Surface hopping from the perspective of quantum-classical Liouville dynamics

TL;DR

This paper explores the connection between surface hopping and quantum-classical Liouville dynamics, revealing how to simplify and improve algorithms for simulating nonadiabatic quantum processes in many-body systems.

Contribution

It demonstrates how fewest-switches surface hopping can be derived from quantum-classical Liouville dynamics by neglecting decoherence terms and constraining nuclear momentum changes.

Findings

Derived surface hopping from quantum-classical Liouville theory.

Identified key elements for accurate nonadiabatic simulations.

Provided insights for computationally efficient algorithms.

Abstract

Fewest-switches surface hopping is studied in the context of quantum-classical Liouville dynamics. Both approaches are mixed quantum-classical theories that provide a way to describe and simulate the nonadiabatic quantum dynamics of many-body systems. Starting from a surface-hopping solution of the quantum-classical Liouville equation, it is shown how fewest-switches dynamics can be obtained by dropping terms that are responsible for decoherence and restricting the nuclear momentum changes that accompany electronic transitions to those events that occur between population states. The analysis provides information on some of the elements that are essential for the construction of accurate and computationally tractable algorithms for nonadiabatic processes.