Density functional theory calculations have been performed on the various proton-bound rare-gas dimers Rg(2)H(+) and (RgHRg＇)(+) (Rg=Ar, Kr, or Xe, and Rg not equal Rg＇) employing the BP86 method coupled with either a Gaussian split valence basis set (DZVP) or a numerical split valence basis set (DN**). The calculations with the DN** basis represent the first calculations in which correct qualitative agreement is obtained with respect to the trend in experimental data for the antisymmetric stretching wavenumbers of the three Rg(2)H(+) cations. Good qualitative agreement is also obtained for the antisymmetric stretching wavenumber of the mixed-rare-gas species (ArHKr)(+). For the xenon-containing mixed-rare-gas cations, the agreement with experimental wavenumbers is not good as is the case for the DZVP basis set with any of the aforementioned cations. This is believed to be due to the inability of these basis sets to predict some physical and chemical properties for these species. Quantitative agreement between theory and experiment with respect to the antisymmetric stretch of the Rg(2)H(+) cations is improved when four radial argon atoms are placed at a fixed distance from the central H, intended to mimic the matrix environment. Based on these calculations, an inverse hydrogen-isotope dependence for the dissociation energy of these species is predicted. No center atom isotope dependence is predicted for the symmetric stretching vibration. Employing a polyatomic model, we have reanalyzed previously published combination band data for Xe2H+ and Xe2D+, and concluded that there is no evidence for an inverse isotope dependence for the symmetric stretching vibrations of these species.