We report vibrational spectra of the cryogenically cooled H₉O₄⁺ cation along with those of the D₂ tagged HD₈O₄⁺ isotopomers using two variations on a two-color, IR-IR double-resonance photoexcitation scheme. The spectrum of the isolated H₉O₄⁺ ion consists of two sharp features in the OH stretching region that indicate exclusive formation of the "Eigen" cation, the H₃O⁺·(H₂O)₃ isomer that corresponds to the filled hydration shell around the hydronium ion. Consistent with this structural assignment, the spectrum of the HD₈O₄⁺ isotopologue is resolved into contributions from two isotopomers: one with the single OH group on one of the three solvent water molecules and another in which it resides on the hydronium core ion. The latter spectrum is dominated by a broad feature assigned to the isolated hydronium OH stretching fundamental with an envelope that is similar to that displayed by the H₃O⁺·(H₂O)₃ isotopologue. The feature appears with a diffuse band ∼380 cm^-1 above it, which is assigned to a combination band involving the hydronium OH stretching vibration and the frustrated translation mode of the HD₂O⁺ core and one of the solvating water molecules. These trends are analyzed with anharmonic calculations involving four-mode coupling on a realistic potential surface and interpreted in the context of vibrationally adiabatic potentials based on insights acquired from analysis of the ground state probability amplitudes obtained from diffusion Monte Carlo calculations.

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