The atoms in molecules theory has been applied to analyze bonding properties in potentially hypervalent structures with chalcogen (O, S, or Se)-chalcogen (O or S) bonds. The topological analyses [based upon the electron charge density rho(r), its Laplacian del(2)rho(r), bond ellipticity, and local energy density Ed(r)] and the charges clearly displayed the dependence of the bonding properties with the central atom: (a) When the central atom is oxygen, the main electron charge concentration remains in the surroundings of the central atom, yielding a very weak coordinate bond. (b) Bonding to the central sulfur and selenium atoms is consistent with a model of a highly polarized sigma-bond, its strength depending mainly on electrostatic interactions, so no evidence was found for double bonding, which has so far been the conventional way to describe the interaction in these systems. The equilibrium geometries were optimized by both density functional theory with a hybrid functional (B3LYP) and ab initio methods at the MP2(full) level? using the 6-311+G* basis set.