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We report electronic, vibrational, and magnetic properties, together with their structural dependences, for the metal-organic framework Fe2(dobdc) (dobdc4- = 2,5-dioxido-1,4-benzenedicarboxylate) and its derivatives, Fe2(O)2(dobdc) and Fe2(OH)2(dobdc)-species arising in the previously proposed mechanism for the oxidation of ethane to ethanol using N2O as an oxidant. Magnetic susceptibility measurements reported for Fe2(dobdc) in an earlier study and reported in the current study for FeII0.26[FeIII(OH)]1.74(dobdc)(DMF)0.15(THF)0.22, which is more simply referred to as Fe2(OH)2(dobdc), were used to confirm the computational results. Theory was also compared to experiment for infrared spectra and powder X-ray diffraction structures. Structural and magnetic properties were computed by using Kohn-Sham density functional theory both with periodic boundary conditions and with cluster models. In addition, we studied the effects of different treatments of the exchange interactions on the magnetic coupling parameters by comparing several approaches to the exchange-correlation functional: generalized gradient approximation (GGA), GGA with empirical Coulomb and exchange integrals for 3d electrons (GGA+U), nonseparable gradient approximation (NGA) with empirical Coulomb and exchange integrals for 3d electrons (NGA+U), hybrid GGA, meta-GGA, and hybrid meta-GGA. We found the coupling between the metal centers along a chain to be ferromagnetic in the case of Fe2(dobdc) and antiferromagnetic in the cases of Fe2(O)2(dobdc) and Fe2(OH)2(dobdc). The shift in magnetic coupling behavior correlates with the changing electronic structure of the framework, which derives from both structural and electronic changes that occur upon metal oxidation and addition of the charge-balancing oxo and hydroxo ligands.