  In this paper we use a zero-range potential (ZRP) method to model positron
interaction with molecules. This allows us to investigate the effect of
molecular vibrations on positron-molecule annihilation using the van der Waals
dimer Kr2 as an example. We also use the ZRP to explore positron binding to
polyatomics and examine the dependence of the binding energy on the size of the
molecule for alkanes. We find that a second bound state appears for a molecule
with ten carbons, similar to recent experimental evidence for such a state
emerging in alkanes with twelve carbons.
