where x i and x j are the Cartesian position of atoms i and j, σ is a scalar parameter which in Sella defaults to 1.25, and r cov i and r cov j are the covalent radii of atoms i and j. After all pairs of atoms have been checked, a flood fill algorithm is used to count the number of disconnected fragments in the molecular graph. This algorithm works by walking along the graph and noting which atoms belong to the same fragment, then counting the number of distinct fragments. If only a single fragment is found, the algorithm exits; otherwise, σ is increased by 5 % and the above procedure is repeated with the additional rule that only pairs of atoms in different molecular fragments are checked for connectivity. This additional rule helps ensure that geometries with large separation between clusters of atoms do not become densely connected. This procedure For systems composed of independent molecules, it may not be chemically meaningful to consider internal coordinates that connect two molecules together. However, the previously described procedure will necessarily add bonds, angles, and dihedrals that span across molecules. This can have a negative impact on performance, as the optimizer will limit the extent to which these chemically irrelevant coordinates can change at each step. To resolve this problem, we also implement as an alternative the translational and rotation internal coordinates (TRIC) method of Wang and Song. When using the TRIC method, our algorithm will stop adding bonds between atoms after a single iteration of the procedure described above. Each disconnected fragment of the molecular graph is then augmented with translational coordinates of the fragment barycenter and rotational coordinates following the TRIC procedure.