developed for one-dimensional molecule diffusion and can be extended to two
dimensions by using the same methodology. Explicit results are derived for an
harmonic attractive and repulsive tip-molecule interaction. Applications of the
theory allows one to estimate the type and strength of interactions between the
STM tip and the molecule. This includes the possibility of an estimation of
molecule-molecule interaction when the tip is decorated by a molecule. Despite
our focus on STM, this theory can analogously be applied to other experimental
probes that monitor single molecules.
