Redundant internal coordinate systems increase the complexity of the optimization problem, as the coordinate system is by construction of a higher dimensionality than the space of all possible molecular configurations. We have described these problems and the methods we developed and implemented in Sella to ameliorate them in a previous work. Our algorithm constructs a complete set of internal coordinates by mapping all possible pairs, triplets, and quadruplets of sequentially-bonded atoms from a molecular graph to bond distance, bending angle, and dihedral angle coordinates, respectively. This procedure is described in detail in appendix A.