Geometry Optimization in Internal Coordinates Based on Gaussian Process Regression: Comparison of Two Approaches.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Molecular Modeling

Background:

• Geometry optimization is crucial for determining molecular structures.
• Gaussian process regression (GPR) offers a data-efficient approach to modeling potential energy surfaces.
• Existing GPR methods for optimization often rely on Cartesian coordinates, which can be computationally intensive.

Purpose of the Study:

• To extend Gaussian process regression (GPR) based geometry optimization to internal coordinates.
• To compare the efficiency and robustness of GPR using internal coordinates versus Cartesian coordinates.
• To investigate the impact of different methods for incorporating internal coordinates into GPR models.

Main Methods:

• Developed GPR models trained on geometries in internal coordinates (distances, angles).
• Implemented two approaches: predicting gradients in Cartesian coordinates and predicting gradients in internal coordinates.
• Tested the methods on 30 small molecules and a Rh complex from a catalytic mechanism study.

Main Results:

• Both internal coordinate methods reduced the number of optimization steps compared to Cartesian GPR and L-BFGS.
• The method predicting Cartesian gradients showed slightly higher efficiency.
• The method predicting internal gradients demonstrated somewhat greater robustness.
• Automatically adjusted hyperparameters proved advantageous for optimization.

Conclusions:

• Geometry optimization using GPR in internal coordinates is a viable and effective approach.
• Internal coordinate GPR offers significant advantages in reducing computational cost for molecular structure determination.
• The choice between predicting Cartesian or internal gradients depends on the desired balance between efficiency and robustness.