Carbon based filters provide important safety barriers that remove volatile fission products from gas streams. The capacity and efficiency of a filter to trap fission products depends upon the strength of the interaction between the fission products and the filter material. In this study, we apply density functional theory together with a dispersion correction (DFT + D) to predict structures and energies of volatile fission product atoms and molecules trapped by buckminsterfullerene (C60). Endohedral encapsulation energies and exohedral association energies show that Rb and Cs are strongly trapped as ions, each transferring approximately one electron to C60. Kr and Xe are weakly trapped atoms with Xe showing a preference for exohedral association and Kr for endohedral encapsulation. Br, I and Te, while strongly trapped from atoms (and assuming charge from C60) are thermodynamically more stable as neutral covalently bonded Br2, I2 and Te2 molecules weakly trapped through van der Waals forces, exohedrally. Heteronuclear CsBr and CsI were also considered. Both molecules were non-bonded to C60 with similar association energies to those exhibited by Br2, I2 and Te2.