The argonium cation, ArH+, has been previously detected in nature for the first time. This cation is believed to form through the gas-phase reaction of Ar+ and H-2. In this work, quantum chemical techniques show that the reaction of Ar and H-3(+) may be a viable alternative or contributor to the creation of ArH+ corroborating previous analysis. In order to further evaluate this claim, highly accurate quartic force field computations are used to produce spectroscopic data and anharmonic vibrational frequencies for ArH3+ in its 18 isotopologues. NeH3+ is also analyzed but has a low Ne-H-3(+) dissociation barrier. Therefore, it less likely to be observed. Consequently, NeH+ is also unlikely to be formed from NeH3+ as it was also not from NeH2+.