It was shown previously (J. Am. Chem. Soc. 2014, 136, 10846) that bubbling of O2 into a solution of FeII(BDPP) (H2BDPP = 2,6-bis[[(S)-2-(diphenylhydroxymethyl)-1-pyrrolidinyl]methyl]pyridine) in tetrahydrofuran at -80 °C generates a high-spin (SFe = 5/2) iron(III) superoxo adduct, 1. Mössbauer studies revealed that 1 is an exchange-coupled system, Ĥex=JŜFe·ŜR, where SR = 1/2 is the spin of the superoxo radical, of which the spectra were not well enough resolved to determine whether the coupling was ferromagnetic (S = 3 ground state) or antiferromagnetic (S = 2). The glass-forming 2-methyltetrahydrofuran solvent yields highly resolved Mössbauer spectra from which the following data have been extracted: (i) the ground state of 1 has S = 3 (J < 0); (ii) |J| > 15 cm-1; (iii) the zero-field-splitting parameters are D = -1.1 cm-1 and E/D = 0.02; (iv) the major component of the electric-field-gradient tensor is tilted ≈7° relative to the easy axis of magnetization determined by the MS = ±3 and ±2 doublets. The excited-state MS = ±2 doublet yields a narrow parallel-mode electron paramagnetic resonance signal at g = 8.03, which was used to probe the magnetic hyperfine splitting of 17O-enriched O2. A theoretical model that considers spin-dependent electron transfer for the cases where the doubly occupied π∗ orbital of the superoxo ligand is either "in" or "out" of the plane defined by the bent Fe-OO moiety correctly predicts that 1 has an S = 3 ground state, in contrast to the density functional theory calculations for 1, which give a ground state with both the wrong spin and orbital configuration. This failure has been traced to a basis set superposition error in the interactions between the superoxo moiety and the adjacent five-membered rings of the BDPP ligand and signals a fundamental problem in the quantum chemistry of O2 activation.