Second-order vibrational perturbation theory (VPT2) provides an effective tool for obtaining anharmonic corrections to harmonic frequencies and intensities. With VPT2, we gain insights into the vibrational motions that are responsible for the peaks observed in the experimental spectrum. This is especially valuable for systems that contain hydrogen bonds. In this work, we examine the vibrational spectra of the [Py\(^+\)-(CH\(_2\))\(_n\)-COOD]\(_2\)[NTf\(_{2}^{-}\)] (n=1-9) ternary complexes, which contain a double hydrogen bond between the carboxylic acid groups in the cations. At n=1 a single peak is present in the OD stretching region of the spectrum, while for larger alkyl chain lengths (n=2-9), there are three peaks present in this region. Using VPT2 based on electronic structure calculations performed at the B3LYP/6-31+G** level of theory/basis set, we explore the changes in the hydrogen-bonding environment with increasing alkyl chain length, and how these changes affect the calculated spectra. We also explore the effects of the choice of resonance space used in the VPT2 calculation on the calculated spectrum. We find that the inclusion of 2:1 Fermi resonances between the OD stretch and the overtone in the OD bend is essential for obtaining agreement between the calculated and measured spectrum. We also find that as the chain length increases the OD stretching frequency decreases until it is lower in energy than the overtone in the OD bend, reflecting the increased hydrogen bond strength with increasing alkyl chain length.