# Path integral molecular dynamics with surface hopping for thermal equilibrium sampling of nonadiabatic systems

## TL;DR

This paper introduces a new ring polymer approach combined with surface hopping dynamics to efficiently sample the thermal equilibrium of nonadiabatic quantum systems, preserving electronic state discreteness.

## Contribution

It proposes a novel ring polymer representation that maintains electronic state discreteness and develops a path integral molecular dynamics with surface hopping method for nonadiabatic systems.

## Key findings

- The method accurately samples equilibrium distributions.
- The approach is validated through theoretical analysis.
- Numerical examples demonstrate effectiveness.

## Abstract

In this work, a novel ring polymer representation for multi-level quantum system is proposed for thermal average calculations. The proposed presentation keeps the discreteness of the electronic states: besides position and momentum, each bead in the ring polymer is also characterized by a surface index indicating the electronic energy surface. A path integral molecular dynamics with surface hopping (PIMD-SH) dynamics is also developed to sample the equilibrium distribution of ring polymer configurational space. The PIMD-SH sampling method is validated theoretically and by numerical examples.