A descriptor is all you need: accurate machine learning of nonadiabatic coupling vectors

particularly in Tully’s fewest-switches surface hopping (FSSH). They dictate how molecules jump between electronic states during light-driven processes—key for understanding everything from vision to solar energy conversion. Traditionally, simulating these transitions requires Tully’s fewest-switches surface hopping (FSSH), a powerful but computationally intensive method. Running FSSH trajectories demands hundreds of thousands of expensive quantum chemical calculations, severely limiting the size of molecules and the number of trajectories we can study. Machine learning (ML) promises to change this—but predicting NACs is far from straightforward. Unlike energies or forces, NACs are vectorial, double-valued, and can spike near conical intersections (CIs), where two electronic states cross. Additionally, the arbitrary phase of quantum wave functions can flip NAC vectors, introducing inconsistencies that derail ML training.

Scatterplots showing the DFT dipole moment (left) and polarizability components (right) of the test set consisting of 1200 points with respect to ML predictions of the models trained on 1000 points. The dipole moment components were learned with the Matérn kernel, while for polarizability, the Gaussian kernel performed better. In both cases, the RExyzCl descriptor was used.

For more information, check out the paper: (Martinka et al., 2025).

References

2025