Machine Learning Seams of Conical Intersection: A Characteristic Polynomial Approach.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Machine Learning

Background:

• Machine learning (ML) has advanced rapidly for ground-state potential energy surfaces (PESs).
• Extending ML to excited-state PESs requires accurately handling conical intersections.
• Adiabatic potentials are non-differentiable at conical intersections, hindering standard ML approaches.

Purpose of the Study:

• To develop a robust ML method for excited-state PESs.
• To overcome challenges posed by non-differentiable points at conical intersections.
• To enable accurate modeling of seams of conical intersections.

Main Methods:

• Learning coordinate-dependent coefficients of the characteristic polynomial.
• Utilizing a specific decomposition of the potential matrix.
• Applying ML to model seams of conical intersections.

Main Results:

• A novel approach to learning excited-state PESs was demonstrated.
• The method successfully models coordinate-dependent coefficients.
• Quantitative accuracy in ML models of conical intersection seams was achieved.

Conclusions:

• The proposed method effectively overcomes the non-differentiability issue at conical intersections.
• This approach enables reliable ML modeling of excited-state PESs.
• Accurate machine learning models for seams of conical intersections are now feasible.