State dependent ring polymer molecular dynamics for investigating excited nonadiabatic dynamics

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 nonadiabatic dynamics while explicitly quantize nuclei.

Non-adiabatic Matsubara Dynamics and Non-adiabatic Ring Polymer Molecular Dynamics

“…Thus, we explicitly show that NRPMD is capable to simulate non-equilibrium TCF, explaining the recent numerical success of using NRPMD to simulate the nonequilibrium population dynamics. 56 Similar numerical success in simulating non-equilibrium TCF has also be achieved in MV-RPMD. 58…”

“…54,57 We have further proven that the NRPMD is capable to simulate non-equilibrium TCF, hence justifies such simulations and explains the recent numerical success. 56 At this moment, we are not sure whether non-adiabatic Matsubara dynamics preserves the quantum Boltzmann distribution (QBD), except for the special limit when the electronic and nuclear DOFs are completely decoupled. Nevertheless, we derived the condition under which the QBD will be preserved by non-adiabatic Matsubara dynamics.…”

“…19 is the Wigner transform of MMST mapping Hamiltonian (Eq. 1) associated with the l th bead, which can be shown 25,56,81…”

“…85,93,94 This Thermostatting approach has also been recently incorporated into the NRPMD approach. 56 Note that the NRPMD approach (Eq. 86) in the current work (which can be viewed as an approximation of the non-adiabatic Matsubara dynamics C…”

Ring-Polymer Quantization of Photon Field in Polariton Chemistry

“…However, the classical Wigner model 25,26 is not expected to preserve the quantum distribution associated with the photon field, 28 which often leads to the incorrect quantum dynamics due to the leakage of the zero-point energy (ZPE). [29][30][31] These shortcomings of the quasi-classical treatment can be readily addressed with the recently developed state-dependent ring polymer molecular dynamics (RPMD) approaches. [32][33][34][35][36][37] These approaches are based upon the imaginary-time pathintegral description of the quantum DOF in the extended phase space.…”