The library does not normally purchase "public performance rights" to films and documentaries, but instead purchases materials that are licenced for "home use" or educational use. The TEACH Act allows faculty to use these materials in the classroom and in mediated instruction, in person or on-line where only students registered for the class can view the material.
If you have a film showing that is open to the public, whether or not you charge a fee, it is considered a public performance and you must receive special permission from the copyright holder. There is usually a licensing fee and possibly royalties involved.