surfacehopping

Surface hopping is a computational method used in theoretical chemistry and physics to simulate the dynamics of quantum systems that evolve on multiple potential energy surfaces. These surfaces represent different electronic states of a molecule or material. When a system transitions between these electronic states, it is said to "hop" from one potential energy surface to another.

Standard quantum mechanical methods often assume the system remains on a single potential energy surface, which is a good approximation when electronic transitions are rare. However, in many situations, such as photochemical reactions or light-induced processes, the system can rapidly switch between electronic states. Surface hopping methods aim to capture this non-adiabatic behavior.

The most common approach, often referred to as the fewest-swimming-states (FSS) or simply surface hopping algorithm, combines classical dynamics for the nuclear motion with probabilistic transitions between electronic states. The nuclei are treated as classical particles moving on a potential energy surface. At each step of the simulation, the probability of hopping to another surface is calculated based on the coupling between the electronic states and the nuclear velocity. If a hop is deemed to occur, the nuclear momentum is adjusted to be consistent with the new electronic state.

This technique allows for the study of phenomena like internal conversion, intersystem crossing, and exciton dynamics. It provides a way to bridge the gap between purely adiabatic (single-surface) and fully quantum mechanical treatments of coupled electronic-nuclear motion, offering a computationally tractable way to explore complex non-adiabatic processes.