  The aim of this work is to identify the mechanisms responsible for very large
rates and other peculiarities observed in low-energy positron annihilation on
molecules. The two mechanisms considered are: (i) Direct annihilation of the
incoming positron with one of the molecular electrons. This mechanism dominates
for atoms and small molecules. I show that its contribution to the annihilation
rate can be related to the positron elastic scattering cross section. This
mechanism is characterized by strong energy dependence of the annihilation rate
at small positron energies if a low-lying virtual level or a weakly bound state
exists for the positron. (ii) Resonant annihilation, which takes place when the
positron undergoes resonant capture into a vibrationally excited quasibound
state of the positron-molecule complex. This mechanism dominates for larger
molecules capable of forming bound states with the positron. For this mechanism
the energy-averaged annihilation rate is proportional to the level density of
the positron-molecule complex, which is basically determined by the spectrum of
molecular vibrational states populated in the positron capture. For
room-temperature positrons this mechnism can produce annihilation rates up to 5
orders of magnitude greater than the first one. Its contribution is inversely
proportional to the positron momentum at small positron energies.
