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The high-pressure properties of fluorine and chlorine are not yet wellunderstood because both are highly reactive and volatile elements, which hasmade conducting diamond anvil cell and x-ray diffraction experiments achallenge. Here we use ab initio methods to search for stable crystalstructures of both elements at megabar pressures. We demonstrate how symmetryand geometric constraints can be combined to efficiently generate crystalstructures that are composed of diatomic molecules. Our algorithm extends thesymmetry driven structure search method [Phys. Rev. B 98 (2018) 174107] byadding constraints for the bond length and the number of atoms in a molecule,while still maintaining generality. As a method of validation, we have testedour approach for dense hydrogen and reproduced the known molecular structuresof Cmca-12 and Cmca-4. We apply our algorithm to study chlorine and fluorine inthe pressure range from 10--4000 GPa while considering crystal structures withup to 40 atoms per unit cell. We predict chlorine to follow the same series ofphase transformations as elemental iodine from Cmca to Immm to Fm$\bar{3}$m,but at substantially higher pressures. We predict fluorine to transition from aC2/c to an Cmca structure at 70 GPa, to a novel orthorhombic and metallicstructure with P$4_2$/mmc symmetry at 2500 GPa, and finally into its cubicanalogue form with Pm$\bar{3}$n symmetry at 3000 GPa.

Prediction of Chlorine and Fluorine Crystal Structures at High Pressure Using Symmetry Driven Structure Search with Geometric Constraints