Comprehensive simulations of the processing plasmas used in semiconductor fabrication will depend on the availability of basic data for many microscopic processes that occur in the plasma and at the surface. Cross sections for electron collisions, a principal mechanism for producing reactive species in these plasmas, are among the most important such data; however, electron-collision cross sections are difficult to measure, and the available data are, at best, sketchy for the polyatomic feed gases of interest. While computational approaches to obtaining such data are thus potentially of significant value, studies of electron collisions with polyatomic gases at relevant energies are numerically intensive. In this article, we report on the progress we have made in exploiting large-scale distributed-memory parallel computers, consisting of hundreds of interconnected microprocessors, to generate electron-collision cross sections for gases of interest in plasma simulations.