The electronic structure of the XO and XO⁺ (X = I, At) species, as well that of a AtO⁺-H₂O complex have been investigated using relativistic wave-function theory and density functional theory (DFT)-based approximations (DFAs). The n-electron valence state perturbation method with the perturbative inclusion of spin–orbit coupling including spin-orbit polarization effects (SO-NEVPT2) was shown to yield transition energies within 0.1 eV of the reference four-component intermediate Fock-space coupled cluster (DC-IHFSCCSD) method at a significantly lower computational cost and can therefore be used as a benchmark to more approximate approaches in the case of larger molecular systems. These wavefunction calculations indicate that the ground state for the AtO⁺ and AtO⁺-H₂O systems is the Ω = 0⁺ component of the ³Σ^- LS state, which is quite well separated (by ≅ 0.5 eV) from the Ω = 1 components of the same state and from the Ω = 2 state related to the ¹Δ LS state (by ≅1 eV). Time-dependent DFT calculations, on the other hand, place the Ω = 1 below the Ω = 0⁺ component with the spurious stabilization of the former increasing as one increases the amount of Hartree–Fock exchange in the DFAs, while those employing the Tamm–Dancoff approximation and DFAs not including Hartree–Fock exchange yield transition energies in good agreement with SO-NEVPT2 or DC-IHFSCCSD for the lower-lying states. These results indicate the ingredients necessary for devising a DFA-based computational protocol applicable to the study of the properties of large AtO⁺ clusters so that it may (at least) qualitatively reproduce reliable reference (SO-NEVPT2) calculations.