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The high-pressure properties of fluorine and chlorine are not yet well understood because both are highly reactive and volatile elements, which has made conducting diamond anvil cell and x-ray diffraction experiments a challenge. Here we use ab initio methods to search for stable crystal structures of both elements at megabar pressures. We demonstrate how symmetry and geometric constraints can be combined to efficiently generate crystal structures that are composed of diatomic molecules. Our algorithm extends the symmetry driven structure search method [Phys. Rev. B 98 (2018) 174107] by adding constraints for the bond length and the number of atoms in a molecule, while still maintaining generality. As a method of validation, we have tested our approach for dense hydrogen and reproduced the known molecular structures of Cmca-12 and Cmca-4. We apply our algorithm to study chlorine and fluorine in the pressure range from 10--4000 GPa while considering crystal structures with up to 40 atoms per unit cell. We predict chlorine to follow the same series of phase transformations as elemental iodine from Cmca to Immm to Fm$\bar{3}$m, but at substantially higher pressures. We predict fluorine to transition from a C2/c to an Cmca structure at 70 GPa, to a novel orthorhombic and metallic structure with P$4_2$/mmc symmetry at 2500 GPa, and finally into its cubic analogue form with Pm$\bar{3}$n symmetry at 3000 GPa.