The resonance theory of dissociative electron attachment developed by O'Mal
ley and Bardsley more than thirty years ago has become an efficient tool fo
r ab initio calculations of dissociative attachment to diatomic molecules.
We illustrate this by discussing application of non-local complex potential
theory to the process of dissociative attachment to the HF molecule. For p
olyatomics we have developed a semiempirical resonance method based on the
one-pole approximation for the R matrix. We demonstrate results of applicat
ion Of this theory to methyl halides in the gas and condensed phases. Many
interesting observations, particularly a strong temperature effect for meth
yl chloride, vibrational Feshbach resonances for methyl iodide, and condens
ed-matter effects in dissociative atttachment to methyl- and perfluoromethy
l chloride are explained by our theoretical calculations.