these molecules is approximately the same as molecules with no linear bending angles, suggesting our algorithm's approach of replacing linear bending angles with improper dihedrals is highly efficient. Only four of the molecules in this test set (0.8 %, black) required the addition of a dummy atom in their initial geometry. There is not enough information available in this benchmark set to indicate how optimization performance is affected by the addition of dummy atoms, but the four molecules with dummy atoms in this test set are not outliers. The remaining molecules (8.0 %, red) acquired a linear bending angle partway through optimization, and therefore required the internal coordinate system to be reconstructed from scratch. When our algorithm discards and reconstructs the internal coordinate system, the Hessian matrix must also be rediagonalized. This results in an increase in the total number of gradient evaluations required to reach convergence on average for these systems, which can be observed in figure , though these points do not appear to be outliers.