Cumulative Surface Hopping: Faster and More Reproducible*

Photochemistry simulations powered by trajectory surface hopping (TSH) dynamics have become an essential tool for understanding light-driven reactivity. In TSH, electronic transitions are mimicked using stochastic hops between electronic surfaces and the statistics of hopping are sampled using independent trajectories. In the conventional approach to TSH, hops are determined by comparing the instantaneous hopping probability to a random number at each time step. Here, we describe an alternative scheme using the cumulative hopping probability. We will show how this seemingly simple alteration opens the door to semi-stochastic sampling algorithms that drastically reduce computational time, and new strategies to numerically evaluate propagation algorithms, all while improving computational reproducibility. We argue that using cumulative hopping probabilities has myriad advantages over the conventional approach and no apparent disadvantages. Thus, we recommend cumulative surface hopping as the default approach in all TSH implementations.