# An extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berry's phase and "magnetic" forces

## TL;DR

This paper extends the fewest switches surface hopping algorithm to complex Hamiltonians to better model photoexcited molecules in magnetic fields, incorporating Berry's phase effects and magnetic forces.

## Contribution

It introduces a novel extension of FSSH for complex Hamiltonians, including Berry's phase and magnetic forces, addressing limitations of the original algorithm.

## Key findings

- Partial success in capturing Berry's phase effects
- Incorporation of magnetic forces in surface hopping
- Highlighting limitations of local FSSH for topological effects

## Abstract

We present a preliminary extension of the fewest switches surface hopping (FSSH) algorithm to the case of complex Hamiltonians as appropriate for modeling the dynamics of photoexcited molecules in magnetic fields. We make ansatze for the direction of momentum rescaling and we account for Berry's phase effects through "magnetic" forces as applicable in the adiabatic limit. Because Berry's phase is a nonlocal, topological characteristic of a set of entangled potential energy surfaces, we find that Tully's local FSSH algorithm can only partially capture the correct physics.