Recently, we reported the spectrum of Ar-D4HO2+ [McCunn; et, al. J. Phys. Chem. B 2008, 112, 321], and here, we extend that work to include the Ar center dot H4DO2+ isotopologue in order to explore why the Ar atom has a much greater propensity for attachment to a dangling OD group than it does for OH, even when many more of the latter binding sites are available. Calculated (MP2/6-311+G(d,p) level of theory/basis) harmonic frequencies reproduce the observed multiplet patterns of OH and OD stretches and confirm the presence of various isomers arising from the different Ar binding sites. The preferential bonding of Ar to OD is traced to changes in the frequencies of the wag and rock modes of the H5O2+ moiety rather than to shifts in the oscillator that directly binds the Ar atom.