Machine Learning Seams of Conical Intersection: A Characteristic Polynomial Approach

20 June 2023, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


The machine learning of potential energy surfaces (PESs) has undergone rapid progress in recent years. The vast majority of this work, however, has been focused on the learning of ground state PESs. To reliably extend machine learning protocols to excited state PESs, the occurrence of seams of conical intersections between adiabatic electronic states must be correctly accounted for. This introduces a serious problem, for at such points the adiabatic potentials are not differentiable to any order, complicating the application of standard machine learning methods. We show that this issue may be overcome by instead learning the coordinate-dependent coefficients of the characteristic polynomial of a simple decomposition of the potential matrix. We demonstrate that, through this approach, quantitatively accurate machine learning models of seams of conical intersection may be constructed.


Conical Intersection
Machine Learning
Characteristic Polynomial
excited state
potential energy surface

Supplementary materials

Supplementary Information for Machine Learning Seams of Conical Intersection: A Characteristic Polynomial Approach
Additional information on the generation of the training sets, KRR hyperparameter op- timization, choice of kernel, proof of Equation 5, and the ability of the ω-CP models to extrapolate.


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