Theoretical studies are proposed of the excitation of a molecule by an electron whose incident energy is near the threshold of that excitation. There are serious discrepancies with experiment, including the observation of unexplained threshold structures. The full quantum physics of the system enters the description of these processes. The goal here is the development of a scattering theory for this domain. There are three main components of the investigation. (1) Development of parameter-free model polarization/correlation potentials. (2) Development of new approximate theoretical treatments of the quantum dynamics of near-threshold collisions. (3) Examination of the discrepancies between existing theoretical and experimental cross sections for low-energy excitations.