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.