Using the gradient-corrected BPW91 method and 6311++G(2d,2p) basis sets, it was found that adsorption of benzene by iron atoms forms a multiple-decker sandwich (MDS) geometry for the ground state (GS) of Fe-2-(C6H6)(3), as Fe-2 is broken. Though decoordination occurs, the ligands are bonded symmetrically to the Fe sites by eta(6) (for the two external rings) and two eta(3) (for the central ring) Fe-C coordinations; this big amount of Fe-C bonds enhances the stability of the MDS GS. This is unexpected, as the experiment suggests MDS for TMn-(C6H6)(m) species of earlier transition metals (TMs) and clusters covered with benzene, i.e., rice-ball (RB) structures, for late 3d atoms. However, preserving Fe-2, an RB state was found, quasi-degenerate with the GS, with a smaller amount of Fe-C contacts and a stronger Fe-2 bond. The MDS shows higher stability for electron attachment and deletion events, but its adiabatic electron affinity, 1.11 eV, differs more from the experiment (0.80 +/- 0.1 eV) than the one (0.97 eV) for RB. Thus, MDS and RB states can appear in a sample of Fe-2-(C6H6)(3). Like the electron affinity, the ionization energy of the complex is also smaller than those of the metal and benzene moieties, but closer to the former, signifying that the electron, delocalized through the 3d-pi bonds, is mainly deleted from the metallic units.