Restricted-Variance Molecular Geometry Optimization Based on Gradient-Enhanced Kriging.

Area of Science:

• Computational Chemistry
• Machine Learning
• Quantum Chemistry

Background:

• Molecular geometry optimization is crucial for understanding chemical properties.
• Conventional methods often require extensive data or computational resources.
• Gradient-enhanced Kriging (GEK) offers a data-efficient machine learning alternative.

Purpose of the Study:

• To adapt GEK for efficient molecular geometry optimization with limited data.
• To leverage GEK's surrogate modeling capabilities for robust potential energy surface exploration.
• To integrate GEK's expected error for variance-restricted optimizations.

Main Methods:

• Utilized GEK for molecular geometry optimization, mimicking conventional second-order methods.
• Employed GEK's expected error to guide restricted-variance optimizations.
• Reduced empirical parameters by relating Hessian eigenvalues to GEK characteristic lengths, trained on e-Baker and Baker-TS datasets.

Main Results:

• The GEK-based method robustly guides optimization to potential energy surface minima even with few data points.
• Performance was evaluated using e-Baker, Baker-TS, and S22 test suites at DFT and MP2 levels.
• The new method demonstrated comparable or superior performance to state-of-the-art conventional techniques.

Conclusions:

• GEK provides a flexible and efficient machine learning approach for molecular geometry optimization.
• The developed procedure effectively handles limited data scenarios, outperforming traditional methods in some cases.
• This work highlights the potential of machine learning for accelerating computational chemistry tasks.