Machine-Learned Leftmost Hessian Eigenvectors for Robust Transition State Finding

Area of Science:

• Computational Chemistry
• Chemical Reaction Discovery
• Machine Learning Applications

Background:

• Accurate transition state (TS) determination is crucial for understanding chemical reactions.
• Second-order information (Hessians) improves TS optimization but is computationally expensive.
• Current methods face challenges with convergence and computational cost.

Purpose of the Study:

• To develop a computationally efficient machine-learning (ML) driven TS optimizer.
• To directly predict the leftmost Hessian eigenvector (LMHE) for TS approximation.
• To achieve second-order accuracy at first-order computational cost.

Main Methods:

• Developed an ML model to predict the LMHE, approximating the TS reaction coordinate.
• Integrated LMHE prediction into an iterative TS optimization workflow.
• Implemented uncertainty quantification for fallback to full-Hessian updates when LMHE prediction fails.

Main Results:

• The ML-driven optimizer achieves TS recovery rates comparable to full-Hessian methods.
• Robust performance from degraded initial geometries, reducing wall times.
• Lower total gradient evaluations compared to standard quasi-Newton methods.
• Uncertainty quantification prevents costly active learning cycles.

Conclusions:

• The proposed method offers a highly efficient engine for high-throughput reaction discovery.
• Delivers second-order stability with first-order computational expense.
• Enables reliable TS determination for broader chemical research applications.