Single determinant Moller-Plesset perturbation (MP) theory at second order (MP2), third order (MP3), and fourth order (MP4) with standard basis sets ranging from cc-pVDZ to cc-pVQZ quality predicts the equilibrium geometry of FOOF qualitatively incorrect. Sixth-order MP (MP6), CCSD(T), and DFT lead to a qualitatively correct FOOF equilibrium geometry r(e), provided a sufficiently large basis set is used; however, even these methods do not succeed in reproducing an exact r(e) geometry. The latter can be achieved only by artificially increasing anomeric delocalization of electron lone pairs at the O atoms into the o*(OF) orbitals by selectively adding diffuse basis functions, adjusting exponents of polarization functions, or enforcing an increase of electron pair correlation effects via the choice of a rigid basis set. DFT geometries of FOOF can be improved in a similar way and, then, DFT presents the best cost-efficiency compromise currently available for describing FOOF and related molecules. DFT and CCSD(T) calculations reveal that FOOF can undergo either rotation at the OO bond or dissociation into FOO and F because the corresponding barriers (trans barrier: 19.4 kcal/mol; dissociation barrier 19.5 kcal/mol) are comparable. Previous estimates as to the height of the rotational barriers of FOOF are largely exaggerated. Rotation at the OO bond raises the barrier to dissociation because the anomeric effect is switched off. The molecular dipole moment is found to be a sensitive antenna for probing the quality of the quantum chemical description of FOOF.