Needless (Anime) (2009)
Plot Summary: In the near future, mankind has suffered from a Third World War, leaving extreme damage all over and forced mankind to become even more distinct from their species. The world was at chaos and from this chaos comes a new species: “Needless”. The Needless are humans who have contracted a “disease” as humans may call them, and allow them to wield extraordinary powers far superior to any mankind. Their abilities include telekinesis, elemental powers, gravity control, adaptation, radioactive release, and all manners of scientific impossibility.
A very short animation was done which covered the St. Rose Academy Arc, but was treated more like an Omake of sorts. It was called "The secret of St. Rose Academy" or "The secret of St. Lilly Academy" in the Dubbed version. It can be found easily in Youtube.