State dependent ring polymer molecular dynamics for investigating excited nonadiabatic dynamics

A recently proposed nonadiabatic ring polymer molecular dynamics (NRPMD) approach has shown to provide accurate quantum dynamics by incorporating explicit state descriptions and nuclear quantizations. Here, we present a rigorous derivation of the NRPMD Hamiltonian and investigate its performance on simulating excited state nonadiabatic dynamics. Our derivation is based on the Meyer-Miller-Stock-Thoss 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 the photoinduced nonadiabatic 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 state nonadiabatic dynamics. This work provides a solid theoretical foundation of the promising NRPMD Hamiltonian and demonstrates the possibility of using the state-dependent RPMD approach to accurately simulate electronic nonadiabatic dynamics while explicitly quantizing nuclei.