JPCL: A Descriptor Is All You Need: Accurate Machine Learning of Nonadiabatic Coupling Vectors

Just published in JPCL, an accurate approach for machine learning nonadiabatic coupling vectors! The story behind this work is very long, going back many years. When we were developing ML-driven FSSH, we noticed that learning NACs always has worse R^2 compared to learning energies. Talking with Mario, we have finally started to ask the right question: Is there any physics-informed descriptor for NACs? Is there any property that has a clear correlation with NAC magnitudes? The obvious answer was the energy gap, but it is not very descriptive (although it works to some extent, too). That’s how the energy gradient difference came into consideration.

That was not the end of the story, because although we found a good descriptor, ML-FSSH back then still did not work. The key was sampling of the small-gap region. That took a while to figure out how to do properly. Even then, we saw a major setback: we had very accurate ML models for NACs that worked brilliantly with CASSCF adiabatic energies and gradients, but not with ML surrogate potentials for CASSCF. Ironically, although NACs were believed to be more difficult to learn than potentials, we had an opposite situation: we had excellent models for NACs, but not for potentials.

Only after @Mikołaj Martyka managed to get working ML potentials that were accurate enough for ML-NACs, could we pick up this research direction again. Thanks to the interest of Jiri and Jakub in this topic, we could join forces to crack the problem. We had to re-implement the KRR in Julia (done by Yi-Fan) to make it seamlessly connected with MLatom’s Python scripts to speed up FSSH, essential for extensive testing.

The major bulk of the work fell on the shoulders of Jakub, who picked up on now-graduated Lina’s early explorations. Remarkably, to enable quick tests in Python, Jakub ended up implementing FSSH in MLatom, which is an achievement on its own! (On that, some day later). He did systematic tests of different descriptors and their combinations, developed fast protocols for phase-correction and fitting of NACs, and their use in fully ML-driven FSSH.

Kudos to Jakub and Lina for their great patience and care with many implementations and thousands of tests, ultimately making this work finally see its publication to tell the story! Congratulations on the great work!

Paper

Jakub Martinka, Lina Zhang, Yi-Fan Hou, Mikołaj Martyka, Jiří Pittner*, Mario Barbatti*, Pavlo O. Dral*. A Descriptor Is All You Need: Accurate Machine Learning of Nonadiabatic Coupling Vectors. J. Phys. Chem. Lett. 2025, 16, 11732–11744.
Preprint on ChemRxiv: https://doi.org/10.26434/chemrxiv-2025-wzkst (2025.05.29) | arXiv: https://arxiv.org/abs/2505.23344 (2025.05.29).

P.S. No LLM involved in writing the above post 😂