High-quality ab initio potential energy curves are presented for the F(-)-Rg series (Rg = He-Rn). Calculations are performed at the CCSD(T) level of theory, employing d-aug-cc-pV5Z quality basis sets, with "small core" relativistic effective core potentials being used for Kr-Rn. The quality of the curves is judged by agreement with recent high-level calculations in the case of F(-)-He and F(-)-Ne and by excellent agreement with mobility data for the systems F(-)-Rg (Rg = He-Xe). Except for these recent high-level calculations on the two lightest systems, we are able to deduce that all other previous potentials for the whole set of these systems are inadequate. We also present spectroscopic information for the titular species, derived from our potential energy curves.