Scanning tunneling microscopy (STM) is used to study two dinuclear organometallic molecules, meta-Fe2 and para-Fe2, which have identical molecular formulas but differ in the geometry in which the metal centers are linked through a central phenyl ring. Both molecules show symmetric electron density when imaged with STM under ultrahigh-vacuum conditions at 77 K. Chemical oxidation of these molecules results in mixed-valence species, and STM images of mixed-valence meta-Fe2 show pronounced asymmetry in electronic state density, despite the structural symmetry of the molecule. In contrast, images of mixed-valence para-Fe2 show that the electronic state density remains symmetric. Images are compared to constrained density functional (CDFT) calculations and are consistent with full localization of charge for meta-Fe2 on to a single metal center, as compared with charge delocalization over both metal centers for para-Fe2. The conclusion is that electronic coupling between the two metal centers occurs through the bonds of the organic linker, and through-space coupling is less important. In addition, the observation that mixed-valence para-Fe2 is delocalized shows that electron localization in meta-Fe2 is not determined by interactions with the Au(111) substrate or the position of neighboring solvent molecules or counterion species.