Ring Polymer Surface Hopping: Incorporating Nuclear Quantum Effects into Nonadiabatic Molecular Dynamics Simulations

Abstract

We apply a recently proposed ring polymer surface hopping (RPSH) approach to investigate the real-time nonadiabatic dynamics with explicit nuclear quantum effects. The nonadibatic electronic transitions are described through Tully's fewest-switches surface hopping algorithm and the motion of the nuclei are quantized through the ring polymer Hamiltonian in the extended phase space. Applying the RPSH method to simulate Tully's avoided crossing models, we demonstrate the critical role of the nuclear tunneling effect and zero-point energy for accurately describing the transmission and reflection probabilities with low initial momenta. In addition, in Tully's extended coupling model, we show that the ring polymer quantization effectively captures decoherence, yielding more accurate reflection probabilities. These promising results demonstrate the potential of using RPSH as an accurate and efficient method to incorporate nuclear quantum effects into nonadiabatic dynamics simulations.

Probing photodissociation dynamics using ring polymer molecular dynamics

“…Several ways have been proposed to describe nonadiabatic effects in RPMD. [41][42][43][44][45][46][47][48]56 In this work, we will use an extension which is based on FSSH. 45 We will briefly review FSSH first and then discuss the combination of RPMD with FSSH.…”

“…Several modifications to the original RPMD approach to investigate nonadiabatic dynamics have been proposed. [41][42][43][44][45][46][47][48] These extensions make use of the Meyer-Miller-Stock-Thoss representation, [41][42][43][44] FSSH, [45][46][47] or the position representation of RPMD. 48 Ideally, any nonadiabatic version of RPMD would exhibit the following features: preserving the quantum Boltzmann distribution and capturing the correct electron dynamics, e.g., capturing Rabi oscillations in a two-level system.…”

Coherent state mapping ring polymer molecular dynamics for non-adiabatic quantum propagations

“…Nevertheless, our numerical results (provided in Appendix C) suggest that the quantum statistics obtained from this approximated partition function is close to the exact QBD, and the time correlation function is close to both exact results and the CS-RPMD calculation with multiple beads for all DOFs. We want to further emphasize that this limiting case has already proven to be useful in recently developed approaches, such as Ehrenfest RPMD 33 and RPSH 31,32 which assume one bead for the electronic DOF and multiple beads for the nuclear DOF.…”

“…Mapping-variable RPMD (MV-RPMD) 29 approach does employ explicit electronic state variables and preserves the exact QBD, but it cannot accurately capture Rabi oscillations in a bare two-state system. 1 On the other hand, mapping CMD, 30 ring polymer surface-hopping (RPSH), 31,32 ring polymer Ehrenfest Dynamics, 33 and non-adiabatic mapping RPMD (NRPMD) 34 are promising methods to provide explicit and accurate electronic dynamics. However, these approaches usually lack rigorous derivations and they do not preserve detailed balance in general.…”

Microcanonical rates from ring-polymer molecular dynamics: Direct-shooting, stationary-phase, and maximum-entropy approaches

“…T = E/k B . This protocol has been employed in several model calculations, 38,39 although its reliability has not been systematically examined. a) Electronic mail: tfm@caltech.edu.…”