Time Reversible MASH

Our latest research advances the Mapping Approach to Surface Hopping (MASH), a method developed earlier in the group for simulating nonadiabatic processes. These processes are key to understanding photochemical reactions, electron transfer and excited-state dynamics in materials.

We have developed time-reversible, piecewise-continuous integrators that significantly improve the efficiency of the simulation: For a given time-step, Δt, it is demonstrated that the global error for these methods is 𝒪(Δ𝑡2) compared to the 𝒪(Δ𝑡) error of standard implementations. This allows larger time-steps to be used for a desired error tolerance, or conversely, more accurate observables given a fixed value of Δt.

The new algorithms are only formally possible because of the deterministic nature of the underlying MASH equations of motion and thus sets MASH further apart from other surface-hopping methods like FSSH. These cannot construct such time-reversible integrators due to their stochastic nature.