Photochemical reactions are often simulated with an approach known as Fewest Switches Surface Hopping (FSSH) which describes electronic transitions as probabilistic “hops” between energy surfaces. However, this thirty-year-old method has its issues. The simulations use probabilities calculated at every timestep, which makes them dependent on the chosen timestep and hard to reproduce. Shane Parker and Colin Schiltz set out to fix the issues with FSSH and came up with a cumulative probability method.

“I never really liked the idea that when you change purely numerical parameters in the simulations, you can get totally different results,” said Parker. “I’m more of a believer that there should be a way to define things so that only the physics matters and not how you translate that into the computer.”

Instead of calculating the probability of a hop at each timestep, the new method calculates an overall probability for the whole time period. In their paper, the authors proved their method is statistically identical to the old. They also showed the old method overestimates hopping rates because it uses a first order approximation of the hopping probability, whereas the new method provides correct hopping rates for any timestep size.

Since the cumulative method drives down the number of random variables from around 10,000 to just two or three, it makes it possible to run simulations deterministically and makes the whole process reproduceable. The authors believe it will be helpful for anyone simulating a range of photochemical reactions, from new solar fuel generation to photodynamic medical therapies.

Source: “Surface hopping with cumulative probabilities: Even sampling and improved reproducibility,” by Shane M. Parker and Colin J. Schiltz, Journal of Chemical Physics (2020). The article can be accessed at