Geometry Optimization: A Comparison of Different Open-Source Geometry Optimizers

Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open-source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and energy calculations. The findings demonstrate how the choice of the coordinate system influences the optimization process to reach an equilibrium structure. With fewer steps, internal coordinates outperform Cartesian coordinates, while the choice of the initial Hessian and Hessian update method in quasi-Newton approaches made by different optimization algorithms also contributes to the rate of convergence. Furthermore, an available open-source machine learning method based on Gaussian process regression (GPR) was evaluated for energy minimizations over surrogate potential energy surfaces with both Cartesian and internal coordinates with internal coordinates outperforming Cartesian. Overall, geomeTRIC and DL-FIND with their default optimization method as well as with the GPR-based model using Hartree-Fock theory with the 6-31G** basis set needed a comparable number of geometry optimization steps to the approach of Baker using a unit matrix as the initial Hessian to reach the optimized geometry. On the other hand, the Berny and Sella offerings in ASE outperformed the other algorithms. Based on this, we recommend using the file-based approaches, ASE/Berny and ASE/Sella, for large-scale optimization efforts, while if using a single executable is preferable, we now distribute QUICK integrated with DL-FIND.