To measure the relative performance of our algorithm, we have optimized the set of 500 molecules using four alternative algorithms. The relative performance is summarized in figure , which plots the number of effective gradient evaluations for the alternative algorithms against our algorithm as implemented in Sella with its default parameters. Figure compares the performance of our algorithm using Sella's default parameters versus Sella with full calculation of the Hessian matrix, which is achieved by setting the convergence criterion for the iterative diagonalization routine to be extremely tight. The majority of the structures require more gradient evaluations to converge when the Hessian matrix is calculated in full as compared to the partial diagonalization that is performed using Sella's default parameters. Notably, the red data points, which represent structures for which the internal coordinate system is reconstructed midway through optimization, experience a more significant increase in the number of gradient evaluations compared to other structures. This is to be expected, as the Hessian will be evaluated in full at least twice throughout the course of the optimization. For the data points which lie below the line, full diagonalization actually results in an overall reduction in the number of gradient evaluations required to reach convergence. It is likely that for these structures, the initial Hessian diagonalization failed to fully converge the true leftmost eigenvector of the Hessian matrix. This would The color scheme is identical to that of figure 5. For Sella, the effective number of gradient evaluations is the number of geometry optimization steps plus the number of Hessian diagonalization iterations, while for NWChem, Q-Chem, and Psi4 it is the number of geometry optimization steps plus a factor of 3n to account for analytical evaluation of the full Hessian.