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The possible formation of the (AlF₄(HF)_n)⁻ (n = 1–8 and 12), (AsF₆(HF)_n)⁻, and (SbF₆(HF)_n)⁻ (n = 1–6 and 12) anionic clusters of a superhalogen nature is predicted in the solutions of binary HF/AlF₃, HF/AsF₅, and HF/SbF₅ Lewis–Brønsted superacids on the basis of ab initio calculations. Our results show that all systems investigated represent extremely strongly bound anions characterized by vertical electron detachment energies (VDEs) that significantly exceed 10 eV. The VDE values estimated for the (AlF₄(HF)₁₂)⁻, (AsF₆(HF)₁₂)⁻, and (SbF₆(HF)₁₂)⁻ systems are predicted to be 13.96, 14.03, and 14.03 eV, respectively, and are the largest vertical electron detachment energies reported in the literature thus far.