# State Dependent Ring Polymer Molecular Dynamics for Investigating Excited Nonadiabatic Dynamics

## TL;DR

This paper rigorously derives and tests the non-adiabatic ring polymer molecular dynamics (NRPMD) method, demonstrating its accuracy in simulating excited state non-adiabatic dynamics and its ability to address zero-point energy leakage.

## Contribution

The paper provides a rigorous derivation of the NRPMD Hamiltonian using MMST mapping and path-integral nuclear description, validating its effectiveness for excited state dynamics.

## Key findings

- NRPMD alleviates zero-point energy leakage.
- NRPMD accurately simulates excited state non-adiabatic dynamics.
- Theoretical foundation established for state-dependent RPMD methods.

## Abstract

Recently proposed non-adiabatic ring polymer molecular dynamics (NRPMD) approach has shown to provide accurate quantum dynamics by incorporating explicit electronic state descriptions and nuclear quantizations. Here, we present a rigorous derivation of the NRPMD Hamiltonian and investigate its performance on simulating excited state non-adiabatic dynamics. Our derivation is based on the Meyer-Miller-Stock-Thoss (MMST) mapping representation for electronic states and the ring-polymer path-integral description for nuclei, resulting in the same Hamiltonian proposed in the original NRPMD approach. In addition, we investigate the accuracy of using NRPMD to simulate photoinduced non-adiabatic dynamics in simple model systems. These model calculations suggest that NRPMD can alleviate the zero-point energy leakage problem that is commonly encountered in the classical Wigner dynamics, and provide accurate excited states non-adiabatic dynamics. This work provides a solid theoretical foundation of the promising NRPMD Hamiltonian and demonstrates the possibility of using state-dependent RPMD approach to accurately simulate electronic non-adiabatic dynamics while explicitly quantize nuclei.