I can describe the effect on ozone. Perhaps others know of additional examples? See below...
One effect that is well understood is the effect on ozone.
The reaction follows a mechanism like this:
All told, it "costs" two ozone molecules for each photon of UV radiation that will not reach the ground.
Also, high-energy gamma radiation reaches the atmosphere continually, but I am not aware of specific effects on the make-up of the atmosphere that results from this.