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We investigate bond-rearrangement driven by photo-double-ionization (PDI) near and above the double-ionization threshold in a sequence of carbon-carbon double-bonded hydrocarbon molecules: ethylene, fluoroethylene, and 1,1-difluoroethylene. We employ the kinematically complete cold target recoil ion momentum spectroscopy method to resolve all photo-double-ionization events leading to two-ion fragments. We observe changes in the branching ratios of different dissociative ionization channels depending on the presence of no, one, or two fluorine atoms. The role of the fluorine atom in the bond-rearrangement channels is intriguing, as evident by the reordering of the threshold energies of the PDI in the fluorinated molecules. These effects offer a compelling argument that the electronegativity of the fluorine (or the polarity of the molecule) strongly influences the potential energy surfaces of the molecules and drives bond rearrangement during the dissociation process. The energy sharing and the relative angle between the three-dimensional momentum vectors of the two electrons enable us to distinguish between knockout and other ionization mechanisms of the PDI processes.

We investigate the dissociation of H_{2}^{+} into a proton and a H^{0} after single ionization with photons of an energy close to the threshold. We find that the p^{+} and the H^{0} do not emerge symmetrically in the case of the H_{2}^{+} dissociating along the 1sσ_{g} ground state. Instead, a preference for the ejection of the p^{+} in the direction of the escaping photoelectron can be observed. This symmetry breaking is strongest for very small electron energies. Our experiment is consistent with a recent prediction by Serov and Kheifets [Phys. Rev. A 89, 031402 (2014)]. In their model, which treats the photoelectron classically, the symmetry breaking is induced by the retroaction of the long-range Coulomb potential onto the dissociating H_{2}^{+}.