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

Nonadiabatic couplings (NACs) play a crucial role in modeling photochemical and photophysical processes with methods such as the widely used fewest-switches surface hopping (FSSH). There is, therefore, a strong incentive to machine learn NACs for accelerating simulations. However, this is challenging due to NACs' vectorial, double-valued character and the singularity near a conical intersection seam. For the first time, we design NAC-specific descriptors based on our domain expertise and show that they allow learning NACs with never-before-reported accuracy of R² exceeding 0.99. The key to success is also our new ML phase-correction procedure. We demonstrate the efficiency and robustness of our approach on a prototypical example of fully ML-driven FSSH simulations of fulvene targeting the SA-2-CASSCF(6,6) electronic structure level. This ML-FSSH dynamics leads to an accurate description of S₁ decay while reducing error bars by allowing the execution of a large ensemble of trajectories. Our approach is generalizable to more states as we demonstrate for a three-state ML-FSSH simulation of methylenimmonium cation. Our implementations are available in open-source MLatom.