Molecules HRgF (Rg = Ar, Kr, Xe, Rn) were studied at levels of theory that included electron correlation, taking relativistic effects into account either by using the recently developed parametrization of the extended model core potentials and basis sets or by using the Douglas-Kroll method with all-electron basis sets. Charge distributions were calculated according to Mulliken, Lowdin, and natural bond orbital methods of population analysis and the results of these methods were compared, confirming that bonding in these molecules corresponds to interaction between the fluoride anion and the RgH(+) moiety In contrast to previously reported results, the present calculations show that the radon compound, HRnF, is more stable than compounds of the lighter congeners Trends in the first ionization energies, bond lengths, energies of formation and decomposition, and harmonic vibrational frequencies were discussed and found to be consistent with the periodic trends of the atomic properties of the rare gas atoms.