Figures , and 6d compare the performance of our algorithm that that of NWChem, Q-Chem, and Psi4 42 respectively. Each of these programs implements a saddle point optimization algorithm in a basis of internal coordinates that requires full evaluations of the Hessian matrix, either analytically or through finite difference. For these codes, the effective number of gradient evaluations is taken to be the number of geometry optimization steps plus a factor of 3n to account for evaluation of the Hessian matrix in full. We note that the cost of evaluating the Hessian matrix using analytical methods -such as coupled-perturbed Hartree-Fock or density functional perturbation theory -is generally lower than the cost of 3n gradient evaluations. However, when analytical Hessians are not available, the actual cost of evaluating the full Hessian matrix will be at least 3n, rising to 6n if central finite difference is used. Based on the result in figure , NWChem, Q-Chem, and Psi4 all show comparable performance to Sella when the Hessian is fully diagonalized. NWChem shows the overall worst performance, likely due to its use of a minimal Z-matrix internal coordinate basis rather than a redundant internal coordinate basis. Nonredundant internal coordinate systems such as the Zmatrix approach necessarily omit some chemically relevant degrees of freedom from the coordinate system, which can have a deleterious impact on optimization performance.