Potential energy curves for the broken-symmetry states of the edge-shared bimetallic systems, M2Cl104- (M = Cr, Mo, W), are analyzed using approximate density functional theory. The potential energy curves are made up of distinct sections, depending on which subsets of metal-based electrons are localized or delocalized. Starting from the fully delocalized limit, the metal-based electrons localize in the order delta before pi before sigma as the metal-metal separation is progressively increased. As a result there are four distinct regions of the potential energy curve, corresponding to (a) sigma + pi + delta delocalized; (b) sigma + pi delocalized, delta localized; (c) sigma delocalized, pi + delta localized; and (d) sigma + pi + delta localized. Localization of the delta subset of electrons is particularly facile, because interactions with the bridging ligands destabilize the delta orbital relative to delta*. As a result, at metal-metal separations greater than approximately 2.30 Angstrom, delocalization of the delta electrons would result in formation of a M-M antibond rather than a bond. For Cr2Cl104-, the fully localized region of the curve lies much lower than the others, but for the molybdenum and tungsten congeners, all four regions lie within 1.0 eV of each other, giving rise to complex and relatively flat potential energy curves. The decahalides of the chromium triad therefore exhibit the well-established trend toward greater delocalization in complexes of the heavier transition metals. This trend is, however, found to be far less prominent than in the face-shared analogues, M2Cl93-, and the difference between the two structural types is traced to the inability of the edge-shared bridge to support the short metal-metal separations necessary for complete electron delocalization.