The electronic and geometrical structures of the Fe(n), Fe(n)(–), and Fe(n)(+) series (n = 7–20) are studied using all-electron density functional theory with the generalized gradient approximation. Equilibria of the geometrical configurations of the lowest total energy states in all three series are found to be similar except for Fe(9)(–), Fe(9)(+), Fe(10)(–), Fe(10)(+), Fe(15)(–), and Fe(19)(+). Our computed ionization energies of the neutrals, vertical electron detachment energies, and energies of Fe atom abstraction are in good agreement with experiment. It is found that the one-electron model corresponding to the change in the total magnetic moment of ±1.0μ(B) due to either attachment or detachment of an electron is valid in most cases. The exceptions are Fe(4)(+), Fe(10)(–), Fe(10)(+), Fe(12)(–), Fe(13)(+), and Fe(14)(+), where the change in the total magnetic moment is +3μ(B) (Fe(10)(–) and Fe(12)(–)), −3μ(B) (Fe(4)(+), Fe(11)(+), and Fe(14)(+)), and −9μ(B) (Fe(13)(+)). The reason for an anomalously large quenching of the total spin magnetic moment in Fe(13)(+) is explained. Our computed total spin magnetic moments per atom match the recent experimental values within the experimental uncertainty bars.