Geometrical and electronic structures of the neutral and singly negatively charged Fe6 On and Fe7 Om clusters in the range of 1 ≤ n ≤ 20 and 1 ≤ m ≤ 24, respectively, are computed using density functional theory with the generalized gradient approximation. The largest clusters in the two series, Fe6 O20 and Fe7 O24 , can be described as Fe(FeO4 )5 and Fe(FeO4 )6 or alternatively as [FeO5 ](FeO3 )5 and [FeO6 ](FeO3 )6 , respectively. The Fe6 O20 and Fe7 O24 clusters possess adiabatic electron affinities (EAad ) of 5.64 eV and 5.80 eV and can be attributed to the class of hyperhalogens since FeO4 is an unique closed-shell superhalogen with the EAad of 3.9 eV. The spin character of the lowest total energy states in both series changes from ferromagnetic to ferrimagnetic or antiferromagnetic when the first FeOFe bridge is formed. Oxidation decreases substantially the polarizability per atom of the initial bare clusters; namely, from 5.98 Å(3) of Fe6 to 2.47 Å(3) of Fe6 O20 and from 5.67 Å(3) of Fe7 to 2.38 Å(3) of Fe7 O24 . The results of our computations pertaining to the binding energies of O, Fe, O2 , and FeO in the Fe7 Om series provide an explanation for the experimentally observed abundance of the iron oxide nanoparticles with stoichiometric compositions. © 2016 Wiley Periodicals, Inc.